Identifying general links between energetics and information in realistic open quantum systems is a long-standing problem in quantum thermodynamics and quantum information processing. However, the generality of existing efforts is often impeded by their specific assumptions about environments. Here we address the problem by developing a trajectory-level thermodynamic inference theory to establish general links using just the knowledge of the system, enabling a single framework applicable to a diverse range of environments. Underpinning the framework is a notion of excess energy introduced for inferring the net energy gain of the system after completing an information processing trajectory. We show that fluctuation behaviors of the excess energy encode general links between energetics and information with a conceptual advantage that they completely avoid a priori assumptions about environments and system-environment coupling forms. Crucially, we obtain a single thermodynamic inequality that integrates upper bounds on heat dissipation and extracted work in terms of system's information content change, providing complementary constraints that greatly expand the context of existing well-adopted results based on the second law of thermodynamics. We also uncover lower bounds on the precision of the fluctuating system's energy and information content changes in terms of their Fano factors and a correlation function between them. By extending relations between energetics and information to higher-order fluctuations, we thus reveal a trade-off that a more precise inference of energy or information content changes requires a looser energetic-information link. We showcase the implications of these general links in a number of quantum information and thermodynamic tasks of application relevance. Our framework provides a toolkit for analyzing the interplay between energetics and information from the trajectory level in generic quantum systems, thereby adding an indispensable structure to the thermodynamics of information.

Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized Ansatz is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis.

We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy.

The realization of excitonic insulators in transition metal dichalcogenide systems has opened the door to explorations of the exotic properties that such a state exhibits. We study theoretically the potential for excitonic insulators to show an anomalous form of quantum oscillations: the de Haas–van Alphen effect in an insulating system. We focus on the role of the interactions that generate the energy gap and show that it is crucial to consider quantum fluctuations that go beyond the mean-field treatment. Remarkably, quantum fluctuations can be dominant and lead to quantum oscillations that are significantly larger than those predicted using mean-field theory. Indeed, in experimentally accessible parameter regimes these fluctuation-generated quantum oscillations can even be larger than what would be found for the corresponding gapless system.

Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics.

Time reversal in a macroscopic system contradicts daily experience. It is practically impossible to restore a shattered cup to its original state by just time reversing the microscopic dynamics that led to its breakage. Yet, with the precise control capabilities provided by modern quantum technology, the unitary evolution of a quantum system can be reversed in time. Here, we implement a time-reversal protocol in a dipolar interacting, isolated many-body spin system represented by Rydberg states in an atomic gas. By changing the states encoding the spin, we flip the sign of the interaction Hamiltonian, and demonstrate the reversal of the relaxation dynamics of the magnetization by letting a demagnetized many-body state evolve back in time into a magnetized state. We elucidate the role of atomic motion using the concept of a Loschmidt echo. Finally, by combining the approach with Floquet engineering, we demonstrate time reversal for a large family of spin models with different symmetries. Our method of state transfer is applicable across a wide range of quantum simulation platforms and has applications far beyond quantum many-body physics, reaching from quantum-enhanced sensing to quantum information scrambling.

Waveguide quantum electrodynamics constitutes a modern paradigm for the interaction of light and matter, in which strong coupling, bath structure, and propagation delays can break the radiative conditions that quantum emitters typically encounter in free space. These characteristics intertwine the excitations of quantum emitters and guided radiation modes to form complex multiphoton dynamics. So far, combining the collective decay of the emitters with the non-Markovian effects induced by the modes has escaped a full solution and the detailed physics behind these systems remains unknown. Here we analyze such a collective non-Markovian decay in a minimal system of two excited emitters coupled to a one-dimensional single-band waveguide. We develop an exact solution for this system in terms of elementary functions that unveils hidden symmetries and predicts new forms of spontaneous decay. The collective non-Markovian dynamics, which are strongly dependent on the vacuum coupling and the detuning from the center of the band, show exotic features that can be characterized with a simple and readily available criterion. Our analytic methods shed light on the complexity of collective light-matter interactions and open up a pathway for understanding multiparticle open quantum systems.

We report on a photonic simulator of the critical state forming at the quantum phase transition between topologically distinct Anderson insulator phases. We observe a time-staggered profile in the circular photon polarization, which originates from the interplay of a chiral and sublattice symmetry, and has recently been suggested as a signature for topological Anderson criticality within the setup. We discuss the role of statistical detuning from criticality and show that the controlled breaking of phase coherence removes the signal, revealing its origin in quantum coherence.

In this study, we discuss a type of bulk-boundary correspondence, which holds for topological insulators and superconductors when the parity-time ($PT$) and/or parity-particle-hole ($PC$) symmetry are present. In these systems, even when the bulk topology is nontrivial, the edge spectrum is generally gapped, and thus the conventional bulk-boundary correspondence does not hold. We find that, instead of the edge spectrum, the single-particle entanglement spectrum becomes gapless when the bulk topology is nontrivial: i.e., the bulk-entanglement spectrum correspondence holds in $PT$- and/or $PC$-symmetric topological insulators and superconductors. After showing the correspondence using $K$-theoretic approach, we provide concrete models for each symmetry class up to three dimensions where nontrivial topology because of $PT$ and/or $PC$ is expected. An implication of our results is that, when the bulk topology under $PT$ and/or $PC$ symmetry is nontrivial, the noninteracting many-body entanglement spectrum is multiply degenerate in one dimension and is gapless in two or higher dimensions.

The mixed-valence compound ${\mathrm{SmB}}_6$ with partially filled samarium $4f$ flat bands hybridizing with $5d$ conduction bands is a paramount example of a correlated topological heavy-fermion system. In this study, we revisit the topology of ${\mathrm{SmB}}_6$ within the formalism of topological quantum chemistry and symmetry-based indicators. Based on this approach, we reach a detailed classification of the material's topology, and we reformulate the origin of topology in terms of band representations. We corroborate these aspects by constructing a minimal TB model that is consistent with all the symmetries of the system and is able to reproduce the topology of the material. We finally unveil the previously overlooked formation of multiple topological gaps, and we discuss its implications for experiments.

Exploring operational regimes of many-body cavity QED with multilevel atoms remains an exciting research frontier for their enhanced storage capabilities of intralevel quantum correlations. In this work, we consider an experimentally feasible many-body cavity QED model describing a four-level system, where each of those levels is formed from a combination of different spin and momentum states of ultracold atoms in a cavity. The resulting model comprises a pair of Dicke Hamiltonians constructed from pseudospin operators, effectively capturing two intertwined superradiant phase transitions. The phase diagram reveals regions featuring weak and strong entangled states of spin and momentum atomic degrees of freedom. These states exhibit different dynamical responses, ranging from slow to fast relaxation, with the added option of persistent entanglement temporal oscillations. We discuss the role of cavity losses in steering the system's dynamics into such entangled states and propose a readout scheme that leverages different light polarizations within the cavity. Our work paves the way to connect the rich variety of non-equilibrium phase transitions that occur in many-body cavity QED to the buildup of quantum correlations in systems with multilevel atom descriptions.

We explore thermal transport in a one-dimensional Fermi-Pasta-Ulam-Tsingou-type (FPUT-type) system with long-range (LR) interactions. In such a system, the harmonic part of the potential is nearest-neighbor coupled, while the strength of the quartic part of the potential between two lattice sites decays as a power $\sigma$ of the inverse of their distance, demonstrating the LR feature of the system. The relevant strong LR model $(0\le \sigma \le 1)$ has been considered in detail in our recent study [Xiong and Wang, Phys. Rev. E 109, 044122 (2024)], and here, we focus on the weak LR regime $(1\le \sigma \le 3)$. We show that the thermal transport behaviors in this regime are quite unexpected. We discovered a subregime $(1\le \sigma \le 1.5)$ wherein the thermal transport behaviors are very close to diffusive. This suggests that even a momentum-conserving system with appropriate LR interactions can still exhibit normal heat conduction. By meticulously analyzing the space-time scaling properties of equilibrium heat correlations, we also determine the center of this diffusive thermal transport at approximately $\sigma \simeq 1.25$. These discoveries, together with our prior results, provide a comprehensive understanding of thermal transport of this kind of LR-FPUT-type model.

In this paper, we investigate the dynamics of the two-dimensional Ising model with stochastic resetting, utilizing a constant resetting rate procedure with zero-strength initial magnetization. Our results reveal the presence of a characteristic rate $r_c\sim L^{-z}$, where $L$ represents the system size and $z$ denotes the dynamical exponent. Below $r_c$, both the equilibrium and dynamical properties remain unchanged. At the same time, for $r>r_c$, the resetting process induces a transition in the probability distribution of the magnetization from a double-peak distribution to a three-peak distribution, ultimately culminating in a single-peak exponential decay. Furthermore, we also find that at the critical points, as $r$ increases, the diffusion of the magnetization changes from anomalous to normal, and the correlation time shifts from being dependent on $L$ to being $r$-dependent only.

Boson stars are horizonless compact objects and they could possess novel geodesic orbits under the equilibrium assumption, which differ from those in black hole backgrounds. However, unstable boson stars may collapse into black holes or migrate to stable states, resulting in an inability to maintain the initially bound geodesic orbits within the backgrounds of unstable boson stars. To elucidate the fate of initially bound geodesic orbits in boson stars, we present a study of geodesics within the spherical space times of stable, collapsing, and migrating boson stars. We focus on timelike geodesics that are initially circular or reciprocating. We verify that orbits initially bound within a stable boson star persist in their bound states. For a collapsing boson star, we show that orbits initially bound and reciprocating finally either become unbound or plunge into the newly formed black hole, depending on their initial maximal radii. For initially circular geodesics, we have discovered the existence of a critical radius. Orbits with radii below this critical value are found to plunge into the newly formed black hole, whereas those with radii larger than the critical radius continue to orbit around the vicinity of the newly formed black hole, exhibiting nonzero eccentricities. For the migrating case, a black hole does not form. In this case, the reciprocating orbits span a wider radial range. For initially circular geodesics, orbits with small radii become unbound, and orbits with large radii remain bound with nonvanishing eccentricities. This geodesic study provides an approach to investigating the gravitational collapse and migration of boson stars.

Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and vortex QDs with vorticity $S=1$ (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescentlike components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with $S=2$. Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand and VQDs on the other.

Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time-translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in various driven-dissipative quantum platforms. The current understanding of CTCs is mainly based on mean-field theories, which fail to address the problem of whether the continuous time-translation symmetry can be broken in noisy, spatially extended systems absent in all-to-all couplings. Here, we propose a CTC realized in a quantum contact model through self-organized bistability. The CTCs stem from the interplay between collective dissipation induced by the first-order absorbing phase transitions and slow constant driving provided by an incoherent pump. The stability of such oscillatory phases in finite dimensions under the action of intrinsic quantum fluctuations is scrutinized by the functional renormalization group method and numerical simulations. Occurring at the edge of many-body synchronization, the CTC phase exhibits an inherent period and amplitude with a coherence time linearly diverging with system size, thus also constituting a boundary time crystal. Our results serve as a solid route towards self-protected CTCs in strongly interacting open systems.

Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of a general family of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at an arbitrary mutual distance. Using neutron scattering data for the compound ${\mathrm{KCuF}}_3$—a system of weakly coupled $S=1/2$ Heisenberg chains—and numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a different emergent length scale—the quantum coherence length—which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials.