Expansion of one-dimensional lattice hard-core bosons at finite temperature

Xu, Wei; Rigol, Marcos

doi:10.1103/physreva.95.033617

Cited by 33 publications

(31 citation statements)

References 51 publications

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“…[1], it is not the in situ density that is being measured, but the density profile after a trap release in 1d: in order to have a cloud that is large enough compared to the resolution of the camera, the longitudinal potential is suddenly released, and the atomic cloud expands for a time t TOF , before a picture is taken. When t TOF is sufficiently large, the real-space density profile n TOF (x) is directly related to the momentum distribution function (MDF) of integrable quasi-particles ρ p (θ, x ) just before the expansion, as [32][33][34][35][36][37] and Appendix VI). However, importantly, it is not only the asymptotic distribution for t TOF → ∞ that is accessible thanks to GHD.…”

Section: Microscopics and Coarse-grainingmentioning

confidence: 99%

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

et al. 2019

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Describing and understanding the motion of quantum gases out of equilibrium is one of the most important modern challenges for theorists. In the groundbreaking Quantum Newton Cradle experiment [Kinoshita, Wenger and Weiss, Nature 440, 900, 2006], quasi-one-dimensional cold atom gases were observed with unprecedented accuracy, providing impetus for many developments on the effects of low dimensionality in out-of-equilibrium physics. But it is only recently that the theory of generalized hydrodynamics has provided the adequate tools for a numerically efficient description. Using it, we give a complete numerical study of the time evolution of an ultracold atomic gas in this setup, in an interacting parameter regime close to that of the original experiment. We evaluate the full evolving phase-space distribution of particles. We simulate oscillations due to the harmonic trap, the collision of clouds without thermalization, and observe a small elongation of the actual oscillation period and cloud deformations due to many-body dephasing. We also analyze the effects of weak anharmonicity. In the experiment, measurements are made after release from the onedimensional trap. We evaluate the gas density curves after such a release, characterizing the actual time necessary for reaching the asymptotic state where the integrable quasi-particle momentum distribution function emerges.

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Section: Microscopics and Coarse-grainingmentioning

confidence: 99%

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

et al. 2019

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“…Since the pioneering work by Lieb, Schultz, and Mattis [66], the Jordan-Wigner transformation has been used as a standard tool to study quantum magnetism. It can be efficiently implemented numerically using properties of Slater determinants [72], and has been used to study quantum quenches in 1D hard-core boson systems [15,23,71,72,88,109,114,115,148].…”

Section: B Spin-charge Decompositionmentioning

confidence: 99%

“…As a second application, we study the expansion of harmonically trapped SU(N ) fermions after suddenly turning off the trap. Those quenches provide a fertile playground to unveil remarkable properties of correlated many-body systems [23,52,54,59,71,88,[108][109][110][111][112][113][114][115][116][117]. They can be viewed as nontrivial time-of-flight expansions that occur in the presence of interactions.…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices

2019

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We study quantum quench dynamics in the Fermi-Hubbard model, and its SU(N ) generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized Neel order, namely, initial state in which there is a periodic N -spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) Neel domain walls. Those correlations resemble the ones in the ground state of the SU(N ) model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting SU(N ) gas into the rapidity distribution after long times. Finally, we study equilibration in SU(N ) gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated SU(N ) fermions at large U . :1903.10521v3 [cond-mat.quant-gas] arXiv

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“…One can efficiently compute one-body observables of hard-core bosons solving for the fermions and using properties of Slater determinants [18,44,51,55]. The site occupations of fermions n l = n l , withn l =f † lf l , and hard-core bosons are identical.…”

Section: Dynamical Fermionizationmentioning

confidence: 99%

Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices

Vidmar

Rigol

2017

Phys. Rev. A

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Within the emergent eigenstate solution to quantum dynamics [Phys. Rev. X 7, 021012 (2017)], one can construct a local operator (an emergent Hamiltonian) of which the time-evolving state is an eigenstate. Here we show that such a solution exists for the expansion dynamics of Tonks-Girardeau gases in optical lattices after turning off power-law (e.g., harmonic or quartic) confining potentials, which are geometric quenches that do not involve the boost operator. For systems that are initially in the ground state and undergo dynamical fermionization during the expansion, we show that they remain in the ground state of the emergent local Hamiltonian at all times. On the other hand, for systems at nonzero initial temperatures, the expansion dynamics can be described constructing a Gibbs ensemble for the emergent local Hamiltonian (an emergent Gibbs ensemble).

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Expansion of one-dimensional lattice hard-core bosons at finite temperature

Cited by 33 publications

References 51 publications

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup

Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices

Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices

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