Universal scaling of density and momentum distributions in Lieb-Liniger gases

Xu, Wei; Rigol, Marcos

doi:10.1103/physreva.92.063623

Cited by 55 publications

(64 citation statements)

References 66 publications

(117 reference statements)

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“…The same behavior can be observed for the large-k tail of the corresponding momentum distribution ( )  n k , which we plot in figure 3(b). Indeed, at larger momenta  p k n 2 , ( )  n k appears to exhibit a rapid collapse to a single curve with increasing N [21,109]. However, the differences in ( )  n k are so small that they can not be seen in figure 3(b).…”

Section: System-size Dependencementioning

confidence: 91%

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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Section: System-size Dependencementioning

confidence: 91%

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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“…The local-density approximation could be tested by comparing with ab-initio numerical simulations. It would be interesting to generalize this method to the case of multicomponent 1D gases as well as to finite temperature, beyond the infinitely repulsive Tonks-Girardeau limit of references [31,37].…”

Section: Discussionmentioning

confidence: 99%

Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

Lang

Vignolo

Minguzzi

2017

Eur. Phys. J. Spec. Top.

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Abstract. We study Tan's contact, i.e. the coefficient of the highmomentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion.Our results are relevant for ongoing experiments with ultracold atomic gases.

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“…[33]. As for hard-core boson systems [49,51], our numerical approach in the lattice allows one to resolve those tails better than approaches that work directly in the continuum.…”

Section: Total One-body Correlationsmentioning

confidence: 99%

Impenetrable SU(N) fermions in one-dimensional lattices

2018

Self Cite

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We study SU(N ) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.

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Universal scaling of density and momentum distributions in Lieb-Liniger gases

Cited by 55 publications

References 66 publications

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

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

Tan’s contact of a harmonically trapped one-dimensional Bose gas: Strong-coupling expansion and conjectural approach at arbitrary interactions

Impenetrable SU(N) fermions in one-dimensional lattices

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