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:2408.14428 · Physical review. B./Physical review. B

Relaxation dynamics in the (double) sine-Gordon model: An open-system viewpoint

D. Szász-Schagrin, Dávid X. Horváth, G. Takács

Published Nov 18, 2024• 0 citations
arXivHTMLPDF

Abstract

We study the effects of integrability breaking on the relaxation dynamics of the (double) sine-Gordon model. Compared to previous studies, we apply an alternative viewpoint motivated by open-system physics by separating the phase field into homogeneous and inhomogeneous parts, describing a quantum pendulum (subsystem) and an interacting phononic bath (environment). To study the relaxation dynamics in the model, we perform quantum quenches using the mini-superspace-based truncated Hamiltonian approach developed recently and simulate the real-time evolution of various entanglement measures and the energy transfer between the subsystem and its environment. Our findings demonstrate that in the presence of integrability-breaking perturbations, the relaxation dynamics is substantially faster, signaled by the increase of entanglement and energy transfer between the quantum pendulum and the phonon bath.

DOI
10.1103/physrevb.110.174307

Related papers

Nonequilibrium time evolution in the sine-Gordon model

D. Szász-Schagrin, Izabella Lovas, G. Takács

We study the nonequilibrium dynamics of the quantum sine-Gordon model describing a pair of Josephson-coupled one-dimensional bosonic quasicondensates. Motivated by experimentally accessible quench procedures where the zero mode of the quasicondensates is weakly coupled to finite momentum modes, we develop a Hamiltonian truncation scheme relying on a mini-superspace treatment of the zero mode (MSTHA). We apply this method to simulate the time evolution after both weak and strong quantum quenches, injecting a low or high energy density into the system, and we demonstrate that MSTHA accurately captures the dynamics from the hard-core boson limit to the experimentally relevant weakly interacting regime for sufficiently mild quenches. In the case of high energy densities, MSTHA breaks down for weak interaction but still extends the range of validity of previous Hamiltonian truncation schemes. We also compare these results to the semiclassical truncated Wigner approximation, and we establish that the dynamics can be well approximated by the semiclassical description in the weakly interacting regime realized in the experiments. In addition, we clarify the importance of the phononic modes depending on the sine-Gordon interaction strength.

arXiv:2309.03596•Physical review. B./Physical review. B•Jan 16, 2024•6 citations

Nonequilibrium time evolution and rephasing in the quantum sine-Gordon model

Dávid X. Horváth, Izabella Lovas, Márton Kormos +2 more

We discuss the nonequilibrium time evolution of the phase field in the sine-Gordon model using two very different approaches: the truncated Wigner approximation and the truncated conformal space approach. We demonstrate that the two approaches agree for a period covering the first few oscillations, thereby giving a solid theoretical prediction in the framework of the sine-Gordon model, which is thought to describe the dynamics of two bosonic condensates in quasi-one-dimensional traps coupled via a Josephson tunneling term. We conclude, however, that the recently observed phase-locking behavior cannot be explained in terms of homogeneous sine-Gordon dynamics, which hints at the role of other degrees of freedom or inhomogeneity in the experimental system.

arXiv:1809.06789•Physical Review A•Jul 12, 2019•59 citations

Inhomogeneous quantum quenches in the sine-Gordon theory

Dávid X. Horváth, Spyros Sotiriadis, Márton Kormos +1 more

We study inhomogeneous quantum quenches in the attractive regime of the sine--Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine--Gordon Hamiltonian. Varying either the interaction strength of the sine--Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein--Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine--Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine--Gordon dynamics in arbitrary inhomogeneous settings.

arXiv:2109.06869•SciPost Physics•May 3, 2022•0 citations

Inhomogeneous quantum quenches in the sine-Gordon theory

Dávid X. Horváth

We study inhomogeneous quantum quenches in the attractive regime of the sine-Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian. Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.

•May 1, 2022•29 citations

Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium

Ivan Kukuljan, Spyros Sotiriadis, G. Takács

Complete information on the equilibrium behavior and dynamics of quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. This has recently become an experimentally relevant problem, due to progress in cold-atom experiments simulating QFT models and directly measuring higher order correlations. Here we compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental points of view. Building upon the so-called truncated conformal space approach, we numerically construct higher order correlations in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We measure deviations from Gaussianity due to the presence of interaction and analyze their dependence on temperature, explaining the experimentally observed crossover between Gaussian and non-Gaussian regimes. We find that correlations of excited states are markedly different from the thermal case, which can be explained by the integrability of the system. We also study dynamics after a quench, observing the effects of the interaction on the time evolution of correlation functions, their spatial dependence, and their non-Gaussianity as measured by the kurtosis.

arXiv:1802.08696•Physical Review Letters•Sep 13, 2018•82 citations

Sine-Gordon model from coupled condensates: A generalized hydrodynamics viewpoint

Alvise Bastianello

The sine-Gordon model captures the low-energy effective dynamics of a wealth of one-dimensional quantum systems, stimulating the experimental efforts in building a versatile quantum simulator of this field theory and fueling the parallel development of new theoretical toolkits able to capture far-from-equilibrium settings. In this work, we analyze the realization of the sine-Gordon model from the interference pattern of two one-dimensional quasicondensates: we argue that the emergent field theory is well described by its classical limit, and we develop its large-scale description based on generalized hydrodynamics. We show how, despite the sine-Gordon model being an integrable field theory, trap-induced inhomogeneities cause instabilities of excitations and provide exact analytical results to capture this effect.

arXiv:2310.04493•Physical review. B./Physical review. B•Jan 10, 2024•18 citations
We study the effects of integrability breaking on the relaxation dynamics of the (double) sine-Gordon model. Compared to previous studies, we apply an alternative viewpoint motivated by open-system physics by separating the phase field into homogeneous and inhomogeneous parts, describing a quantum pendulum (subsystem) and an interacting phononic bath (environment). To study the relaxation dynamics in the model, we perform quantum quenches using the mini-superspace-based truncated Hamiltonian approach developed recently and simulate the real-time evolution of various entanglement measures and the energy transfer between the subsystem and its environment. Our findings demonstrate that in the presence of integrability-breaking perturbations, the relaxation dynamics is substantially faster, signaled by the increase of entanglement and energy transfer between the quantum pendulum and the phonon bath.
We study the nonequilibrium dynamics of the quantum sine-Gordon model describing a pair of Josephson-coupled one-dimensional bosonic quasicondensates. Motivated by experimentally accessible quench procedures where the zero mode of the quasicondensates is weakly coupled to finite momentum modes, we develop a Hamiltonian truncation scheme relying on a mini-superspace treatment of the zero mode (MSTHA). We apply this method to simulate the time evolution after both weak and strong quantum quenches, injecting a low or high energy density into the system, and we demonstrate that MSTHA accurately captures the dynamics from the hard-core boson limit to the experimentally relevant weakly interacting regime for sufficiently mild quenches. In the case of high energy densities, MSTHA breaks down for weak interaction but still extends the range of validity of previous Hamiltonian truncation schemes. We also compare these results to the semiclassical truncated Wigner approximation, and we establish that the dynamics can be well approximated by the semiclassical description in the weakly interacting regime realized in the experiments. In addition, we clarify the importance of the phononic modes depending on the sine-Gordon interaction strength.
We discuss the nonequilibrium time evolution of the phase field in the sine-Gordon model using two very different approaches: the truncated Wigner approximation and the truncated conformal space approach. We demonstrate that the two approaches agree for a period covering the first few oscillations, thereby giving a solid theoretical prediction in the framework of the sine-Gordon model, which is thought to describe the dynamics of two bosonic condensates in quasi-one-dimensional traps coupled via a Josephson tunneling term. We conclude, however, that the recently observed phase-locking behavior cannot be explained in terms of homogeneous sine-Gordon dynamics, which hints at the role of other degrees of freedom or inhomogeneity in the experimental system.
We study inhomogeneous quantum quenches in the attractive regime of the sine--Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine--Gordon Hamiltonian. Varying either the interaction strength of the sine--Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein--Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine--Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine--Gordon dynamics in arbitrary inhomogeneous settings.
We study inhomogeneous quantum quenches in the attractive regime of the sine-Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian. Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.
Complete information on the equilibrium behavior and dynamics of quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. This has recently become an experimentally relevant problem, due to progress in cold-atom experiments simulating QFT models and directly measuring higher order correlations. Here we compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental points of view. Building upon the so-called truncated conformal space approach, we numerically construct higher order correlations in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We measure deviations from Gaussianity due to the presence of interaction and analyze their dependence on temperature, explaining the experimentally observed crossover between Gaussian and non-Gaussian regimes. We find that correlations of excited states are markedly different from the thermal case, which can be explained by the integrability of the system. We also study dynamics after a quench, observing the effects of the interaction on the time evolution of correlation functions, their spatial dependence, and their non-Gaussianity as measured by the kurtosis.
The sine-Gordon model captures the low-energy effective dynamics of a wealth of one-dimensional quantum systems, stimulating the experimental efforts in building a versatile quantum simulator of this field theory and fueling the parallel development of new theoretical toolkits able to capture far-from-equilibrium settings. In this work, we analyze the realization of the sine-Gordon model from the interference pattern of two one-dimensional quasicondensates: we argue that the emergent field theory is well described by its classical limit, and we develop its large-scale description based on generalized hydrodynamics. We show how, despite the sine-Gordon model being an integrable field theory, trap-induced inhomogeneities cause instabilities of excitations and provide exact analytical results to capture this effect.