Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

Zill, Jan C.; Wright, Tod M.; Kheruntsyan, K. V.; Gasenzer, Thomas

doi:10.1103/physreva.91.023611

Cited by 34 publications

(111 citation statements)

References 128 publications

(341 reference statements)

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“…This allows us to clarify the utility and limitations of calculations, such as ours here and in Ref. [166], that involve only small particle numbers.…”

Section: Ground-state Correlation Functionsmentioning

confidence: 79%

“…[7,73,166,204,210,[324][325][326]) and a quench from the correlated ground state obtained for a strong interaction strength γ 0 = 100. AsĤ(γ) is time independent following the quench, energy is conserved during the dynamics.…”

Section: A Coordinate Bethe Ansatz Approach To the One-dimensional Bomentioning

confidence: 96%

“…[166]. We characterize several dynamical correlation functions, as well as the instantaneous fidelity for several representative post-quench interaction strengths.…”

Section: Outline Of Thesismentioning

confidence: 99%

“…However, our results also suggest that the effects of finite system size are comparatively less important for local correlations, particularly in the limit of large interaction strengths γ 1. To further elucidate the potential significance of finite-size effects in our calculations of nonequilibrium dynamics [166], here we give a brief characterization of the dependence of correlation functions of the Lieb-Liniger ground state on the particle number N at a fixed value of the interaction strength γ.…”

Section: System-size Dependencementioning

confidence: 99%

“…In the spirit of the methodology of Refs. [266,305], Gritsev et al In our previous work we applied this methodology to quenches from the ideal gas ground state to positive γ for up to N = 5 particles [166]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Zill¹

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This thesis is concerned with non-equilibrium phenomena in interacting quantum manybody systems. Specifically, we investigate the time-evolution and relaxation dynamics of Bose gases in a highly restricted geometry, which constrains the dynamics to one spatial dimension. This leads to a description of the system in terms of a simple model Hamiltonian which permits exact many-body quantum mechanical solutions due to its integrability.In the first part of this thesis, a computational method is developed to obtain experimentally relevant correlation functions in the framework of the coordinate Bethe ansatz.We employ this method to compute exact ground-state correlation functions of the LiebLiniger gas for up to seven particles covering the whole regime of repulsive interactions. We also investigate the dynamics of the system after an instantaneous change of the interaction strength. This quantum quench deposits large amounts of energy that cannot be dissipated due to the system being closed, and so the dynamics far from equilibrium are probed. We prepare the system in two different initial states, and quench to the same final interaction strength. The latter is determined in such a way that the added energy due to the quench is the same for both scenarios. Conventional statistical mechanics predicts the same relaxed state, but due to the integrability of the system all considered correlation functions of the relaxed states differ from each other and also from the thermal ones.We then investigate the dynamics and relaxed state for a quench from zero to repulsive interactions in more detail, focussing on the mechanism of relaxation and the involved time-scales. We find that local correlation functions relax on time-scales determined by the interaction strength, in contrast to non-local correlation functions, whose relaxation time-scale is proportional to the system size.Next, we employ the same methodology to study the one-dimensional Bose gas with attractive interactions. In this case many-body bound states are permissible solutions of the Lieb-Liniger model. We compare exact ground-state correlation functions of up to seven particles to their corresponding mean-field solution. The latter displays a quantum phase transition at a critical interaction strength, marking the transition from a uniformdensity state to a localized bright soliton. Our exact results agree remarkably well with the corresponding mean-field solution past the critical point. We also investigate the dynamics following an interaction strength quench, starting again from the non-interacting ground state. Bound states strongly influence correlation functions for all post-quench interaction strengths, and local correlation functions are largely increased compared to their initial value.In the last part of this thesis, we investigate the behavior of the one-dimensional Bose gas under periodic driving of the interaction strength. To this end, we extend the coordinate Bethe-ansatz formalism by employing Floquet theory to obtain solutions for the...

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“…This allows us to clarify the utility and limitations of calculations, such as ours here and in Ref. [166], that involve only small particle numbers.…”

Section: Ground-state Correlation Functionsmentioning

confidence: 79%

Section: A Coordinate Bethe Ansatz Approach To the One-dimensional Bomentioning

confidence: 96%

“…[166]. We characterize several dynamical correlation functions, as well as the instantaneous fidelity for several representative post-quench interaction strengths.…”

Section: Outline Of Thesismentioning

confidence: 99%

Section: System-size Dependencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Zill¹

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Exact overlaps in the Lieb-Liniger model from coordinate Bethe ansatz

Chen

2020

Physics Letters B

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A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas

et al. 2016

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We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb-Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on interaction strength, and analyze the effects of system size in the crossover from few-body to mesoscopic regimes for up to seven particles. We also obtain time-dependent nonequilibrium correlation functions for five particles following quenches of the interaction strength from two distinct initial states. One quench is from the noninteracting ground state and the other from a correlated ground state near the strongly interacting Tonks-Girardeau regime. The final interaction strength and conserved energy are chosen to be the same for both quenches. The integrability of the model highly constrains its dynamics, and we demonstrate that the time-averaged correlation functions following quenches from these two distinct initial conditions are both nonthermal and moreover distinct from one another.

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Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

Cited by 34 publications

References 128 publications

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Exact overlaps in the Lieb-Liniger model from coordinate Bethe ansatz

A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas

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