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:2004.05955

Dissipative Bethe Ansatz: Exact Solutions of Quantum Many-Body Dynamics Under Loss

Berislav Buča, Cameron Booker, Marko Medenjak, Dieter Jaksch

Published Apr 13, 2020• 11 citations
arXivHTMLPDF

Abstract

We use the Bethe Ansatz technique to study dissipative systems experiencing loss. The method allows us to exactly calculate the Liouvillian spectrum. This opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.

DOI
10.48550/arxiv.2004.05955

Related papers

Bethe ansatz approach for dissipation: exact solutions of quantum many-body dynamics under loss

Berislav Buča, Cameron Booker, Marko Medenjak +1 more

Abstract We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.

New Journal of Physics•Dec 1, 2020•59 citations

Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model

Masaya Nakagawa, Norio Kawakami, Masahito Ueda

A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.

arXiv:2003.14202•Physical Review Letters•Mar 18, 2021•129 citations

Exact metastability in a class of driven-dissipative quantum many-body systems

David D. Noachtar, Aashish A. Clerk

Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.

quant-pharXiv:2606.07736•Jun 9, 2026•0 citations

Algebraic solutions to the dynamics of dissipative many-body quantum systems

Cameron Booker

From the motion of hurricanes to the cooling of a cup of tea, dissipative dynamics are ubiquitous in nature. Unfortunately, when studying lattice-based strongly correlated quantum systems, a common focus of experiments and highly relevant for material science, the curse of dimensionality prevents us from directly solving the exact equations describing the dissipative motion. We instead often use approximations and numerical analysis, as few analytical techniques currently exist which can provide useful insights. This thesis studies the constraints that non-abelian algebraic structures place on the dynamics of such non-equilibrium many-body quantum systems. In doing so, we develop novel algebraic methods that provide previously absent analytic insight into a range of problems. We apply these new techniques to study dynamical phases of quantum matter that are of both theoretical and experimental interest. We study how simple algebraic structures imply persistent non-stationarity in dissipative many-body quantum systems. These results enable us to develop a theory of quantum synchronisation based on symmetries and to explore a novel class of time crystals where order is induced by noise. These dynamical phases of matter have been gaining recent interest for their insights into thermalisation and their potential application in quantum technologies. We therefore use our results to explore experimentally realisable models. We also use the general principles of prethermalisation to propose a new theory to potentially explain recent experiments studying light-induced superconductivity in terms of eta-pairing and approximate symmetries. We discuss the merits and weaknesses of our proposal in relation to the experimental evidence. We also indicate techniques that, within our theory, stabilise superconducting states by harnessing the quantum Zeno effect For certain systems, known as integrable, there are enough symmetries to allow for exact solutions using the Bethe ansatz. We demonstrate that Bethe ansatz techniques can be extended and applied to non-equilibrium problems. As an example, we use this method to analytically study the dynamical phase transitions of an XXZ spin chain with boundary loss.

•Jan 1, 2022•0 citations

Dissipative dynamics in open XXZ Richardson-Gaudin models

Pieter W. Claeys, Austen Lamacraft

In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, the Hamiltonian is $\text{pseudo-Hermitian}/\mathcal{P}\mathcal{T}$ symmetric, and as the strength of the coupling to the environment is increased, the spectrum in a fixed symmetry sector changes from a broken pseudo-Hermitian phase with complex conjugate eigenvalues to a pseudo-Hermitian phase with real eigenvalues, passing through a series of exceptional points and associated dissipative quantum phase transitions. The homogeneous limit supports a nontrivial steady state, and away from this limit this state gives rise to a slow logarithmic growth of the decay rate (spectral gap) with system size. Using the exact solution, it is furthermore shown how at large coupling strengths the ratio of the imaginary to the real part of the eigenvalues becomes approximately quantized in the remaining symmetry sectors.

arXiv:2108.01677•Physical Review Research•Jan 14, 2022•13 citations

Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise

Mariya V. Medvedyeva, Fabian H. L. Eßler, Tomaž Prosen

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

arXiv:1606.09122•Physical Review Letters•Sep 21, 2016•162 citations
We use the Bethe Ansatz technique to study dissipative systems experiencing loss. The method allows us to exactly calculate the Liouvillian spectrum. This opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.
Abstract We develop a Bethe ansatz based approach to study dissipative systems experiencing loss. The method allows us to exactly calculate the spectra of interacting, many-body Liouvillians. We discuss how the dissipative Bethe ansatz opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.
A one-dimensional dissipative Hubbard model with two-body loss is shown to be exactly solvable. We obtain an exact eigenspectrum of a Liouvillian superoperator by employing a non-Hermitian extension of the Bethe-ansatz method. We find steady states, the Liouvillian gap, and an exceptional point that is accompanied by the divergence of the correlation length. A dissipative version of spin-charge separation induced by the quantum Zeno effect is also demonstrated. Our result presents a new class of exactly solvable Liouvillians of open quantum many-body systems, which can be tested with ultracold atoms subject to inelastic collisions.
Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.
From the motion of hurricanes to the cooling of a cup of tea, dissipative dynamics are ubiquitous in nature. Unfortunately, when studying lattice-based strongly correlated quantum systems, a common focus of experiments and highly relevant for material science, the curse of dimensionality prevents us from directly solving the exact equations describing the dissipative motion. We instead often use approximations and numerical analysis, as few analytical techniques currently exist which can provide useful insights. This thesis studies the constraints that non-abelian algebraic structures place on the dynamics of such non-equilibrium many-body quantum systems. In doing so, we develop novel algebraic methods that provide previously absent analytic insight into a range of problems. We apply these new techniques to study dynamical phases of quantum matter that are of both theoretical and experimental interest. We study how simple algebraic structures imply persistent non-stationarity in dissipative many-body quantum systems. These results enable us to develop a theory of quantum synchronisation based on symmetries and to explore a novel class of time crystals where order is induced by noise. These dynamical phases of matter have been gaining recent interest for their insights into thermalisation and their potential application in quantum technologies. We therefore use our results to explore experimentally realisable models. We also use the general principles of prethermalisation to propose a new theory to potentially explain recent experiments studying light-induced superconductivity in terms of eta-pairing and approximate symmetries. We discuss the merits and weaknesses of our proposal in relation to the experimental evidence. We also indicate techniques that, within our theory, stabilise superconducting states by harnessing the quantum Zeno effect For certain systems, known as integrable, there are enough symmetries to allow for exact solutions using the Bethe ansatz. We demonstrate that Bethe ansatz techniques can be extended and applied to non-equilibrium problems. As an example, we use this method to analytically study the dynamical phase transitions of an XXZ spin chain with boundary loss.
In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, the Hamiltonian is pseudo-Hermitian/PT\text{pseudo-Hermitian}/\mathcal{P}\mathcal{T}pseudo-Hermitian/PT symmetric, and as the strength of the coupling to the environment is increased, the spectrum in a fixed symmetry sector changes from a broken pseudo-Hermitian phase with complex conjugate eigenvalues to a pseudo-Hermitian phase with real eigenvalues, passing through a series of exceptional points and associated dissipative quantum phase transitions. The homogeneous limit supports a nontrivial steady state, and away from this limit this state gives rise to a slow logarithmic growth of the decay rate (spectral gap) with system size. Using the exact solution, it is furthermore shown how at large coupling strengths the ratio of the imaginary to the real part of the eigenvalues becomes approximately quantized in the remaining symmetry sectors.
We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.