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:2309.03596 · Physical review. B./Physical review. B

Nonequilibrium time evolution in the sine-Gordon model

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

Published Jan 16, 2024• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.109.014308

Related papers

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

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

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

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.

arXiv:2408.14428•Physical review. B./Physical review. B•Nov 18, 2024•0 citations

Sudden interaction quench in the quantum sine-Gordon model

Javier Sabio, Stefan K. Kehrein

We study a sudden interaction quench in the weak-coupling regime of the quantum sine-Gordon model. The real time dynamics of the bosonic mode occupation numbers is calculated using the flow equation method. While we cannot prove results for the asymptotic long-time limit, we can establish the existence of an extended regime in time where the mode occupation numbers relax to twice their equilibrium values. This factor two indicates a non-equilibrium distribution and is a universal feature of weak interaction quenches. The weak-coupling quantum sine-Gordon model therefore turns out to be on the borderline between thermalization and non-thermalization.

arXiv:0911.1302•New Journal of Physics•May 28, 2010•26 citations

Quantum quenches in the sine-Gordon model: A semiclassical approach

Márton Kormos, Gergely Zaránd

We compute the time evolution of correlation functions after quantum quenches in the sine-Gordon model within the semiclassical approximation, which is expected to yield accurate results for small and slow quenches producing slow quasiparticles with low density. We demonstrate this by reproducing results of a recent form-factor calculation of the relaxation of expectation values [B. Bertini, D. Schuricht, and F. H. L. Essler, J. Stat. Mech. (2014) P100351742-546810.1088/1742-5468/2014/10/P10035]. Extending these results, we find that-in the universal limit of vanishingly small quasiparticle velocities-the expectation values of most vertex operators do not decay to zero. We give analytic expressions for the relaxation of dynamic correlation functions and show that they have diffusive behavior for large timelike separation.

arXiv:1507.02708•Physical review. E•Jun 1, 2016•72 citations

Quantum sine-Gordon dynamics in coupled spin chains

Elisabeth Wybo, Michael Knap, Alvise Bastianello

The sine-Gordon field theory emerges as the low-energy description in a wealth of quantum many-body systems. Recent efforts have been directed towards realizing quantum simulators of the model, by interfering two weakly coupled one-dimensional cold atomic gases. The weak interactions within the atomic clouds provide a sine-Gordon realization in the semiclassical regime. Furthermore, the intricate microscopic dynamics prevents a quantitative understanding of the effective sine-Gordon validity realm. In this work, we focus on a spin-ladder realization and observe the emergent sine-Gordon dynamics deep in the quantum regime. We use matrix-product state techniques to numerically characterize the low-energy sector of the system and compare it with the exact field-theory predictions. From this comparison, we obtain quantitative boundaries for the validity of the sine-Gordon description. We provide encompassing evidence for the emergent field theory by probing its rich spectrum and by observing the signatures of integrable dynamics in scattering events.

arXiv:2203.09530•Physical review. B./Physical review. B•Aug 1, 2022•24 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
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 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 a sudden interaction quench in the weak-coupling regime of the quantum sine-Gordon model. The real time dynamics of the bosonic mode occupation numbers is calculated using the flow equation method. While we cannot prove results for the asymptotic long-time limit, we can establish the existence of an extended regime in time where the mode occupation numbers relax to twice their equilibrium values. This factor two indicates a non-equilibrium distribution and is a universal feature of weak interaction quenches. The weak-coupling quantum sine-Gordon model therefore turns out to be on the borderline between thermalization and non-thermalization.
We compute the time evolution of correlation functions after quantum quenches in the sine-Gordon model within the semiclassical approximation, which is expected to yield accurate results for small and slow quenches producing slow quasiparticles with low density. We demonstrate this by reproducing results of a recent form-factor calculation of the relaxation of expectation values [B. Bertini, D. Schuricht, and F. H. L. Essler, J. Stat. Mech. (2014) P100351742-546810.1088/1742-5468/2014/10/P10035]. Extending these results, we find that-in the universal limit of vanishingly small quasiparticle velocities-the expectation values of most vertex operators do not decay to zero. We give analytic expressions for the relaxation of dynamic correlation functions and show that they have diffusive behavior for large timelike separation.
The sine-Gordon field theory emerges as the low-energy description in a wealth of quantum many-body systems. Recent efforts have been directed towards realizing quantum simulators of the model, by interfering two weakly coupled one-dimensional cold atomic gases. The weak interactions within the atomic clouds provide a sine-Gordon realization in the semiclassical regime. Furthermore, the intricate microscopic dynamics prevents a quantitative understanding of the effective sine-Gordon validity realm. In this work, we focus on a spin-ladder realization and observe the emergent sine-Gordon dynamics deep in the quantum regime. We use matrix-product state techniques to numerically characterize the low-energy sector of the system and compare it with the exact field-theory predictions. From this comparison, we obtain quantitative boundaries for the validity of the sine-Gordon description. We provide encompassing evidence for the emergent field theory by probing its rich spectrum and by observing the signatures of integrable dynamics in scattering events.
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.