Papers

In neutron-star and dense quantum chromodynamics (QCD) physics, it is important to understand how baryonic matter evolves into quark matter at high density. A continuous hadron–quark crossover is one of the most attractive candidates because it can reconcile the comparatively soft equation of state around nuclear density with the rapid stiffening required to support massive neutron stars. Recent neutron-star observations motivate equations of state that stiffen rapidly across the intermediate-density regime, while quarkyonic-matter descriptions feature a shell-like baryon momentum distribution there. In this paper, we review our recent work on the microscopic description and interpretation of these phenomena by drawing an analogy with the Bose–Einstein condensate (BEC) to Bardeen–Cooper–Schrieffer (BCS) crossover in ultracold Fermi gases and two-color QCD. As pairing fluctuations play a crucial role in the BEC–BCS crossover, we discuss the role of its three-body counterpart, that is, tripling fluctuations associated with baryon formation in the hadron–quark crossover. In terms of a phase-shift representation of tripling fluctuations, the interplay between a three-body bound-state pole and the scattering continuum suppresses low-momentum baryonic occupation, generates a baryonic momentum shell, and reduces the density susceptibility, thereby producing a peak in the speed of sound. We review the demonstration of this mechanism in a one-dimensional three-component Fermi gas, its relativistic extension, and its connection to phenomenological quarkyonic equations of state.

We investigate collective modes in charge-neutral altermagnetic superconductors with $d$-wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying $d$-wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.

We investigate vortex nucleation and dynamics in a dipolar Bose-Einstein condensate stirred by a rotating Gaussian obstacle. Two stirring protocols are compared: continuous stirring with constant amplitude (Case 1), and obstacle removal at $t = 15$ ms with linear amplitude ramp-down (Case 2). In both cases, a smooth angular velocity ramp ($t_{\text{acc}} = 3$ ms) suppresses spurious phonon excitations. The first vortex pairs exit the obstacle at $t \sim 3$ ms, and by $t \sim 8$ - $10$ ms the individual vortices and antivortices are fully resolved in the phase maps. Case 1 yields a vortex population that grows up to $t \sim 40$ ms and then roughly saturates, while Case 2 yields a population that peaks around $t \sim 15$ - $25$ ms and then decreases. Remarkably, both protocols lead to local triangular-like ordering in selected regions of the condensate by $t \sim 50$ ms, exhibiting clear dipolar signatures: elliptical distortion and elongated vortex cores along the polarization axis. The mixed vortex-antivortex population remains stable up to $100$ ms with no observable annihilation, indicating that dipolar interactions strongly suppress vortex decay. Kinetic energy decomposition confirms that incompressible (vortex) energy dominates at late times. These results establish a controlled platform for vortex studies in dipolar superfluids and provide benchmarks for future experiments on quantum turbulence with long-range anisotropic interactions.

We investigate Krylov state complexity in a tilted extended Bose-Hubbard chain in which both the on-site interaction $U$ and nearest-neighbor interaction $V$ are present. The tilted extended Bose-Hubbard model can be realized with Rydberg-dressed interactions in optical lattices. Using exact diagonalization and Lanczos recursion from three physically motivated Fock states, we compute the time-dependent complexity, its long-time saturation value, and the fluctuations of the Lanczos coefficients for an open chain at unit filling. Crucially, we identify a pronounced quasi-chaotic diagonal regime near $U\simeq V$ in which the Krylov complexity saturation exhibits a sharp ridge while the spectral level-spacing statistics remain partially chaotic. This dissociation arises from the competition between the on-site and nearest-neighbor interaction, which generates a dense manifold of near-resonant many-body configurations that is efficiently coupled by the state-dependent dynamics but retains residual spectral structure. Our results show that Krylov state complexity provides complementary, state-sensitive information about many-body chaos that is not captured by the spectral diagnostics alone, establishing Krylov complexity as a useful diagnostic for studying thermalization and information scrambling in experimentally accessible quantum simulators.

In this work we give an overview on a couple of decades of theoretical and experimental research on the many-body physics of driven-dissipative quantum fluids of light in optical cavities. These systems consist of a large number of photons enclosed in a cavity device where spatial confinement induces a finite photon mass and the Kerr optical nonlinearity of the cavity material mediates finite photon-photon interactions. Differently from standard Bose gases of material particles like liquid Helium or ultracold atomic gases, photons are inevitably subject to radiative and/or non-radiative losses, which must be compensated by some pumping mechanism. As a result, the properties of the steady state are not imposed by a thermal equilibrium condition, but are determined by a dynamical interplay of pumping and losses. Among the many collective phenomena that are observed in these systems, we focus here on the collective excitations around the steady state and we characterize the impact of the driven-dissipative nature of the gas on their properties, in particular on their dispersion relation. Different pumping configurations give very different behaviors: a specific discussion is provided for the most important configurations used in the experiments. Observable consequences of the various forms of the dispersion -gapped, gapless, sonic, band-sticking, diffusive Goldstone- are illustrated with a special eye towards their consequences on the superfluidity properties. We conclude the article with a presentation of a few research avenues that we personally find most exciting for the next years, namely the osbervable consequences of the concurrently superfluid and solid nature of supersolid states of light and the collective dynamics of quantum correlated states of strongly interacting photon gases in the presence of strong nonlinearities, in particular Mott insulator states.

Exploring exotic quantum phases of matter at room temperature represents a frontier challenge in modern physics. The supersolid phase, uniquely merging crystalline order with frictionless superfluid flow, stands among the most intriguing macroscopic quantum phenomena. However, all previous demonstrations of supersolidity, whether in ultracold atomic gases or III-V semiconductor-based polariton systems, have been strictly confined to cryogenic temperatures. Here, we report the observation of room-temperature supersolids in photonic-crystal polariton condensates. By integrating a room-temperature-stable perovskite semiconductor with a dispersion-engineered photonic-crystal waveguide, we create a polariton condensate with multi-mode dispersion landscapes and pronounced parametric nonlinearities. Above a critical condensation density, the interacting condensates spontaneously break continuous translational symmetry, creating a non-rigid supersolid phase that simultaneously exhibits emergent crystalline order and global quantum coherence. This work establishes a room-temperature platform for investigating quantum hydrodynamics and developing coherent quantum simulation devices.

Motivated by the first experimental realization of the antiferromagnetic phase transition in the three-dimensional Fermi-Hubbard model, we present a theoretical study of the model's 3D superconducting phase. By formulating a 3D extension of the Feshbach mechanism, we provide a unified microscopic picture at strong coupling in which pairing is driven by near-resonant bound states of dopants. These long-lived bound states acquire a qualitatively different internal structure in three dimensions compared to their two-dimensional counterparts, giving rise to a distinct superconducting state, namely a time-reversal symmetry breaking $d_{x^2-y^2}+id_{z^2}$ pairing state. We also provide an estimate of the corresponding critical temperature, and provide evidence that the resulting superconducting phase hosts gapless Weyl points. Our results represent a new milestone for the field of quantum simulation, challenging experiments and large-scale numerics alike to test our predictions.

In mean-field theory, the ground state of a two-component Bose-Einstein condensate (BEC) in a uniform system is either uniformly mixed or totally separated. Beyond-mean-field effects introduce an additional phase, the mixed-bubble state, in which the two components remain mixed within one of the separated domains. Here we show that a mixed-bubble state can emerge in a binary mixture of spin-1 ${}^{7}{\rm{Li}}$ and ${}^{23}{\rm{Na}}$ BECs even within the mean-field framework. We further demonstrate the existence of a metastable uniformly-mixed state, which undergoes a transition to the mixed-bubble state triggered by a local perturbation.

Understanding the physics underlying high-temperature superconductivity in cuprates and, more recently, infinite-layer nickelates has remained a central challenge in condensed-matter physics. We establish neural quantum states (NQS), specifically Hidden Fermion Determinant States (HFDS), as a scalable variational approach to the three-band Emery model of the copper- and nickel-oxide layers in these materials. After benchmarking HFDS against matrix product states on width-two geometries, we study ground states of fully two-dimensional (2D) systems of up to $10\times10$ unit cells ($300$ sites). We characterize the momentum-space distribution of dopants and find a pronounced electron-hole dichotomy similar to cuprate experiments. We further downfold the three-band model to effective single-band descriptions by constructing interacting Wannier functions. We consider a wide range of parameters – from the charge-transfer regime relevant to cuprates to the Hubbard-Mott regime of nickelates, as well as systematic scans of the charge-transfer gap that has been demonstrated to impact the critical superconducting temperatures. Across all regimes, the effective model significantly deviates from the usual Fermi-Hubbard model: The typical ratio $U/t$ is enhanced, some parameters experience a significant doping dependence, and sizable terms beyond the conventional Hubbard model are present, most notably a density-assisted hopping $t_n$. Notably, in all effective models, $t_n$ has the largest contribution to particle-hole asymmetry, rather than next-nearest-neighbor hopping contributions. The effective parameters sensitively depend on the charge-transfer energy, doping, and interaction ratios. Our results establish HFDS as an efficient tool for studying the 2D Emery model and demonstrate that single-band descriptions can require interaction terms generated by the underlying multi-band models.

Atomic bilayers of transition metal dichalcogenides (TMDs) host quantum phases governed by the layer degree of freedom, including bilayer Wigner crystals, fractional Chern insulators, and exciton condensates. These phases are probed primarily through exciton spectroscopy, yet it remains poorly understood how excitons and carriers interact to form Fermi polarons in bilayers, where both the impurity and the Fermi sea carry a layer pseudospin. Progress has been limited because most TMD bilayers have momentum-indirect optical bandgaps, in which non-radiative decay and inhomogeneous broadening obscure the intrinsic spectra. Here, we show that bilayer MoTe$_2$, unlike most TMD bilayers, retains a direct optical bandgap, providing a clean platform for studying bilayer Fermi-polaron physics. In a dual-gated device, an out-of-plane electric field continuously tunes the hybridization between intralayer and interlayer excitons, forming layer-coherent excitons. Upon electrostatic doping, the excitonic spectrum evolves into multiple polaron branches, controlled by both carrier doping and the out-of-plane electric field. Among these, we identify a polaron with no analog in monolayers, in which a layer-coherent exciton is dressed by carriers in the opposite layer, and is quantitatively captured by our field-theoretic model. Our results establish that pseudospin structure in both the impurity and the bath reshapes polaron formation, opening new avenues to many-body states such as Bose-Einstein condensates with interlayer coherence.

Arrays of neutral atoms excited to Rydberg levels have emerged as one of the most promising platforms for quantum computation and simulation. With the hope to outperform classical devices, the number of atoms has been increased by orders of magnitude. However, the interaction time, i.e., the maximum accumulated time during which an atom interacts with its neighbours, has been limited to a few microseconds only. This restrains the number of gates per atom or prevents the simulation of long-time dynamics of quantum many-body systems. Here, we observe the spin-exchange interaction between two spin 1/2s encoded in laser-trapped circular Rydberg atoms over more than $60\mu s$ and 40 spin-oscillation periods, improving the state of the art by an order of magnitude. These unprecedented timescales allow us to record for weak atomic trapping a collapse and revival of the spin-exchange oscillation contrast induced by spin-motion coupling. Our results constitute the first observation of this coupling with laser-trapped Rydberg atoms. To counteract its detrimental effect for quantum simulation, we demonstrate a novel dynamical decoupling method that prevents the collapse of the spin oscillations. This method exploits the advantages of our recently developed hybrid platform that enables the measurement and the optical manipulation of long-lived circular Rydberg atoms with auxiliary Rydberg atoms. This work opens a direct route to long-duration quantum simulation of strongly-interacting many-body systems.

We propose a quantum heat engine based on a two-component Fermi gas with s-wave contact interaction, operating across the BCS-BEC crossover. The work is extracted from the statistical properties of the gas, which are controlled by the interaction, rather than relying solely on compression and expansion stages. Using the functional renormalization group formalism, we obtain the equation of state in a non-perturbative form along the crossover, encompassing the superfluid-normal phase transition. The cycle combines isentropic density strokes, isochoric thermalization, and isothermal interaction sweeps. This construction makes it possible to integrate features of both Otto and Carnot cycles, in which the system simultaneously saturates both efficiency limits without the net work vanishing. In the absence of density variations, the cycle reduces to a statistical Stirling-like engine, in which the work generated arises exclusively from the interaction, achieving efficiencies up to $38\%$. A pronounced asymmetry emerges through the crossover, giving rise to distinct operating regimes depending on the trajectory followed in the phase diagram. Consequently, the same architecture can be tuned to function as an engine, refrigerator, accelerator, or heater. These findings highlight pairing correlations as a versatile thermodynamic resource for quantum heat machines.

We study spin-current fluctuations of the folded XXZ chain, which describes the strong-anisotropy limit of the XXZ chain. We obtain an exact expression for the moment-generating function of the time-integrated spin current at infinite temperature. A long-time asymptotic analysis establishes that the rescaled time-integrated current converges to a non-Gaussian distribution described by the M-Wright function. The derivation relies on a nonlocal map to the one-dimensional t-0 model and its exact spin-charge separation. By extending this approach, we also show that the dynamical correlation function of the spins summed over two adjacent sites exhibits a diffusive Gaussian profile at long times.

The two-fluid model provides a powerful phenomenological framework for superfluids, where components interact through vortex-induced mutual friction. Quantum turbulence in such coupled two-fluid systems has become a central theme in low-temperature physics. However, the fundamental incompatibility between discrete vortex-line and continuum descriptions has historically forced reliance on phenomenological parameters. Here, we present an ab initio holographic simulation of this active two-fluid dynamics. Using a fully backreacted gravitational model, we intrinsically incorporate reciprocal momentum exchange and finite-temperature dissipation without empirical inputs. Contrasting continuously driven and freely decaying turbulence, we uncover pronounced non-Gaussian tails and spatial anisotropy in the normal-fluid velocity statistics, arising directly from the dynamical quantized vortex backreaction. Raising the temperature suppresses normal-fluid velocity fluctuations despite increasing the vortex density. This suppression is unambiguously traced to the thermal depletion of the superfluid condensate. Our results establish holographic duality as a rigorous first-principles framework for quantum turbulence, revealing the active role of the normal fluid far from equilibrium and yielding predictions for ongoing cold-atom and superfluid experiments.

The first-order coherence properties of strongly coupled systems supporting polariton lasing and Bose-Einstein condensation (BEC) have been thoroughly studied and show consistent results. In contrast, second-order coherence properties have been found to vary for different systems, and the second-order coherence function can deviate from the value of one, typical for atomic BEC, revealing super-Poissonian fluctuations even above the BEC/polariton lasing threshold. This calls for a deeper understanding of the emission statistics and dynamics in light-based condensates, especially in the non-equilibrium regime. Here we demonstrate a coherent state of polariton emission from a plasmonic lattice measured as the second-order coherence function value separately for $\mathrm{\Gamma}$- and non-$\mathrm{\Gamma}$-point radiation (ground state and high-energy tail). We observe a high degree of coherence with the value $g^{(2)}(\tau=0)-1<10^{-4}$. We also demonstrate the ultrafast ($>$1 THz) nature of the dynamics. The process can be interpreted as a BEC with ultrafast, sub-50-fs thermalization, but we also suggest an alternative explanation as superradiance in a system where the emitters have vibrational degrees of freedom.

Stochastic resetting can generate strong correlations in many-body systems through a shared fluctuating environment. Here, we investigate how such dynamically emergent correlations (DEC) coexist with intrinsic (direct) interactions in a weakly repulsive Bose-Einstein condensate described within the Gross-Pitaevskii framework. The condensate undergoes free expansion from an initial Thomas-Fermi state and is stochastically reset to this initial state at a constant rate. We show that the resetting protocol drives the system into a unique nonequilibrium steady state and obtain its density profile, edge statistics, and full counting statistics analytically. The steady-state density retains an inverted-parabolic form within the core, while developing exponentially decaying tails outside it. We further show that resetting induces nontrivial fluctuations of the condensate edge and particle number, yielding exact scaling forms for the edge distribution and the full counting statistics. Our results provide a tractable setting for exploring the interplay between intrinsic repulsive interactions and attractive DEC generated by a common stochastic environment in quantum many-body systems.

We demonstrate proximity-induced localization and re-entrant delocalization in a detuned quasiperiodic ladder. In the weak-quasiperiodic regime, where uncoupled Aubry-André chains are extended, a staggered detuning applied to only one leg induces localization in the neighboring leg through inter-leg hybridization. With further increasing detuning, the pure chain re-enters a delocalized regime, producing a delocalized-localized-delocalized sequence without directly modifying its quasiperiodic potential. We identify these regimes using static localization diagnostics and demonstrate experimentally accessible dynamical signatures on IBM Quantum hardware: strongly suppressed wavefunction spreading in the proximity-localized regime and its re-entrant recovery at larger detuning. These results establish leg-selective detuning as a programmable control knob for inducing and reversing localization in coupled quasiperiodic systems.

We study finite-momentum trimers and Cooper quartets in a one-dimensional two-component Fermi gas with coexistent $s$- and $p$-wave interactions, regularized in the relative momentum of each pair so that they remain Galilean invariant. Pauli blocking alone then makes the trimer dispersion deviate from free center-of-mass motion, so the trimer energy can be lowest at finite total momentum. Allowing this motion expands the $abb$ region among pairs and trimers and removes the region where an odd-wave pair is lowest. The $aabb$ quartet lies below all these branches at every sampled coupling, and in a strip starting on the crossing of the two dimer-pair channels its lowest breakup channel is a moving $abb$ trimer and an atom. At weak interspecies attraction, a variational bound shows that two odd-wave Cooper pairs bind into a quartet, whose binding exceeds that of the coexisting trimer by orders of magnitude as the attraction weakens. At stronger interspecies attraction, the quartet binding relative to two unlike-species dimers disappears when the odd-wave interaction is switched off, although the even-wave interaction dominates the interaction energy. Relative to the in-vacuum case, the Fermi sea enhances the weak-coupling quartet binding, and at fixed scattering lengths the quartet binding grows with density while the coexisting trimer becomes much shallower. These results show that neither the most strongly bound pair nor the dominant interaction energy alone determines whether the quartet binds.

Weakly breaking a continuous symmetry in an ordered phase can convert its Goldstone modes into topological collective bands. We establish this mechanism in a neutral dipole condensate whose conserving parent supports two independent Goldstone phase modes. Weak real flavor mixing pins the phases and selects a chiral condensate. The resulting gyroscopic coupling acts on their winding polarization texture, producing a pseudo-Goldstone sector containing a topological lowest band. Restoring dipole conservation forces the two modes to meet at zero frequency, where their separate band Chern numbers cease to be defined. The same parent dipole charges define a tensor current whose circular response permits model-assisted reconstruction of low-energy embedded local Berry curvature in the benchmark regime. Analytical stability bounds and a large-occupation limit provide a controlled realization of this mechanism.

We develop a generalized effective spin-chain (GESC) formalism for strongly interacting multicomponent anyons in a one-dimensional (1D) optical lattice. By mapping particle motion onto spinless fermions and spin states onto an ordered chain, this framework provides a spin–charge-separated perspective on the physical effects of fractional exchange statistics. In the strong-interaction regime, the leading-order charge Hamiltonian becomes independent of the statistical phase; instead, virtual tunneling through doubly occupied states directly imprints this phase on the spin-exchange coefficients. The GESC formalism captures ground-state properties of the full Anyon–Hubbard model reported in S.~Basak, X.-W.~Guan, and H.~Pu, unpublished manuscript (2026), and reveals that their statistical dependence is predominantly encoded in the explicit anyonic structure of the observables rather than the underlying spin ground state. This formalism uncovers that, out of equilibrium, successive spin exchanges accumulate direction-dependent phases; the resulting interference drives crossover from dispersive to localized impurity transport and generates inversion-asymmetric propagation at intermediate statistics. Suppressed expansion persists for identical and distinguishable impurities, with differences in propagation governed by the interplay between impurity identity and interaction anisotropy. Ultimately, GESC offers a versatile, computationally efficient theoretical framework that connects macroscopic dynamics to microscopic virtual exchange processes, conferring a unique spin–charge-separated vantage for resolving how fractional exchange statistics survives strong interactions and manifests distinctly across static and dynamical regimes.

We investigate the ground-state and dynamical properties of multicomponent interacting anyons confined in a one-dimensional (1D) optical lattice. Adopting the Anyon–Hubbard model, we explore spin and charge correlations as functions of interaction strength and the anyonic statistical parameter. Our results demonstrate that multicomponent effects combined with fractional exchange statistics substantially reshape both charge and spin correlations. For fractional exchange statistics, the canonical symmetric shell structure with prominent singularities in the spinor fermionic momentum distribution undergoes notable structural reconstruction, exhibiting emergent asymmetry, new spectral peaks, and broadened singular features. Unlike the Tonks–Girardeau bosonic gas, pseudobosons, representing a limiting case of anyons, cease to display a dominant zero-momentum peak. Instead, a quasi-fermionic shell structure emerges with finite-momentum peaks, whose locations are modulated by lattice site occupancy and interaction strength. The structure factor of spin correlations uncovers antiferromagnetic ordering in spinor anyon systems, with correlation magnitudes tunable by anyonic exchange statistics. Furthermore, quench dynamics analysis reveals the statistical phase parameter as an effective tuning knob. It enables the switching of dipole oscillations between underdamped and overdamped relaxation regimes and governs overall cloud expansion dynamics. Our findings pave the way for exploring statistics-driven ground-state and dynamical phase transitions in spinor anyon systems.

Synthetic gauge fields provide a powerful route to engineer photonic wave dynamics, especially in synthetic frequency dimensions formed by modulated resonator modes. While most previous realizations have focused on Abelian or lower-rank non-Abelian structures, a photonic implementation of SU(3) gauge fields in the synthetic frequency dimension has remained lacking. Here we propose a route to realize SU(3) gauge structure using three coupled ring resonators with modulation- and interference-engineered mode conversion. We formulate a tight-binding Hamiltonian with matrix-valued hopping generated by the Gell-Mann matrices and show how its evolution can be decomposed into experimentally implementable optical elements. The resulting platform supports SU(3)-structured band dispersions with color-resolved texture and wave-packet dynamics shaped by SU(3) gauge fields. Full-wave-inspired numerical modeling further confirms the expected spectral response and Zitterbewegung-like motion in SU(3) subspaces. Our results introduce SU(3) gauge fields into synthetic frequency photonics and establish a route toward higher-rank non-Abelian control of light in modulated resonator systems.

Hamiltonian engineering (HE) simulates quantum dynamics under a target Hamiltonian using a native entangling system Hamiltonian and restricted control, with applications from quantum gate design to analog quantum simulation. Observing that, for many systems, formulating HE as a linear program only requires specific commutation relations between the control pulses and the system Hamiltonian, we provide a unified framework for broad classes of $2$-local qubit, qudit, and fermionic systems. We reformulate time-optimal HE as a complex $k$-cut polytope problem, with $k$ the number of distinct phases in these commutation relations, and prove it NP-complete for every finite $k$. We therefore relax the polytope to the elliptope and apply a Krivine-type rounding, yielding pulses informed by the system and target Hamiltonians, which we then use in a linear program. We derive how many informed pulses are necessary and sufficient for the linear program to be reliably feasible. Additionally mixing in uniformly sampled pulses guarantees a solution close to the relaxation value from $\mathrm{O}(m)$ pulses, with $m$ the number of interaction terms. Together with upper and lower bounds on the optimal quantum run time, this yields an $\mathrm{O}(\sqrt{m})$ approximation ratio. In benchmarks on a fully connected Ising model, a chiral clock model for qudits, and the fermionic Harper-Hofstadter model, our approach attains near-optimal quantum run times wherever the optimum is computable, reaches run times that saturate with the lattice size in the fermionic case, and outperforms state-of-the-art methods with $\mathrm{O}(m)$ pulses. This establishes a unified approach with provable guarantees to the automatic programming of analog quantum simulators.

Discrete scale invariance often arises from resonant few-body or singular scale-invariant dynamics. We show that it can instead emerge in the internal motion of a composite excitation in an ordered quantum magnet. In the marginal $1/r^4$ transverse-field Ising chain, long-range bonds generate an asymptotic inverse-square attraction between dressed domain walls, with strength fixed by the spontaneous magnetization. The dressed two-kink threshold curvature sets the relative kinetic scale. Together, these independently accessible quantities determine the scale-anomaly exponent and hence the meson hierarchy. In the supercritical regime, the same exponent governs geometric binding-energy and size ratios, logarithmic level accumulation, and log-periodic threshold scattering. Full-spin exact diagonalization and a fourth-order weak-field Hamiltonian support the coupled energy–size scaling in the finite window between core and ring effects. This provides a microscopic many-body realization of quantum limit-cycle physics, with its universal scaling fixed by magnetic order and kink mobility.

A mobile impurity particle immersed in a quantum degenerate gas leads to the formation of a quasiparticle, which can serve as a sensor for its environment. Here, we develop a unified wave function description of an impurity in a two-dimensional Bose-Hubbard model across the Mott-insulator to superfluid transition. Using a multi-mode variational ansatz based on the quantum Gutzwiller approach, we show that the impurity can form several kinds of polaronic and molecular states. In addition to their spectral properties, the wave function provides direct access to the microscopic structure of these states, and we demonstrate that strong correlations in the critical regime of the quantum phase transition give rise to several non-analytic features in the polaron properties. Increasing the impurity-boson interaction leads to transitions between polaron and molecular ground states, and the number of bosons in the impurity dressing cloud grows rapidly at the quantum critical point as the bath modes soften. We furthermore reveal qualitatively distinct non-equilibrium many-body dynamics after the injection of the impurity in the different phases of the Bose-Hubbard model. Our spectral, real space, and dynamical predictions describe complementary properties of polarons in a strongly correlated bosonic bath, which can be observed using current techniques with atoms in optical lattices.

The Efimov effect manifests discrete scale invariance through a geometric series of three-body bound states. Analogous discrete scale symmetry has been observed in the Efimovian expansion of scale-invariant strongly interacting Fermi gases. However, it is unclear whether strong correlation is necessary. Here we investigate the spontaneous breaking of continuous scale invariance in a simple driven-dissipative harmonic oscillator whose driving and dissipation parameters scale as $1/t$. By transforming to logarithmic time, we show that the dynamics is governed by a non-Hermitian superoperator whose spectral decomposition reveals the emergence of a pair of eigenmodes with opposite real parts and equal imaginary parts. This signals the spontaneous breaking of continuous scale invariance and gives rise to Efimovian-like oscillations: log-periodic decay oscillations obeying discrete scaling laws. The onset of oscillations coincides with a PT-symmetry breaking transition in logarithmic time. The Efimovian-like oscillations are robust against weak nonlinear interactions and perturbations. Our work implies that the spontaneous breaking of continuous temporal scale symmetry and the emergence of Efimovian-like dynamics can even be observed in a simple driven-dissipative system without many-body interactions.

We employ a projection operator technique to study the equilibrium phases and the non-equilibrium quench and ramp dynamics of ultracold bosons described by a two-dimensional (2D) Bose-Hubbard model coupled to a high-finesse cavity with competing local short-range and cavity-mediated long-range interactions. Our analysis relies on a systematic elimination of high-energy virtual hopping processes; this enables us to capture the effects of short-range quantum fluctuations on the phase diagram of the model while treating the cavity-induced long-range interaction within mean-field theory. We find that the phase boundaries between the superfluid (SF), supersolid (SS), charge-density-wave (CDW) and Mott insulating (MI) phases are significantly modified by the presence of these fluctuations. We use this approach to study the dynamics of bosons following a quench/ramp from the CDW to the SS and SF phases; our analysis indicates the presence of oscillatory dynamics characterized by a single frequency due to a quench which takes the system near the critical point. In contrast, for a quench deep inside the SF phase, the dynamics involves multiple frequencies. An explicit comparison with Gutzwiller mean-field theory shows the importance of quantum fluctuations in shaping such post-quench dynamics; this feature may be tested experimentally as we discuss. We also study the ramp dynamics of these bosons and identify a bound on the ramp rate above which the present method is expected to produce accurate results.

Helium dimer in its metastable triplet electronic state, He$_2(a~^3\Sigma_u^+)$, is a promising candidate for direct laser cooling and precision measurements. Interactions and collisions involving He$_2(a~^3\Sigma_u^+)$ remain unexplored in ultracold and cold energy domains. Here, we present the first theoretical investigation of intermolecular interactions and collision dynamics of He$_2(a~^3\Sigma_u^+)$+Ne van der Waals complex. For the ground electronic state, $X~^3\mathrm{A}'$, we employ a spin-restricted coupled cluster method with single, double, and noniterative triple excitations. The resulting interaction potential exhibits an extremely shallow well with a depth of 4.612 cm$^{-1}$. We construct a three-dimensional vibrationally averaged potential energy surface. Using this surface, we perform full close-coupling calculations including fine-structure levels of He$_2(a~^3\Sigma_u^+)$ to investigate collisional excitation and quenching induced by Ne. We analyze the low-energy scattering dynamics and model resonant features associated with quasi-bound states supported by interaction potential. Propensity rule for fine-structure conserving transitions is established. We additionally consider He$_2$+Ar collisions and compare their energy dependence and resonance structure with those of He$_2$+Ne. The He$_2$+Ar system exhibits a richer resonance structure, highlighting the sensitivity of low-energy scattering to interaction potential and reduced mass. Calculated PES and scattering properties provide a reliable benchmark for description of He$_2$+Ne van der Waals complex and may be useful for interpretation of future experimental spectra and collision measurements.

A charge-$r$ coupling vortex can remain as one fused order-$r$ zero or split into $r$ nearby unit-charge zeros after weak symmetry breaking. The two configurations have the same total winding and the same number of dark states in the lowest-Landau-level projection, so neither the imposed orbital angular momentum nor the total winding number distinguishes their local geometry. We study this distinction in a two-component Haldane-sphere model coupled by a Raman field. For monopole flux $N$, the detuning $\tau_{\rm c}$ at which a defect branch crosses zero energy scales as $|\tau_{\rm c}|\sim N^{-(r+1)}$ for a fused zero and $N^{-2}$ for resolved unit zeros. A Feshbach reduction establishes these asymptotic laws for the full multiband Hamiltonian, and numerical calculations in a monopole-harmonic basis confirm the fused-vortex scaling for $r=1,2,3$. For a partially split cluster of diameter $d$, the scaling crosses over when $d$ is comparable to the magnetic length $\ell_B$, allowing $d$ to be inferred spectroscopically even below the spatial resolution of direct imaging.

We study three particles on the square lattice with contact interactions of infinite strength, for all total quasimomenta, for three statistics: three identical bosons, two identical fermions plus a third particle, and two identical bosons plus a third particle. Previous work treated only the trimer and zero quasimomentum. Here the atom-dimer sector is analyzed on the whole Brillouin zone. A Feshbach-Schur reduction onto the infinitely degenerate eigenvalue 1 of the pair-contact operator gives explicit effective Hamiltonians with proved first-order error. The threshold problem reduces to a 4x4 Hermitian matrix criterion built from the two-point resistances of the square lattice, and hence to a quartic polynomial. This yields the complete atom-dimer zone and the critical mass ratio on the Brillouin zone, with bound between 1 and pi/(pi-2), and closed forms at all symmetry points. We prove: the zones in closed form; the critical mass ratio with exact value pi/(pi-2) at zero quasimomentum, reproducing a numerical value; at most two atom-dimer states for every quasimomentum and mass ratio; the onset laws, an essential singularity on the zone boundary and a linear-over-logarithm onset in the pure p-wave; two exact dualities showing that a change of statistics is equivalent to a shift of quasimomentum by pi; and the global range of the second fermionic threshold. The onset laws admit a renormalization-group reading: the inverse lattice Green function is a marginal s-wave coupling, binding energies arise by dimensional transmutation with lattice scale 16, and the zone boundary is of marginal (BCS/Kondo) type rather than of Berezinskii-Kosterlitz-Thouless type. All constants are verified independently by lattice quadrature, computer algebra, exact diagonalisation, and infinite-lattice solvers.