Papers

Collective excitations in one-dimensional (1D) quantum fluids are expected to propagate almost without dissipation. Here we directly excite phonon modes in a weakly interacting 1D Bose gas and study their time evolution. In the linear response regime, damping is surprisingly fast and quantitatively follows the non-analytic scaling predicted by Andreev's hydrodynamic description. For stronger excitations, we observe a crossover to a highly nonlinear regime characterized by wave breaking, captured by the finite-temperature nonlinear Schrödinger evolution. Our results resolve a long-standing question on the fate of phonons in 1D Bose gases, and open new pathways to study non-linear relaxation in quantum many-body systems.

We investigate the behavior of the Schmidt gap, the von Neumann entanglement entropy, and the non-stabiliserness in proximity to the classical phase transition of the one-dimensional long-range transverse-field Ising model (LRTFIM). Leveraging the time-dependent variational principle (TDVP) within a tensor-network formulation, we simulate thermal states through their purified tensor-network representations. Our results show that these observables, typically regarded as hallmarks of quantum criticality, exhibit pronounced and coherent signatures even at a classical thermal transition, highlighting the emergence of quantum complexity as the system nears thermal criticality.

We introduce a three-stroke quantum isochoric cycle that functions as a heat engine operating between two thermal reservoirs. Implemented for a particle confined in a one-dimensional infinite potential well, the cycle's performance is benchmarked against the classical three-stroke triangular and isochoric engines. We find that the quantum isochoric cycle achieves a higher efficiency than both classical counterparts and also surpasses the efficiency of the recently proposed three-stroke quantum isoenergetic cycle. Owing to its reduced number of strokes, the design substantially lowers control complexity in nanoscale thermodynamic devices, offering a more feasible route to experimental realization compared to conventional four-stroke architectures. We further evaluate the cycle in graphene-based systems under an external magnetic field, including monolayer graphene (MLG), AB-stacked bilayer graphene (BLG), and twisted bilayer graphene (TBG) at both magic and non-magic twist angles. Among these platforms, magic-angle twisted bilayer graphene (MATBG) attains the highest efficiency at fixed work output, highlighting its promise for quantum thermodynamic applications.

We derive the condition for the occurrence of the integer quantum Hall effect in two-dimensional lattice systems with interactions, expressed as $\phi\nu-\rho\in\mathbb{Z}$, where $\phi$, $\nu$, and $\rho$ denote the magnetic flux, the Chern number, and the electron density, respectively. By employing spiral boundary conditions, which treat the system as an extended one-dimensional chain, this condition is obtained directly through a Lieb-Schultz-Mattis-type and Laughlin-type argument. This approach improves upon the preceding work based on conventional periodic boundary conditions, where the condition was derived indirectly with redundant system-size dependence. The key to this approach is that the spatial directions of the external force and the response can be systematically controlled by a factor of the system size.

We apply the methodology of our recent paper 'The Dynamics of the Hubbard Model through Stochastic Calculus and Girsanov Transformation' [1] to thermodynamic correlation functions in the Fermi-Hubbard model. They can be obtained from a stochastic differential equation (SDE) system. To this SDE system, a Girsanov transformation can be applied. This has the effect that the usual determinant or pfaffian which shows up in a pfaffian quantum Monte Carlo (PfQMC) representation [2] basically gets absorbed into the new integration variables and information from that pfaffian moves into the drift part of the transformed SDE system. While the PfQMC representation depends heavily on the choice of how the quartic interaction has been factorized into quadratic quantities in the beginning, the Girsanov transformed formula has the very remarkable property that it is nearly independent of that choice, the drift part of the transformed SDE system as well as a remaining exponential which has the obvious meaning of energy are always the same and do not depend on the Hubbard-Stratonovich details. The resulting formula may serve as a starting point for further theoretical or numerical investigations. Here we consider the spin-spin correlation at half-filling on a bipartite lattice and obtain an analytical proof that the signs of these correlations have to be of antiferromagnetic type, at arbitrary temperatures. Also, by checking against available benchmark data [3], we find that approximate ground state energies can be obtained from an ODE system. This may even hold for exact ground state energies, but future work would be required to prove or disprove this. As in [1], the methodology is generic and can be applied to arbitrary quantum many body or quantum field theoretical models.

We develop an analytic approach to evaluating the density $\rho ({\cal E},\Gamma)$ of complex resonance poles with real energies $\mathcal{E}$ and widths $\Gamma$ in the pure reflection problem from a one-dimensional disordered sample with white-noise random potential. We start with establishing a general link between the density of resonances and the distribution of the reflection coefficient $r=|R(E,L)|^2$, where $R(E,L)$ is the reflection amplitude, at complex energies $E = {\cal E} +i\eta$, identifying the parameter $\eta>0$ with the uniform rate of absorption within the disordered medium. We show that leveraging this link allows for a detailed analysis of the resonance density in the weak disorder limit. In particular, for a (semi)infinite sample, it yields an explicit formula for $\rho ({\cal E},\Gamma)$, describing the crossover from narrow to broad resonances in a unified way. Similarly, our approach yields a limiting formula for $\rho ({\cal E},\Gamma)$ in the opposite case of a short disordered sample, with size much smaller than the localization length. This regime seems to have not been systematically addressed in the literature before, with the corresponding analysis requiring an accurate and rather non-trivial implementation of WKB-like asymptotics in the scattering problem. Finally, we study the resonance statistics numerically for the one-dimensional Anderson tight-binding model and compare the results with our analytic expressions.

We carry out uniaxial continuous and step stretching of various crosslinked polymer networks to demonstrate how characteristics of rupture (from continuous stretching) and delayed rupture (from step stretching) can be used to probe the structure of the emergent kinetic theory of bond dissociation (KTBD) for elastomeric failure. Based on delayed rupture experiments, we show that the network lifetime tntw, taken as the incubation time for delayed rupture, depends on temperature in an Arrhenius like manner and is exponentially sensitive to the degree of network stretching (depicted by step-stretch ratio ). Rupture during continuous stretching for a wide range of stretch rates takes place on timescales inversely proportional to the stretch rate. The elapsed time at rupture is found to be comparable to at various values of L/L0b = L/L0ss in a wide range of temperature, affording the experimental basis for the premise of the KTBD. Having identified the hidden internal clock , continuous stretching tests at different temperatures are performed to show the existence of a new time temperature equivalence (TTE): fast stretching at higher temperatures is equivalent to slow stretching at lower temperatures: different pairs of rate and temperature can produce the rupture at the same tensile strength and strain.

Light element based two dimensional (2D) materials are promising photocatalysts for hydrogen production via water splitting. Boron oxide (BO) is a recently synthesized 2D monolayer which has yet to be thoroughly explored for its potential applications. In this article, using first principles calculations, we report, for the first time, the visible-light photocatalytic activity of a BO monolayer for water splitting under mechanical strain and surface modification with single- and double-atom decorations (C, N, Si, Ge, P, As). The pristine BO monolayer exhibits an indirect band gap of 3.8 eV with band edges spanning the water redox potentials, but its optical absorption lies in the UV region (~ 4.5 eV). Strain engineering tunes the band gap and band alignment with a minimal shifting in the optical absorption (~0.5 eV). Single atom decoration produces a metallic state for elements like N, P, As, and an insulating state for single C, Si, Ge with a partial shifting in optical absorption. In contrast, double atom decoration produces substantial band gap reduction, improved band alignment, a pronounced red-shift in optical absorption into the visible range (1.6 to 3.2 eV) thus satisfying the criteria for water splitting. The stability of all the adsorbed configurations was confirmed by negative formation energy and ab-initio molecular dynamics simulations. These findings suggest BO monolayer functionalization can improve photocatalytic efficiency, providing hydrogen generation insights.

The Hubbard model has attracted considerable interest due to its prototypical role in describing strongly interacting electronic systems, such as high-critical-temperature superconductors as well as many novel quantum materials. By introducing next-nearest-neighbor (NNN) hoppings to the Hubbard model, the phase diagram becomes richer, and fascinating phenomena arise in both, one-dimensional chains and square lattices, such as: antiferromagnetism (AFM), ferromagnetism (FM), superconductivity (SC), as well as charge orders, among others. Moreover, NNN hoppings play a fundamental role in understanding effects of doping on magnetism and pairing orders in strongly interacting regimes. In this article, we review the recent progress in understanding the different competing phases of this model in one and two dimensions from a computational perspective. We comment on the pressing technical challenges, illustrate the controversial results concerning the emergence of the SC phase, and conclude with our perspectives on future explorations.

We study the equilibrium glassy behavior of a multimode random laser model with nonlinear four-body quenched disordered interactions and a global smoothed-cubic constraint on mode intensities. This constraint, which provides a more realistic representation of gain saturation than the commonly used spherical constraint, prevents intensity condensation while preserving the dense, long-range interaction structure characteristic of many multistate random lasers. The model effective Hamiltonian is a function of mode amplitudes with random frequencies and is defined on a complete mode-locked graph. Using large-scale GPU-accelerated Monte Carlo simulations with the Parallel Tempering algorithm, we analyze systems of varying sizes to probe their thermodynamic-limit behavior. Finite-size scaling of the specific heat, of the Parisi overlap distributions, and of the inverse participation ratio's reveals a spin-glass transition, with critical exponents matching the mean-field Random Energy Model universality class. The smoothed-cubic constraint produces broad, non-condensed intensity distributions, avoiding the pseudo-condensation seen in spherical models on the same interaction graph. Our results show that more realistic gain-saturation constraints preserve spin-glass characteristics while enabling simulations of larger, more dilute systems, providing a robust framework for studying glassy random lasers with self-starting mode-locking.

Ferroelastic twin walls in centrosymmetric perovskites can host emergent polar and magnetic properties forbidden in the bulk. We use density functional theory calculations to study the geometry and magnetic properties of ferroelastic domain walls in orthorhombic CaMnO$_3$, which belongs to the most common perovskite space group, $Pnma$. At the wall, the inherent inversion symmetry-breaking induces local polar distortions dependent on the wall geometry, which couple to the magnetic order through the octahedral distortions. Noncollinear calculations reveal enhanced out-of-plane magnetic moments on the Mn atoms and a local, finite magnetization confined to the wall. Strain fields across twin walls thus give rise to coexistence of polarization and magnetization as well as magnetoelectric response that is absent and symmetry-forbidden in bulk CaMnO$_3$. We propose that magnetoelectric coupling and coexisting polarization and magnetization can emerge at twin walls in bulk centrosymmetric antiferromagnets.

Multi-terminal Josephson junction with three or more superconductors is an attractive quantum system to emerge and tune exotic electronic states. In four terminal Josephson junctions, the Weyl physics, namely topologically protected zero energy state, emerges without assuming any exotic materials. In this study, we consider the four-terminal Josephson junction with the quantum point contact structures between the mesoscopic normal region and four superconducting terminals. The quantum point contacts can tune electrically the number of conduction channels. We theoretically investigate an effect of the increase of channels on the emergence of Weyl points. The increase of channels causes the increase of Andreev bound states in the system, which increase the emergence probability of Weyl points. When all terminals have two channels, the emergence probability is up to 17%, which is about four times larger than that for all single channel junctions. We consider the balance of the number of conduction channels in the four terminals. When the number of channels is unbalanced, the increase of emergence probability is suppressed.

Two-dimensional superconductors undergo a Berezinskii-Kosterlitz-Thouless transition driven by vortex-antivortex unbinding, yet experimental signatures beyond transport remain limited. Here, we show that the spin-lattice relaxation rate provides a direct probe of this transition. In a 2-dimensional $s$-wave superconductor, $1/T_1T$ develops a Hebel-Slichter-like peak around $T_{\rm{BKT}}$, originating from the emergence of coherence peaks in the density of states, while no peak appears at the pair formation scale $T_{\rm{BCS}}$. We further extend our analysis to the $d$-wave superconductor. Our results highlight spin-lattice relaxation rate as a sensitive tool to detect the superconducting BKT transition and open routes to exploring its manifestation in unconventional pairing states.

We study double-well systems with strong magnetic fields and deep potential wells. We present lower bounds on tunneling rates for generic values of the coupling constant. This result was recently announced and complements our recent counter-example construction which exhibits vanishing tunneling for specially-constructed double-well potentials.

Magnetic imaging techniques are widespread critical tools used in fields such as magnetism, spintronics or even superconductivity. Among them, one of the most versatile methods is the magneto-optical Kerr effect. However, as soon as light is blocked from interacting with the magnetic layer, such as in deeply buried layers, optical techniques become ineffective. In this work, we present a spin-accumulation based magneto-optical Kerr effect (SA-MOKE) microscopy technique that enables imaging of a magnetic thin-films covered by thick and opaque metallic layers. The technique is based on the generation and detection of transient spin-accumulations that propagate through the thick metallic layer. These spin-accumulation signals are directly triggered and detected optically on the same side, lifting any substrate transparency requirements. The spin-accumulation signals detected on a Cu layer decay with a characteristic length of 60 nm, much longer than the 12 nm optical penetration depth, allowing for detection of magnetic contrast with Cu capping layers up to hundreds of nm. This method should enable magnetic imaging in a wide-range of experiments where the surface of interest is covered by electrodes.

We investigate a generalized Aubry-André-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i) = V\left[ \cos(2\pi \beta i) \right]^p$. Our study reveals that the interplay between nonreciprocity, quasiperiodicity, and the power-law exponent $p$ gives rise to a variety of phase transitions and localization phenomena. In the Hermitian case, the system undergoes a direct transition from extended to localized phases for $p=1, 2$, while for \(p \geq 3\), an intermediate mixed phase emerges, characterized by the coexistence of extended and localized states and the presence of mobility edges. Importantly, we find that prominent high-IPR states associated with well-resolved spectral gaps appear at specific energy levels, whose positions are captured by the relation \(x_n = n\beta - \lfloor n\beta \rfloor\), for low-order $n$. In the non-Hermitian regime, the energy spectrum becomes complex and the \(\mathcal{PT}\) transition coincides with the extended-to-localized phase boundary for \(p = 1, 2\), whereas for \(p \geq 3\), \(\mathcal{PT}\)-symmetry breaking occurs at the mixed-to-localized phase transition. This work reveals how power-law quasiperiodic potentials and non-reciprocal hopping govern phase transitions, providing new insight into localization phenomena of quasiperiodic systems.

Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of their flows. In this work, we focus on a minimal yet physically grounded system that allows us to isolate the fundamental mechanisms by which active flow networks generate and regulate emergent dynamics capable of supporting information transmission. The system is composed of active units that pump fluid and elastic units that store volume. From first principles, we derive a discrete model – an active flow network – that enables the simulation of large systems with many interacting units. Numerically, we show that the pressure field can develop solitary waves, resulting in the spontaneous creation and transmission of localized packets of information stored in the physical properties of the flow. We characterize how these solitary waves emerge from disordered initial conditions in a one-dimensional network, and how their size and propagation speed depend on key system parameters. Finally, when the elastic units are coupled to their neighbors, the solitary waves exhibit even richer dynamics, with diverse shapes and finite lifetimes that display power-law behaviors that we can predict analytically. Together, these results show how simple fluidic elements can collectively create, shape and transport information, laying the foundations for understanding – and ultimately engineering – information processing in active flow systems.

Materials with graphene-like layers attract tremendous attention due to their electronic structures and superconducting properties. In this study, we synthesized LaP2 polycrystalline and observed a superconducting transition around 30 GPa. The critical temperature Tc increases monotonically with pressure, which is nearing saturation and reaches 7.8 K at 78 GPa. The synchrotron X-ray diffraction experiments confirm the superconducting transition originates from a structure transition to the P6/mmm phase under high pressure, suggesting the observation of graphene-like phosphorus layers in transition metal phosphides. By first-principles calculations, we provide more evidence for the stability of the graphene-like phosphorus layers in LaP2. Our findings are helpful for the understanding of the LaP2 phase diagram under high pressure, and could shed light on the research of unique structures in transition metal phosphides under high pressure.

We investigate the Lieb–Liniger model of interacting one-dimensional bosons coupled to a localized impurity, modeled by a delta barrier. While the Lieb–Liniger gas is integrable, the impurity breaks integrability and induces a transition towards quantum chaos. We show that the low-energy spectrum exhibits random-matrix statistics, in striking contrast to the Bohigas–Giannoni–Schmit conjecture, where chaotic behavior typically emerges at high energy. For two bosons, the odd-parity sector remains integrable, whereas the even-parity sector displays clear signatures of chaos at low energy and a crossover back to quasi-integrable behavior at higher energies. For three bosons, both parity sectors exhibit spectral statistics close to chaos at low energy. We argue that this unconventional form of few-body quantum chaos originates from diffractive processes induced by the impurity.

This paper presents an analytical derivation of a frequency-dependent fundamental solution plus a Green's function for the uni-dimensional, hexagonal quasicrystal sheet subjected to elastic waves under anti-plane strain conditions. Furthermore, closed-form solutions for the free-fields developing in this sheet for propagating shear waves are also obtained. The analysis presented here provides a foundation for understanding quasicrystal dynamic behavior and for advancing relevant computational methods.

Coexistence of nontrivial topology and flat electronic bands provides a fertile platform for correlated quantum states. The square-octagon lattice hosts Dirac nodes and flat bands at half-filling, yet the effects of intrinsic spin-orbit coupling (SOC) and staggered magnetic flux on its electronic and topological properties remain largely unexplored. Here, using tight-binding models incorporating SOC and staggered magnetic flux, we uncover a rich topological phase diagram in this lattice, comprising a quantum spin Hall phase with spin Chern number $C_s=1$, crossovers to quantum anomalous Hall phases with $C=1$ and $C=2$, and higher-order topological insulator phases with quantized quadrupolar corner charges. The initially dispersionless flat bands evolve into quasi-flat topological bands with nearly uniform quantum geometry and large flatness ratios, making them promising candidates for fractional Chern insulator states. We further identify realistic materials, including octagraphene, transition-metal dichalcogenides, synthetic $\mathrm{MoSi_2N_4}$, and magnetic $\alpha$-MnO$_2$, that may realize these tunable topological phases intertwined with flat-band physics, opening new opportunities for correlated topological matter.

The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed using the density matrix renormalization group (DMRG) as the WF method for molecules containing strongly correlated fragments [Beran, P. et al. J. Phys. Chem. Lett. 2023, 14, 3, 716-722]. In this work, we demonstrate that the accuracy of the DMRG-in-DFT approach is primarily limited by the approximate treatment of the coupling between the active component and its environment through nonadditive exchange-correlation functionals. To address this issue, we combine exact exchange to reduce the nonadditive exchange error with a multireference adiabatic connection (AC) scheme to recover nonadditive correlation. The performance of the improved DMRG-in-DFT embedding is illustrated on two prototypical strongly correlated systems: the dissociation of the H20 chain and the cleavage of a triple CN bond in propionitrile.

We study exact quantum recurrences in the double kicked top (DKT), a driven spin model that extends the quantum kicked top (QKT) by introducing an additional time-reversal symmetry-breaking kick. Reformulating its dynamics in terms of effective parameters $k_r$ and $k_\theta$, we analytically show exact periodicity of the Floquet operator for $k_r = j\pi/2$ and $k_r = j\pi/4$ with distinct periods for integer and half-odd integer $j$. These exact recurrences were found to be independent of $k_\theta$. The long-time-averaged entanglement and fidelity rate function show dynamical quantum phase transition (DQPT) for $k_r = j\pi/2$ at time-reversal symmetric cases $k_\theta = \pm k_r$. In the other time-reversal symmetric case $k_\theta = 0$, the DQPT exists only for a half-odd integer $j$. Using level statistics, a smooth transition is observed from integrable to non-integrable nature as $k_r$ is changed away from $j\pi/2$. Our work demonstrates that regular and chaotic regimes can be controlled for any system size by tuning $k_r$ and $k_\theta$, making the DKT a useful platform for quantum control and information processing applications.

Recent theoretical and experimental advances have identified cobaltates with a high-spin $d^7$ electronic configuration as promising hosts for spin-orbit entangled $J_{eff} = 1/2$ magnetism that can support bond-dependent exchange interactions. In two-dimensional triangular lattices, the coexistence of such exchange frustration along with geometric frustration gives rise to a rich landscape of competing magnetic phases, establishing monolayer triangular $d^7$ cobaltates as a compelling platform for frustrated magnetism. Here we investigate a representative triangular-lattice monolayer cobaltate CoBr$_2$, where first-principles density functional theory (DFT) calculations reveal a dominant nearest-neighbor $t_{2g}$-$e_g$ hopping channel that enhances the ferromagnetic Kitaev-type exchange interactions. In contrast, the nearest-neighbor Heisenberg term is highly sensitive to a direct $t_{2g}$-$t_{2g}$ hopping path and electronic correlations. The magnetic exchange parameters are evaluated using the hopping amplitudes obtained from DFT calculations within an exact diagonalization framework. We construct the first and third nearest neighbor Heisenberg exchange dependent $J_1$-$J_3$ magnetic phase diagram in the physically relevant regime and identify multiple competing ground states, including ferromagnetic, stripy, spiral, and $120^{\circ}$ antiferromagnetic orders. The Luttinger-Tisza analysis further predicts a Z$_2$ vortex crystal phase, while exact diagonalization reveals a bond-nematic phase stabilized by the longer-range couplings. Going beyond the conventional bond-independent XXZ picture typically applied to Co$^{2+}$ systems, our results on monolayer CoBr$_2$ establish d$^7$ cobalt dihalides as a promising platform to explore the interplay of long-range Heisenberg and bond-dependent exchange interactions that can stabilize diverse magnetic ground states on a triangular lattice.

Lattice spin models featuring kinetic constraints constitute a paradigmatic setting for the investigation of glassiness and localization phenomena. The intricate dynamical behavior of these systems is a result of the dramatically reduced connectivity between many-body configurations. This truncation of transition pathways often leads to a fragmentation of the Hilbert space, yielding highly collective and therefore often slow dynamics. Moreover, this mechanism supports the formation of characteristic elementary excitations, which we investigate here theoretically in a two-dimensional Rydberg lattice gas. We explore their properties as a function of interaction strength and range, and illustrate how they can be experimentally probed via sideband spectroscopy. Here, we show that the transition rate to certain delocalized superposition states of elementary excitations displays collective many-body enhancement.

We study the dynamics of inertial active particles in a one-dimensional chain with harmonic nearest-neighbor interactions, highlighting the interplay of persistence, interaction, and inertial timescales. Using a Green's function approach, we derive the mean-squared displacement (MSD) and mean-squared change in velocity (MSCV), revealing multiple crossovers between ballistic, diffusive, and subdiffusive regimes and providing analytic expressions for scaling coefficients and crossover times. Non-Gaussian deviations in active Brownian particles are captured through excess kurtosis, reflecting heavy-tailed, finite-support, or bimodal distributions that evolve systematically over time. Time-dependent probability distributions exhibit distinct data collapses within different temporal regimes, confirming the robustness of the scaling behavior. Overall, this framework connects multiparticle interactions to microscopic dynamics, revealing experimentally accessible signatures of inertia in active matter.

Starting from the purely microscopic model, we go beyond conventional mean-field theory and develop a self-consistent microscopic thermodynamic framework for disordered 2D superconductors. It incorporates the fermionic Bogoliubov quasiparticles, bosonic Nambu-Goldstone (NG) quantum and thermal phase fluctuations in the presence of long-range Coulomb interactions, and topological Berezinskii-Kosterlitz-Thouless (BKT) vortex-antivortex fluctuations on an equal footing, to self-consistently treat the superconducting gap and superfluid density. This unified phase-fluctuating description naturally recovers the previously known limiting results: the superconducting gap in the 2D limit can remain robust against long-wavelength NG phase fluctuations at $T=0^+$ due to Coulomb-induced regularization, while the gradual proliferation of BKT fluctuations as the system approaches criticality drives a separation between the global superconducting transition temperature $T_c$ and the gap-closing temperature $T^*$. In contrast to mean-field theory, which predicts 2D superconductivity to be independent of carrier density and non-magnetic disorder (Anderson theorem), the incorporation of phase fluctuations generates a density- and disorder-dependent zero-point gap $\Delta(0)$ and consequently $T_c$ and $T^*$. Remarkably, applications to bilayer MoS$_2$ [Nat. Nanotechnol. 14, 1123 (2019)] and disordered InO$_x$ thin films [Nat. Phys. 21, 104 (2025)] quantitatively reproduce key experimental observations in excellent agreement. The framework offers a useful theoretical tool for understanding phase-fluctuation-dominated superconductivity.

The results of numerical simulation using a modified Monte Carlo method with a thermostat algorithm for a pseudospin model of orthonickelates are presented. Temperature phase diagrams are constructed for various degrees of filling and for various parameters of the model, and the effect of local correlations on the critical temperatures of the model orthonickelate is investigated. The possibility of detecting phase inhomogeneous states is shown. The numerical simulation results show good qualitative agreement with the analytical results in the mean field approximation.

This paper extends a field-theoretical dynamical networking formalism for mesoscopic polymer dynamics to explicitly include dedicated cross-linker particles. Cross-linkers are represented within a Martin-Siggia-Rose generating functional and reversibly coupled to polymers through Gaussian networking fields, enabling an approximation scheme that reduces their degrees of freedom while remaining compatible with polymer dynamics. The framework is applied to a two-species polymer system in which intra- and inter-species cross-linking are assigned different statistical advantages. Effective networking potentials are derived and used to calculate correlation functions and dynamic structure factors. To validate these results, molecular dynamics simulations of semi-flexible polymers with reversible intra- and inter-species cross-linking are performed. Simulations show that cross-linking decreases polymer persistence lengths and local alignment, and the resulting trajectories yield dynamic structure factors consistent with theoretical predictions. In both approaches, cross-linking broadens the diffusive peaks and enhances the high-frequency tails of the structure factors. Together, theory and simulation provide complementary insights into the dynamics of cross-linked polymers, establishing a tractable framework that captures essential features observed in experiments and offering a basis for exploring more complex synthetic and biological networks.

Pushing nanoscale optical confinement to its ultimate limits defines the regime of nano-cavity quantum electrodynamics (nano-cQED), where light–matter interactions approach the fundamental quantum limits of individual atoms, e.g., picocavities. However, realizing such extreme confinement in a stable and controllable manner remains a key challenge. Here, we introduce a van der Waals material-based nano-cQED platform by coupling monolayer MoS2 excitons to plasmonic sub-nanocavities formed via assembly of ultrasmall gold clusters (3-5 nm) in the nanogap of a nanoparticle-on-mirror nanocavity. These clusters emulate the field-confining role of atomic protrusions of the picocavities through a resonance-insensitive lightning-rod effect, achieving deep-subwavelength mode volumes. In this nano-cQED testbed, we observe pronounced multi-branch Rabi splittings and ultrastrong lower-branch polaritonic photoluminescence with up to 10^4-fold enhancement. This deterministic architecture provides a controllable pathway to access picocavity-like behavior and opens new opportunities for single-molecule spectroscopy and the exploration of nano-cQED.