Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2209.13377 · PRX Quantum

Quantum and Classical Correlations in Open Quantum Spin Lattices via Truncated-Cumulant Trajectories

Wouter Verstraelen, Dolf Huybrechts, Tommaso Roscilde, Michiel Wouters

Published Jul 12, 2023• 24 citations
arXivHTMLPDF

Abstract

The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their exploitation for technological purposes.A central question in open quantum systems concerns the fate of quantum correlations, and the possibility of controlling them by engineering the competition between the Hamiltonian dynamics and the coupling of the system to a bath.Such a question is very challenging from a theoretical point of view, as numerical methods faithfully accounting for quantum correlations are either relying on exact diagonalization, drastically limiting the sizes that can be treated numerically, or on approximations on the range or strength of quantum correlations, associated with the choice of a specific ansatz for the density matrix.In this work we propose a new method to treat open quantum spin lattices, based on stochastic quantum trajectories for the solution of the open-system dynamics.Along each trajectory, the hierarchy of equations of motion for many-point spin-spin correlators is truncated to a given finite order, assuming that multivariate kth-order cumulants vanish for k exceeding a cutoff k c .This scheme allows one to track the evolution of quantum spin-spin correlations up to order k c for all length scales.We validate this approach in the paradigmatic case of the dissipative phase transitions of the two-dimensional XYZ lattice subject to spontaneous decay.We convincingly assess the existence of steady-state phase transitions from paramagnetic to ferromagnetic, and back to paramagnetic, upon increasing one of the Hamiltonian spin-spin couplings, as well as the classical Ising nature of such transitions.Moreover, the approach allows us to show the presence of significant quantum correlations in the vicinity of the dissipative critical point, and to unveil the presence of spin squeezing, which can be proven to be a tight lower bound to the quantum Fisher information.

DOI
10.1103/prxquantum.4.030304

Related papers

Phase diagram of the dissipative quantum Ising model on a square lattice

Jiasen Jin, Alberto Biella, Oscar Viyuela +3 more

The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic inclusion of (classical and quantum) nonlocal correlations at increasing distances is crucial to determine the structure of the phase diagram, as well as the nature of the transitions in strongly interacting spin systems. In practice, we focus on the paradigmatic dissipative quantum Ising model: In contrast to the nondissipative case, its phase diagram is still a matter of debate in the literature. When dissipation acts along the interaction direction, we predict important quantitative modifications of the position of the first-order transition boundary. In the case of incoherent relaxation in the field direction, our approach confirms the presence of a second-order transition, while does not support the possible existence of multicritical points. Potentially, these results can be tested in up-to-date quantum simulators of Rydberg atoms.

arXiv:1810.08112•Physical review. B./Physical review. B•Dec 14, 2018•64 citations

Quantum jump correlations in long-range dissipative spin systems via cluster and cumulant expansions

Giulia Salatino, Anna Delmonte, Zejian Li +2 more

We characterize nonequilibrium phases in long-range dissipative spin systems through the statistical properties of quantum jump trajectories. While the average dynamics governed by the Lindblad master equation provides access to steady-state expectation values of order parameters, the quantum trajectory framework reveals features encoded in the spatial and temporal correlations of detection events. Focusing on a model exhibiting a paramagnetic-to-ferromagnetic phase transition, we investigate the full counting statistics of quantum jumps using a tilted Lindbladian approach. We combine this with cluster mean-field and cumulant expansion techniques, which allow us to capture, respectively, the short- and long-range structure of jump correlations. In addition, we study the waiting-time distributions of detection events. We show that quantum jump correlations display clear signatures of the underlying phases and reveal distinct dynamical features across the transition. Our results highlight the potential of trajectory-resolved observables as probes of collective behavior in open quantum many-body systems and provide new insights into the role of long-range interactions in shaping nonequilibrium dynamics.

quant-pharXiv:2604.21513•Apr 24, 2026•0 citations

Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices

Raphaël Menu, Tommaso Roscilde

The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state - chosen as the initial state of the dynamics - represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S=1/2 S = 1 / 2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.

arXiv:2301.01363•SciPost Physics•Jun 12, 2023•8 citations

Entanglement, information and non-equilibrium phase transitions in long-range open quantum Ising chains

Daniel A. Paz, Benjamin Maves, Naushad Ahmad Kamar +2 more

Non-equilibrium phase transitions of open quantum systems generically exhibit diverging classical but not quantum correlations. Still entanglement -- characterizing the latter correlations -- can be sensitive to the phase transition. Furthermore, mutual information, bounding the total correlations, should exhibit critical scaling at the transition. In this work, we study these quantities in the steady state of open quantum Ising chains with power-law interactions (with the exponent $0\le α\le 3$) where spins are subject to spontaneous emission. The bulk of this paper is dedicated to a detailed analytical as well as numerical analysis of the infinite-range model ($α=0$), a model that is closely related to the paradigmatic open Dicke model. Our main findings are that the entanglement, while being finite, peaks, exhibits a kink and takes a universal value at the transition, while the mutual information exhibits critical scaling not only at the transition but well into the ordered phase, underscoring a hidden criticality that is not captured by (two-point) correlations. We consider three distinct entanglement measures: logarithmic negativity; quantum Fisher information; and, spin squeezing. Specifically, we show that the collective spin operator that maximizes the quantum Fisher information can be identified with the \textit{gapless} mode of the phase transition, while the squeezed direction is that of the \textit{gapped} mode. Finally, we investigate power-law interacting models using matrix product states where we find comparable bounds on squeezing even when no phase transition is expected (for larger $α$), thus the connection to the phase transition does not appear to hold for shorter-range interactions.

arXiv:2410.05370•Oct 7, 2024•1 citation

Systematic Truncated Wigner Approximation for Open Spin Systems Reveals Long-Range Order Far from Equilibrium

Igor Timofeev, Dawid A. Hryniuk, Marzena H. Szymańska

Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per site. Derived systematically from the exact Stratonovich-Weyl evolution of the Lindblad equation, it generates both drift and reservoir noise for arbitrary spin $S$. Benchmarks against exact and tensor-network calculations validate its description of non-equilibrium dynamics and steady states. Applied to 400-site two-dimensional dissipative anisotropic XY lattices, our method reveals physics missed by mean-field and perturbative approaches: vortex-antivortex proliferation destroys the predicted staggered-XY phase for nearest-neighbour coupling, whereas algebraically decaying interactions stabilize an extended $\mathbb{Z}_2$-ordered phase. We obtain the first beyond-mean-field steady-state phase diagram of the long-range interacting model, revealing reentrant loss of order at strong coupling and closure of the ordered region beyond $α\approx 3.5$. Our new method provides a scalable route to strongly correlated driven-dissipative systems with long-range interactions, higher-dimensional geometries, spin-boson couplings, and spins beyond one half, relevant to modern experiments with magnetic atoms and polar molecules in optical lattices and tweezer arrays.

quant-pharXiv:2610.27462•Oct 21, 2026•0 citations

Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems

Julian Huber, Ana María Rey, Peter Rabl

We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with ${10}^{5}$ interacting two-level systems. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.

arXiv:2105.00004•Physical Review A•Jan 24, 2022•34 citations
The study of quantum many-body physics in Liouvillian open quantum systems becomes increasingly important with the recent progress in experimental control on dissipative systems and their exploitation for technological purposes.A central question in open quantum systems concerns the fate of quantum correlations, and the possibility of controlling them by engineering the competition between the Hamiltonian dynamics and the coupling of the system to a bath.Such a question is very challenging from a theoretical point of view, as numerical methods faithfully accounting for quantum correlations are either relying on exact diagonalization, drastically limiting the sizes that can be treated numerically, or on approximations on the range or strength of quantum correlations, associated with the choice of a specific ansatz for the density matrix.In this work we propose a new method to treat open quantum spin lattices, based on stochastic quantum trajectories for the solution of the open-system dynamics.Along each trajectory, the hierarchy of equations of motion for many-point spin-spin correlators is truncated to a given finite order, assuming that multivariate kth-order cumulants vanish for k exceeding a cutoff k c .This scheme allows one to track the evolution of quantum spin-spin correlations up to order k c for all length scales.We validate this approach in the paradigmatic case of the dissipative phase transitions of the two-dimensional XYZ lattice subject to spontaneous decay.We convincingly assess the existence of steady-state phase transitions from paramagnetic to ferromagnetic, and back to paramagnetic, upon increasing one of the Hamiltonian spin-spin couplings, as well as the classical Ising nature of such transitions.Moreover, the approach allows us to show the presence of significant quantum correlations in the vicinity of the dissipative critical point, and to unveil the presence of spin squeezing, which can be proven to be a tight lower bound to the quantum Fisher information.
The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic inclusion of (classical and quantum) nonlocal correlations at increasing distances is crucial to determine the structure of the phase diagram, as well as the nature of the transitions in strongly interacting spin systems. In practice, we focus on the paradigmatic dissipative quantum Ising model: In contrast to the nondissipative case, its phase diagram is still a matter of debate in the literature. When dissipation acts along the interaction direction, we predict important quantitative modifications of the position of the first-order transition boundary. In the case of incoherent relaxation in the field direction, our approach confirms the presence of a second-order transition, while does not support the possible existence of multicritical points. Potentially, these results can be tested in up-to-date quantum simulators of Rydberg atoms.
We characterize nonequilibrium phases in long-range dissipative spin systems through the statistical properties of quantum jump trajectories. While the average dynamics governed by the Lindblad master equation provides access to steady-state expectation values of order parameters, the quantum trajectory framework reveals features encoded in the spatial and temporal correlations of detection events. Focusing on a model exhibiting a paramagnetic-to-ferromagnetic phase transition, we investigate the full counting statistics of quantum jumps using a tilted Lindbladian approach. We combine this with cluster mean-field and cumulant expansion techniques, which allow us to capture, respectively, the short- and long-range structure of jump correlations. In addition, we study the waiting-time distributions of detection events. We show that quantum jump correlations display clear signatures of the underlying phases and reveal distinct dynamical features across the transition. Our results highlight the potential of trajectory-resolved observables as probes of collective behavior in open quantum many-body systems and provide new insights into the role of long-range interactions in shaping nonequilibrium dynamics.
The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state - chosen as the initial state of the dynamics - represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S=1/2 S = 1 / 2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.
Non-equilibrium phase transitions of open quantum systems generically exhibit diverging classical but not quantum correlations. Still entanglement -- characterizing the latter correlations -- can be sensitive to the phase transition. Furthermore, mutual information, bounding the total correlations, should exhibit critical scaling at the transition. In this work, we study these quantities in the steady state of open quantum Ising chains with power-law interactions (with the exponent 0≤α≤30\le α\le 30≤α≤3) where spins are subject to spontaneous emission. The bulk of this paper is dedicated to a detailed analytical as well as numerical analysis of the infinite-range model (α=0α=0α=0), a model that is closely related to the paradigmatic open Dicke model. Our main findings are that the entanglement, while being finite, peaks, exhibits a kink and takes a universal value at the transition, while the mutual information exhibits critical scaling not only at the transition but well into the ordered phase, underscoring a hidden criticality that is not captured by (two-point) correlations. We consider three distinct entanglement measures: logarithmic negativity; quantum Fisher information; and, spin squeezing. Specifically, we show that the collective spin operator that maximizes the quantum Fisher information can be identified with the \textit{gapless} mode of the phase transition, while the squeezed direction is that of the \textit{gapped} mode. Finally, we investigate power-law interacting models using matrix product states where we find comparable bounds on squeezing even when no phase transition is expected (for larger ααα), thus the connection to the phase transition does not appear to hold for shorter-range interactions.
Long-range interactions can protect dissipative order against fluctuations, but determining when they do so in two dimensions remains out of reach for existing many-body methods. We develop a continuous SU(2)-covariant truncated-Wigner framework that maps the problem onto stochastic dynamics with one Bloch sphere per site. Derived systematically from the exact Stratonovich-Weyl evolution of the Lindblad equation, it generates both drift and reservoir noise for arbitrary spin SSS. Benchmarks against exact and tensor-network calculations validate its description of non-equilibrium dynamics and steady states. Applied to 400-site two-dimensional dissipative anisotropic XY lattices, our method reveals physics missed by mean-field and perturbative approaches: vortex-antivortex proliferation destroys the predicted staggered-XY phase for nearest-neighbour coupling, whereas algebraically decaying interactions stabilize an extended Z2\mathbb{Z}_2Z2​-ordered phase. We obtain the first beyond-mean-field steady-state phase diagram of the long-range interacting model, revealing reentrant loss of order at strong coupling and closure of the ordered region beyond α≈3.5α\approx 3.5α≈3.5. Our new method provides a scalable route to strongly correlated driven-dissipative systems with long-range interactions, higher-dimensional geometries, spin-boson couplings, and spins beyond one half, relevant to modern experiments with magnetic atoms and polar molecules in optical lattices and tweezer arrays.
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which combines the mean-field dynamics of a spin ensemble with a Monte Carlo sampling of discrete initial spin values to account for quantum correlations. Here we show how this approach can be generalized for dissipative spin systems by replacing the deterministic mean-field evolution by a stochastic process, which describes the decay of coherences and populations while preserving the length of each spin. We demonstrate the application of this technique for simulating nonclassical spin-squeezing effects or the dynamics and steady states of cavity QED models with 105{10}^{5}105 interacting two-level systems. This opens up the possibility to perform accurate real-scale simulations of a diverse range of experiments in quantum optics or with solid-state spin ensembles under realistic laboratory conditions.