Papers

Materials usually remember their past through dissipative changes of structure or through a net order. Simulations of caged colloidal ellipsoids at a fluid interface reveal a purely orientational memory. The particles stay in place, the layer has no net alignment, and a pattern written by a field is retained by capillary interactions between neighbors. It lasts hundreds of times longer than a particle takes to reorient, while every particle keeps rotating. The layer also remembers sequence: when two strong fields act one after the other on the same particles, it records which came last.

Interactions turn a gas into a fluid. We show that two-body loss can take their place. Correlated loss induces elastic scattering, as required by the optical theorem, which dominates at strong loss via the quantum Zeno effect. A nondegenerate gas with only two-body loss thus flows hydrodynamically, with viscosity and thermal conductivity close to those of the unitary Fermi gas. As loss heats the gas, both grow in time with a universal exponent 3/8. Unlike single-particle loss, two-body loss can engineer collisions, and hence transport, in quantum matter.

At fixed bulk criticality, every fixed nonsingular real single-end potential preserves a growing local population of real eigenvalues in an open analytic family of non-Hermitian chains. An open region of two-end real potentials removes this population. A boundary-amplitude criterion fixes the minimum number of controlled ends. The population grows as $\sqrt N$, where $N$ is chain length, although its normalized spectral weight vanishes and the local limiting bands remain unchanged. For a representative chain's four zero-detuning settings, an independent passive Hermitian double chain converts this distinction into separated resonances at one fixed local port under a common coupling scan at fixed probe carrier. Its absolute reflection contrast and stability margin both scale as $N^{-1}$, with explicit sufficient resource budgets. Boundary amplitudes thus fix a minimum control requirement that limiting bands and thermodynamic spectral density do not specify.

We present a mass-conservative Darcy-Brinkman-Stokes (DBS) formulation for reactive transport with cell-based surface complexation in image-based porous media, coupled to PHREEQC and implemented in GeoChemFoam, an OpenFOAM-based toolbox. Dissolved species are transported in the physical mobile-water fraction, adsorbed species are stored as conservative cell-scale surface inventories, and each reactive cell is coupled to PHREEQC. Reactive surface area is prescribed independently as a cell field, so that internal area left unresolved by segmentation of microporous phases can be represented while DBS flow and transport are retained in the resolved pore space. The implementation is verified with a test suite that isolates the coupling of transport and chemistry from the construction of reactive surface area. Aqueous and adsorbed mass balance is evaluated against a one-dimensional analytical retardation benchmark and closed-system batch calculations. The smooth-interface surface-area algorithms are tested on idealised two- and three-dimensional geometries. In a two-scale lithium micromodel, DBS reproduces fully resolved aqueous and sorbed inventories within 0.6% across Pe=0.1-10. The applications comprise Pb2+ retardation by hydrous ferric oxide coatings in a two-dimensional fracture network, competitive Mn2+/Mg2+ exchange in a three-dimensional Kelvin-cell sorbent, and Sr2+/Ca2+ exchange in Estaillades limestone. In the fracture-network and limestone cases, the formulation yields spatially resolved aqueous and adsorbed inventories even where reactive surface area is only partly resolved at the image scale. The framework therefore supports conservative surface-complexation modelling in both resolved and unresolved pore structures, with relevance to contaminant retention, selective ion capture, and radionuclide transport.

When a long liquid drop is confined in a Hele-Shaw cell, the pull of surface tension produces a rapid retraction of its tip, causing it to bulge out as it draws up the excess liquid. Using numerical simulations, we demonstrate that this retraction is self-similar at long times, with the speed of retraction slowing like $t^{-1/2}$, where $t$ is the duration of retraction. After showing how this scaling can be understood using force and mass balance, we perform an asymptotic analysis of the Hele-Shaw equations to derive both the shape of the retracting drop, as well as prefactors of the scaling laws. Excellent agreement is found between our simulations and theory, and the experimental consequences are pointed out.

We investigate multilayer d-wave altermagnetic metals with odd-parity helical p-wave pairing. In the minimal bilayer system, interlayer tunneling reconstructs the spin-split Fermi surfaces and generates two layer-hybridized sectors with distinct effective chemical potentials. Without Rashba spin-orbit coupling (RSOC), the emergent mirror symmetry and subsystem chiral symmetry stabilize phases with different numbers of helical Majorana edge-mode pairs and additional counterpropagating pairs, jointly characterized by the mirror Chern number and the winding numbers defined along high-symmetry lines. The combination of RSOC and the altermagnetic exchange field gaps out the helical Majorana pairs while, in a certain parameter regime, leaving another pair of counterpropagating Majorana edge modes gapless, giving rise to second-order topological phases with isolated or twofold Majorana corner modes, as well as a hybrid-order phase in which gapless Majorana edge modes coexist with Majorana corner modes. We identify a layer symmetry that elucidates the physical origin of these phases. For an arbitrary N-layer system, such a symmetry naturally arises from the interlayer-coupling matrix, allowing N-fold Majorana corner modes to emerge when all layer-hybridized sectors enter the nontrivial second-order regime. Our results establish the interplay among the layer degree of freedom, odd-parity pairing, and Fermi-surface configurations as a controllable route to engineering topological superconductivity in layered altermagnetic systems.

Excitons in monolayer transition metal dichalcogenides (TMDs) are highly sensitive to external stimuli, allowing control of resonance energies and lifetimes through electric and magnetic fields, heterostructures, moire potentials and mechanical strain. Observations of single-photon emission (SPE) near sample edges, wrinkles, and strained nanobubbles have motivated strain-engineering aimed at realizing localized emitters in 2D materials. The origin of these emitters remains unclear and prior studies have relied on far-field spectroscopy with strain profiles inferred separately through topography, limiting direct correlation between local strain and excitonic response. We directly probe strain-modified excitonic spectra in monolayer WSe$_2$ using cryogenic scattering-type scanning near-field optical microscopy (s-SNOM). We compare two strain-engineering techniques, nano-indentation and patterned substrates, used to produce SPEs. At 9 K, we spatially resolve exciton resonance shifts with sub-diffraction limit resolution, simultaneously measuring near-field optical response and topography. We observe that strain transferred from nano-indentation into a deformable polymer substrate differs from that produced by draping TMDs over patterned dielectric pillars. Adhesion and tearing during plastic deformation drive a compressive exciton blueshift, while draping produces dominant tensile strain. Comparing the strain model results to the experimentally observed energy shifts shows that the nano-indentation strain is over an order of magnitude smaller than previously inferred, due to puncturing of the fragile monolayer, whereas pillar-strained devices remain intact under more modest strain. These differences suggest SPE arises from complex, strain-mediated interactions rather than simple confinement potentials, establishing s-SNOM as a powerful probe of quantum emission in strained 2D materials.

Symmetries of a quantum field theory or a quantum lattice model are expected to be described not by a group but by a homotopy type, whose homotopy groups are the higher symmetry groups and whose Postnikov invariants encode 't Hooft anomalies. We propose a homotopy-theoretic definition of 't Hooft anomalies based on the structure of localized symmetries in the operator-algebraic approach. The input is a crossed precosheaf: a collection of groups attached to regions of space, equipped with pairings recording that the commutator of two transformations localized in two regions is localized in their intersection. To a crossed precosheaf and a finite family of regions we attach a pointed connected homotopy type, the Cech-Loday classifying space. As the family of regions ranges over finite covers of space, the classifying spaces form a pro-object in the homotopy category. There is a canonical map from the ordinary classifying space of the symmetry group to this pro-type. Composing this map with a group action gives an anomaly whose nontriviality obstructs gauging. In favorable cases, the Cech-Loday space is essentially independent of the cover. In such cases, the homotopy fiber of the canonical map is a candidate for the classifying space of the higher group of symmetries. We give examples of crossed precosheaves arising from gauge transformations in continuum field theory and from quantum cellular automata and finite-depth circuits. For quantum spin systems in one and two dimensions, our construction recovers the Else-Nayak index and its generalizations to two dimensions.

Phonon-photon coupling in quantum materials is commonly treated as an effective direct interaction, neglecting the crucial role played by electrons. Here we develop a gauge-invariant theory of cavity phonon polaritons that captures electronic screening, dissipation, and hybridization. We show that screening can suppress polariton formation in metals, severely constraining cavity control of phonon-mediated superconductivity. By contrast, interband electronic resonances in time-reversal-symmetric gapped systems can strongly enhance phonon-photon coupling, enabling robust polariton formation down to the monolayer limit despite electronic absorption. We illustrate these effects in NbSe2, hBN, and gapped graphene. Finally, we show that gauge invariance enforces photon decoupling from a critical soft phonon, establishing a general no-go mechanism for photon condensation.

Quantum gas microscopy provides single-shot access to many-body configurations, but their microscopic reconstruction has so far largely relied on a predefined discrete spatial basis during fluorescence readout. Here we realize ultrafast atom-resolved fluorescence microscopy of an ultracold $^{162}$Dy gas directly in continuous space, with all external confinement removed during imaging. Exploiting the large mass and broad optical transition of dysprosium together with a high numerical aperture in-vacuum objective, we detect single atoms within $4\,\mu\mathrm{s}$ while maintaining an effective point-spread function with a full width at half maximum of $254.8(3)\,\mathrm{nm}$, and an isolated single-atom classification fidelity of $99.72(3)\%$. We use the measured single-atom response to construct a statistical configuration-inference model that recovers atomic positions and multiplicities, coming from overlapping atoms, directly from single fluorescence snapshots. Benchmarking our model on Monte-Carlo generated images shows a total reconstruction fidelity of $98.7\%$. Our approach extends quantum gas microscopy beyond predefined detection lattices, enabling atom-resolved measurements of counting statistics and higher-order spatial correlations directly on the intrinsic length scales of continuum many-body systems.

Under local Lindbladian evolution, the growth of conditional mutual information and its associated Markov length scale is not limited by Lieb-Robinson bounds, yet it has been unclear how quickly the Markov length can increase. We show that an arbitrarily short, strictly local Lindbladian can generate infinite Markov length from a product state. We also construct strictly local Lindbladians that converge rapidly to steady states with algebraically decaying conditional mutual information. Despite their long-range conditional correlations, the states we construct are local reversibly connected to a product state by sublinear depth circuits. Thus infinite Markov length does not imply slow relaxation nor obstruct phase stability when suitably defined.

Beenakker's formula, $U(\varphi)-U(0)=\Delta\sum_n\bigl(1-\sqrt{1-\tau_n\sin^2(\varphi/2)}\bigr)$, expresses the zero-temperature energy-phase relation of a short Josephson junction through its normal-state transmission eigenvalues. We generalize this transmission representation beyond the short-junction limit and express the phase-dependent free energy of a time-reversal-symmetric $s$-wave junction as a Matsubara sum over channels with frequency-dependent transmissions. The representation constrains the small-phase expansion of the free energy. In particular, we prove that the normalized ratio of its quartic and quadratic coefficients satisfies $-1\le\alpha_r\le7/80$ at finite temperature. We also construct a four-site junction with $\alpha_r>0$, which disproves the conjectured upper bound $\alpha_r\le0$. So that these results can be trusted without repeating the derivations, every numbered equation is formally verified in the Lean proof assistant.

Strong coupling between mobile charge carriers or excitons and lattice vibrations gives rise to polarons: quasiparticles formed by charge carriers dressed by a cloud of phonon excitations. Polaron formation determines transport properties of systems ranging from transition-metal oxides and organic semiconductors to light-harvesting complexes. In excitonic systems that admit a hard-core boson description, mapping the excitations to pseudospins provides a natural framework for studying polaron physics, including the nonperturbative regime in which hopping amplitudes, phonon energies, and coupling strengths are comparable. Here, we propose a trapped-ion blueprint for realizing spin-phonon Hamiltonians with programmable spatial coupling between excitation density and phonon displacements, encompassing local Holstein and long-range Fröhlich-type interactions. To access strongly dressed quasiparticles whose bare spectral weight is suppressed, we introduce displaced Green's functions implemented through spin-dependent phonon displacements. Their spectral response reveals the polaron band spectrum, including binding energies and phonon-excitation sidebands, while spatially resolved measurements probe the structure of the phonon dressing cloud, providing a route to polaron tomography. We further complement this spectroscopy with direct and ancilla-assisted measurements of spin-phonon correlations that track the coupled dynamics of the excitation and its environment. These approaches connect the emergent quasiparticle spectrum to the microscopic buildup of its dressing cloud, enabling controlled studies of how the spatial range of coupling shapes polaron formation and mobility.

Non-Abelian anyons, strange particles forming the basis of fault-tolerant topological quantum computing, are predicted to emerge in fractional quantum Hall states at even-denominator filling factors. Identifying which topological order is realized has proven to be a challenging problem that requires an accurate, non-perturbative treatment of realistic Landau level mixing, which has so far been missing from theoretical studies. Here we present the first complete solution of non-Abelian quantum Hall problem that includes all electrons and all Landau levels, for spin-polarized electrons at filling factor $\nu = 3/2$. We develop a momentum-resolved neural-network variational wave function, optimized solely on the microscopic Hamiltonian, which gives direct access to the topologically degenerate ground states. Without any physics input about the expected outcome, it discovers a degenerate ground-state manifold whose entanglement reveals anyons with quantum dimension $\sqrt{2}$, the hallmark of Ising-type non-Abelian order. By directly computing the overlap with trial wave functions, we further show that Landau level mixing favors the anti-Pfaffian over other candidate states. Our results demonstrate the power of neural-network wave functions in finding and characterizing non-Abelian anyons from first principles, in regimes of strong Landau level mixing, relevant to many recent experiments.

Non-Abelian anyon chains whose interactions favor a single fusion channel host quantum critical ground states described by minimal-model conformal field theories (CFTs) protected by a topological symmetry. We show that their measurement-only counterpart, where non-commuting fusion charge measurements act locally on the anyons of a chain of $L$ sites, provides a fundamental example of a non-unitary CFT controlling a non-Abelian learning problem. Mapping the monitored dynamics to a random tensor network, we numerically find $1/L$ scaling Lyapunov gaps, logarithmic entanglement scaling with the chord length, and an effective central charge in the Shannon entropy of the measurement record. The conserved topological charge sharpens with dynamical exponent $z= 1$ and is learnable by a decoder on an $O(L)$ time scale. As the topological symmetry is a non-invertible symmetry of the $SU(2)_k$ anyon theories, we establish the monitored golden chain $(k=3)$ as a non-Abelian generalization of the weakly (Kramers-Wannier) self-dual quantum critical point of the toric code $(k=2)$, and the first of a family for $k\geq 3$.

Quantum simulators with disordered spin Hamiltonians offer a natural route to Haar-like unitary ensembles, but face a competition. Disorder enhances randomness, yet strong disorder suppresses dynamics and localizes the system in the computational basis. This suggests an optimal intermediate disorder strength for approximating a unitary $k$-design, which has so far been identified mainly empirically. Here, we develop a perturbative theory for the moment gap $\Delta^{(k)}$, the deviation of the $k$-th moment operator from its Haar value, for the full spectrum of the interacting XXZ chain in a fixed-magnetization sector. We find the non-monotonic asymptotic scalings $\ln \Delta^{(k)}\sim -\sigma^2$ at weak disorder and $\ln \Delta^{(k)}\sim -1/\sigma$ at strong disorder, whose crossover sets an optimal disorder strength $\sigma_c\sim J_{xy}$, where $J_{xy}$ is the energy scale of the non-random interaction. We further show that a multi-quench protocol further suppresses the gap exponentially in the number of quenches. Numerical simulations confirm both scalings and this exponential suppression, and we demonstrate the usefulness of the protocol for classical shadow tomography. This work suggests that strong disorder may block both thermalization and the formation of unitary designs through a common localization mechanism.

Chiral topological order is incompatible with strictly two-dimensional local commuting-projector Hamiltonians on finite-dimensional tensor-product Hilbert spaces. Invertible subalgebras (ISAs) provide an alternative framework. We construct an ISA supporting chiral semions, together with its anti-semion commutant, on a square lattice with one qubit per edge. We give explicit non-Pauli generators for both algebras and prove that together they generate all local operators on the Hilbert space. Starting from the $\mathbb{Z}_4$ toric code, we condense the boson $e^2m^2$ and identify the semion and anti-semion algebras. We then decompose each $\mathbb{Z}_4$ qudit into two qubits and use a finite-depth circuit to disentangle one qubit per edge fixed by the condensation constraints. Pumping the semion ISA along the $z$ direction defines an explicit three-dimensional non-Clifford quantum cellular automaton (QCA). We show that pumping eight times is equivalent to a translation followed by a finite-depth quantum circuit with ancillary qubits. We also give an explicit finite-depth circuit relating this construction to the semion QCA previously obtained from topological quantum field theory. A similar condensation construction yields a $U(1)_4$ ISA on a square lattice. Together with the semion and earlier odd-prime ISAs, finite stacking realizes every pointed Witt class of bosonic Abelian anyon theories. Finally, we extend both constructions to all spatial dimensions $d=4k{-}2$, with one qubit or $\mathbb{Z}_4$ qudit on each $(2k{-}1)$-cell for the semion or $U(1)_4$ ISA, respectively.

Existing machine-learning models for perovskite solar cells struggle to predict devices made from new materials. Most treat device layers as arbitrary categorical labels and represent perovskite absorbers either through featureless composition vectors or through rigid crystal graphs that require a pre-solved unit cell. As a result, they cannot generalize to unrecorded alloys or unfamiliar cell architectures. We present the Virtual-Alloy Physics-Aware Semantic System (V-PaSS), an architecture built around the physical continuity of perovskite solid solutions. V-PaSS represents arbitrary mixed-cation, mixed-halide absorbers by interpolating relaxed crystal graphs of 23 pure $ABX_3$ endpoint compounds via Vegard's law with learned bandgap bowing. For the device stack, it couples layer sequence and cell polarity (n-i-p or p-i-n) with interfacial band offsets and encodes chemical descriptions with a scientific language model. Evaluated under an institution-grouped protocol where test devices come exclusively from unseen laboratories, an untuned default configuration of V-PaSS achieves the lowest error among fourteen tested models (2.861% MAE, a 5.2% relative reduction over a gradient-boosted baseline at 3.017%, and outperforming the best tuned benchmark at 2.912%). V-PaSS pulls furthest ahead where test devices differ most from training: reducing error by 15.7-19.0% on unseen absorber alloys, by 16.1% on mixed absorbers from new laboratories, and widening its lead over the baseline by 3.6$\times$ on devices with unobserved transport layers. Combined with tree ensembles, V-PaSS sets a new state of the art across all five benchmark splits.

We develop a bootstrap approach to deriving lower bounds on the spectral gap of the first Haldane pseudopotential Hamiltonian on the sphere with $N_\Phi$ flux quanta for arbitrary $N_\Phi$, including in the thermodynamic limit $N_\Phi \to \infty$. Our approach can in principle be generalized to pseudopotentials describing other model wavefunctions such as the Moore-Read state or Read-Rezayi sequence. Our approach is based on Knabe's observation that if $H$ is a Hamiltonian with ground state energy $0$ then the spectral gap is at least $\epsilon > 0$ if and only if $H^2 \succeq \epsilon H$. To show this inequality, we split $H^2$ into two parts, one that can be analytically bounded and another that can be bounded using a finite semidefinite program (SDP). Crucially, the size of this program is determined only by cutoff parameters, and the program depends on $N_\Phi$ only parametrically, allowing us to obtain numerically exact (up to solver precision) lower bounds on the gap. In order to turn these numerical bounds into mathematically rigorous bounds, we introduce an algorithm that can produce nearly-optimal exact feasible points for large rational SDPs. We additionally provide an algorithm that establishes the rank stability of the semidefinite program in the limit $N_\Phi \to \infty$ which is needed to certify the bound in the thermodynamic limit. Beyond establishing the Laughlin gap and revealing a potential method for deriving spectral gap lower bounds for other pseudopotentials, our work provides a general method for turning numerical semidefinite programming bounds into rigorous mathematical proofs, which may have wide applicability.

Anyons are particles with quantized fractional statistics. In theory, a single anyon can be stabilized as a localized fractional charge within the bulk of a topologically ordered two-dimensional insulator. However, experiments to date have focused on probing anyons in structures in which many anyonic excitations coexist and interact. Here, we demonstrate the trapping of a single anyon in a device consisting of a graphene-based quantum point contact with an embedded tunable quantum Hall dot. Benchmarking our device at v = 1, we demonstrate backscattering between Fermi liquid edge states mediated by the whole-electron Coulomb blockade of the dot. The cleanliness and control available in our device allow depletion of the dot to the last quasihole, and we observe spin blockade for transitions to the opposite-spin Landau level. At v = 1/3 and 2/3, we observe backscattering resonances with three times the frequency, consistent with resonant transmission of e/3 charges via a single anyon transistor. We demonstrate controlled depletion to the last quasiparticle to form a single anyon quantum dot. Tracing the charge addition spectrum for quasiparticle number Nqp = 1-5, we observe highly irregular addition energies, consistent with DMRG modeling showing a complex orbital shell-filling behavior. At higher Nqp = 10-20, the addition energies show a striking pattern: quasiholes at 1/3 (and quasiparticles at 2/3) show a regular addition spectrum while quasiparticles at 1/3 (and quasiholes at 2/3) do not. We trace the origin of this irregularity to an attractive component of the inter-anyon interaction: by experimentally tuning the confining energy, we observe complete suppression of alternating charge sectors, after which the dot charges in increments of twice the fundamental charge. This observation indicates the emergence of an anyon binding energy as large as the charging energy.

Stochastic resetting with stochastic return (SR) has recently emerged as an effective and practically relevant strategy for controlling first-passage phenomena and optimizing search processes by significantly reducing completion times in a wide class of stochastic systems. While most theoretical studies assume instantaneous return (IR), in realistic systems the return to the resetting position typically occurs over a finite time. We consider a 1-d diffusing particle in a harmonic trap with stiffnesses $k_1$ and $k_2$ during search and return, respectively. The particle searches for the target and, upon resetting at rate $r$, enters the return phase, continuing until it reaches either the origin or the absorbing target at $L>0$. Notably, the model permits target detection throughout the return phase, distinguishing it from IR scenarios. We analytically derive the MFPT for our model and determine parameter regions where SR enhances or suppresses search efficiency over the underlying dynamics, constructing the corresponding phase diagram using the coefficient of variation criterion. We further identify regimes in which SR is more efficient than IR using the SR criterion. This behavior is tested across different parameter sets taken from experimental studies by Goerlich et al., Biroli et al., and Besga et al. We map the parameter values reported in existing experimental studies onto our theoretical phase diagram, thereby identifying the regimes in which SR outperforms IR. In particular, we find that the most relevant region of the phase space, where SR is most beneficial corresponds to larger values of the potential strength in the search phase and lower values of potential in the return phase. Our results provide experimentally testable predictions and bridge the gap between theoretical resetting models and optical trap mediated finite-time return dynamics.

We establish theoretically that transverse spin textures are generically induced by the spin-orbit interaction at the Fermi surface of centrosymmetric ferromagnetic metals. We confirm this prediction with ab initio computations for Fe, Co and Ni. By symmetry, this cannot be associated with spin-orbit torques under a uniform current. However, a new current-gradient-induced torque emerges in nanoscale geometries. For a series of Ni-based bilayers, the computed Ni thickness dependence of the current-gradient-induced torque is in quantitative agreement with measurements previously attributed to orbital torques. We discuss how this opens a new avenue for the electrical control of magnetic orders, possibly also including the Néel vector of metallic altermagnets.

We study the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors. The method expresses these asymptotics as a functional of an effective phase shift. We determine its two branches on either side of a quadratic stationary point and the transition profile joining them. The profile is expressed through parabolic-cylinder functions. Its connection to the high-temperature Gaussian $\beta$ ensemble fixes the finite normalization, in agreement with an independent Riemann–Hilbert analysis. We also show that the leading exponential asymptotics suffice to recover the Euler-scale prediction of generalized hydrodynamics for the dynamical structure factor of hard rods.

We investigate how the long-range tail of dipole-dipole interactions modifies the dynamics of strongly interacting hard-core bosons in a one-dimensional lattice. In the nearest-neighbour model, large interactions generate an emergent Hilbert-space fragmentation into manifolds labelled by the number of nearest-neighbour bonds \(N_{\mathrm{NN}}\). The dipolar tail has a non-monotonic effect on this fragmented dynamics as the interaction-to-tunnelling ratio \(V/t\) is increased. At intermediate \(V/t\), it enhances delocalisation relative to the nearest-neighbour model by reducing the energetic detuning between neighbouring \(N_{\mathrm{NN}}\) manifolds and sustaining their hybridisation by hopping. At larger \(V/t\), the same tail lifts degeneracies within each manifold, beginning with the splitting associated with the next-nearest-neighbour bond number \(N_{\mathrm{NNN}}\), and promotes intra-manifold localisation and Hilbert-space shattering. The competition between these two effects produces a crossover from a delocalising to a localising role of the dipolar tail, visible in the late-time spatial inhomogeneity. This crossover occurs for nearly all initial states considered and persists at different fillings. Transverse confinement strengthens the short-range part of the dipolar tail and shifts the crossover to lower \(V/t\), bringing it into the regime relevant to current experiments with magnetic atoms and polar molecules.

Gauge-equivariant graph neural networks generate ordered products of gauge links through local message passing, but the geometry of these internal structures is not captured by the receptive field alone. We investigate the statistical ensemble of closed lattice walks generated by recursive node- and edge-feature operations, independently of network training. Analytical and numerical results reveal a separation between rapid growth of contour length and much slower spatial expansion: deeper compositions generate increasingly long paths through repeated traversal of relatively compact regions. Loop expansions of fermionic observables provide a physical interpretation of this hierarchy, showing how spatial locality remains compatible with high-order dependence on nearby gauge fields. These findings identify complementary roles of network depth in extending spatial reach and enriching the representations constructed within that reach, providing a geometrical perspective on learning lattice gauge observables.

The valence-bond-glass state of the 4d^1 double perovskite Ba2YMoO6 combines Mo^5+ singlets with residual paramagnetic "orphan" spins whose coupling is hard to reach with bulk probes. We probe them by electron paramagnetic resonance of a dilute Gd^3+ ion on the Y^3+ site via broadband coplanar-waveguide transmission at 5 K. The isostructural nonmagnetic niobate Ba2YNbO6, doped with the same Gd^3+ probe, is a fixed-lattice control. The Gd^3+ linewidth nearly doubles in the magnetic host. Dipolar coupling to the sparse orphans is nearly an order of magnitude too weak; the excess is instead reproduced by a transferred f-d superexchange of J ~ 0.2 K, so the width is a static measure of orphan-spin coupling. The half-field (Delta m_S = +/-2) satellite collapses in the magnetic host, a dynamical dephasing channel, while the unchanged g-factor marks a zero-mean random internal field. Together the two channels probe the coupling and dynamics of valence-bond-glass orphan spins.

Explicitly correlated methods, which represent dominant short-range correlations by a diagonal Jastrow-type correlator, are designed to accurately describe systems of strongly correlated electrons, such as the fully periodic 2D Fermi–Hubbard model. However, as the reference state is compact in momentum space whereas the correlator acts naturally in real space, there is a fundamental mismatch of bases that classical algorithms resolve only by restricting the reference or the correlator. Here we propose a hybrid algorithm in which a quantum processor prepares a low-entanglement momentum-space matrix product state (MPS), precomputed classically by the transcorrelated method at the cost of a nonvariational energy, rotates it to real space, and measures in bases fixed by the Hamiltonian. Because the measurement bases are independent of the correlator, the correlator can be variationally optimized entirely in classical post-processing with no quantum-classical feedback loop. We demonstrate our algorithm on 32 qubits of Quantinuum's H2-2 with a bond-dimension-4 MPS for the half-filled $4 \times 4$ lattice and achieve a relative ground-state energy error of $16 \pm 4\%$ after postselection, reduced to $3.5 \pm 0.5\%$ by calibration using low-order moments from the MPS. Compared with other feedback-free hybrid algorithms, even under generous assumptions, our method requires fewer samples than quantum-selected configuration interaction and fewer two-qubit gates than quantum Krylov methods.

Double perovskites (DPs) offer a compositionally versatile platform for photocatalysis and optoelectronics, but their soft lattices favor strong exciton-phonon coupling and self-trapped excitons (STEs), which produce broad, red-shifted photoluminescence (PL). Here, we combine optical spectroscopy and ab initio calculations to study lead-free, Sb-doped Cs2BInCl6 nanocrystals with B-site alloying from Na to K. Alloying tunes the PL energy from about 2.48 to 2.70 eV, while absorption features near 3.8 eV remain nearly unchanged. Calculations reveal that Sb doping enables bright radiative recombination channels and delocalizes the excitonic wavefunction. We identify STEs responsible for the large PL red shift, associated with an upward shift of dopant-hybridized in-gap states. Na-to-K substitution selectively changes the STE lattice distortion, explaining why PL varies strongly with composition while absorption does not. Theory further predicts pronounced PL polarization anisotropy that reflects the STE wavefunction's spatial structure and depends on B-site composition. Time-resolved anisotropy measurements closely agree with these predictions, providing experimental fingerprints of the excitonic wavefunction and its evolution with alloying. Together, these results disentangle the roles of doping and alloying in lead-free DPs and establish polarization-resolved spectroscopy as a probe of STE wavefunctions.

We propose a protocol to prepare and probe dark states in a single-molecule electron spin resonance based on atomic force microscopy (ESR-AFM), thus extending existing techniques developed to address Rabi oscillations. To this end, we simulate in analogy to atomic physics the coherent manipulation of a three-level system in the V-configuration using a multifrequency magnetic field. More specifically, we consider a neutral molecule with a zero-field-split (ZFS) first excited triplet and analyze within a pump-probe scheme the dynamics of the total triplet population. In the triplet subspace, the dark state is a coherent superposition formed by two ZFS states which does not evolve in time despite a continuous resonant driving towards the third one. We characterize the properties of this state comparing it to its fully incoherent counterpart. Within a density-matrix formalism for open systems, we then compute the expected dark state signatures both for ideal scenarios and for the realistic parameterization of ESR-AFM on pentacene.

Rare events, such as crystal nucleation in mildly supercooled liquids, are characterized by waiting times that can be much longer than the timescale of the underlying microscopic dynamics. The mean first-passage time (MFPT) formalism [J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] provides a route to reconstruct one-dimensional free-energy profiles from the MFPT and steady-state distribution measured along a reaction coordinate, but conventional implementations become inefficient for sufficiently high barriers because spontaneous crossings are rarely observed. We introduce a "top-start" extension that initiates trajectories near the barrier top and reconstructs the free-energy profile from their subsequent evolution away from the barrier toward lower-free-energy regions. We establish the equivalence between the top-start and two-region constructions using a Markov-chain transition-matrix formulation. We validate the method using one-dimensional random-walk simulations across low, medium, and high free-energy barriers, with transition-matrix calculations providing an exact benchmark for the corresponding discretized models. The top-start reconstruction remains accurate in the high-barrier regime where conventional MFPT sampling becomes prohibitively inefficient.