Quantum quench dynamics of the attractive one-dimensional Bose gas via  the coordinate Bethe ansatz

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

doi:10.21468/scipostphys.4.2.011

Cited by 16 publications

(11 citation statements)

References 97 publications

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“…It is an interesting strongly correlated model [94] with nontrivial bound states, also observed in experiments [95,96]. Recently its non-equilibrium properties have received a large attention, in particular after a quantum quench [97][98][99]. Connections to the KPZ equation have been discussed in the calculation of overlaps between eigenstates with different value of the coupling [100] and of the LL quantum propagator [101].…”

Section: Overview: the Attractive Lieb-liniger Model On The Half-linementioning

confidence: 99%

Delta-Bose gas on a half-line and the Kardar–Parisi–Zhang equation: boundary bound states and unbinding transitions

Nardis¹,

Krajenbrink²,

Doussal³

et al. 2020

J. Stat. Mech.

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We revisit the Lieb-Liniger model for n bosons in one dimension with attractive delta interaction in a half-space R + with diagonal boundary conditions. This model is integrable for arbitrary value of b ∈ R, the interaction parameter with the boundary. We show that its spectrum exhibits a sequence of transitions, as b is decreased from the hard-wall case b = +∞, with successive appearance of boundary bound states (or boundary modes) which we fully characterize. We apply these results to study the Kardar-Parisi-Zhang equation for the growth of a one-dimensional interface of height h(x, t), on the half-space with boundary condition ∂ x h(x, t)| x=0 = b and droplet initial condition at the wall. We obtain explicit expressions, valid at all time t and arbitrary b, for the integer exponential (one-point) moments of the KPZ height field e nh(0,t) . From these moments we extract the large time limit of the probability distribution function (PDF) of the scaled KPZ height function. It exhibits a phase transition, related to the unbinding to the wall of the equivalent directed polymer problem, with two phases: (i) unbound for b > − 1 2 where the PDF is given by the GSE Tracy-Widom distribution (ii) bound for b < − 1 2 , where the PDF is a Gaussian. At the critical point b = − 1 2 , the PDF is given by the GOE Tracy-Widom distribution.Overview: KPZ in a half-space.There has been much recent progress in physics and mathematics in the study of the 1D (KPZ) universality class, thanks to the discovery of exact solutions and the development of powerful methods to address stochastic integrability and integrable probability. The KPZ class includes a host of models [1]: discrete versions of stochastic interface growth such as the PNG growth model [2][3][4], exclusion processes such as the TASEP, the ASEP, the q-TASEP and other variants [5][6][7][8][9][10][11][12][13], discrete (i.e. square lattice) [3,[14][15][16][17][18][19][20][21][22] or semi-discrete [23-25] models of directed polymers (DP) at zero and finite temperature, random walks in time dependent random media [26,27], dimer models, random tilings, random permutations [28], correlation function in quantum condensates [29][30][31], and more. At the center of this class lies the continuum KPZ equation [32], see equation (3), which describes the stochastic growth of a continuum interface, and its equivalent formulation in terms of continuum directed polymers (DP) [33], via the Cole-Hopf mapping onto the stochastic heat equation (SHE). Recently exact solutions have also been obtained for the KPZ equation at all times for various initial conditions [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. This was achieved by two different routes. First by studying scaling limits of solvable discrete models, which allowed for rigorous treatments. The second, pioneered by Kardar [51], is non-rigorous, but leads to a more direct solution: it starts from the DP formulation, uses the replica method together with a mapping to the attractive delta-Bose gas (LL model), whi...

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Section: Overview: the Attractive Lieb-liniger Model On The Half-linementioning

confidence: 99%

Delta-Bose gas on a half-line and the Kardar–Parisi–Zhang equation: boundary bound states and unbinding transitions

Nardis¹,

Krajenbrink²,

Doussal³

et al. 2020

J. Stat. Mech.

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“…As is known, any numerical approach to physical systems with an infinite energy spectrum suffers from a kind of cutoff of the spectrum. Thus, the control of the accuracy of numerically obtained energy levels is a typical problem in any numerical approach (see, for instance, [30,32,[45][46][47]). The peculiarity of our approach is such that the accuracy of the computation of energy levels is determined by the numerical solver of the equations Eq.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…For the reader convenience we report here the standard procedure for finding eigenvalues and eigenfunctions, see for instance Refs. [29][30][31][32]. The solution for the eigenvalue problem can be obtained firstly by restricting the configuration space to the sector x 1 ≤ x 2 ≤ .…”

Section: The Modelmentioning

confidence: 99%

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Spectrum statistics in the integrable Lieb-Liniger model

2021

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We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is understanding whether Poisson statistics is a characteristic feature of this model. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. On the other hand, when studying long-range correlations between energy levels, we found strong deviations from the predictions given by a Poisson process.

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“…So far, only the sudden interaction quench starting from the non-interacting ground state, i.e. the Bose-Einstein condensate (BEC), has been theoretically understood [34,35] (although results at special values of the interaction [36] or with a finite number of particles exist [37][38][39]). In spite of the importance of the result, this protocol has some limitations: first of all, the realization of 1d BECs is difficult due to their instability under thermal fluctuations [40].…”

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confidence: 99%

Adiabatic formation of bound states in the 1d Bose gas

Koch,

Bastianello,

Caux

2020

Preprint

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We consider the 1d interacting Bose gas in the presence of time-dependent and spatially inhomogeneous contact interactions. Within its attractive phase, the gas allows for bound states of an arbitrary number of particles, which are eventually populated if the system is dynamically driven from the repulsive to the attractive regime. Building on the framework of Generalized Hydrodynamics, we analytically determine the formation of bound states in the limit of adiabatic changes in the interactions. Our results are valid for arbitrary initial thermal states and, more generally, Generalized Gibbs Ensembles.

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Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz

Cited by 16 publications

References 97 publications

Delta-Bose gas on a half-line and the Kardar–Parisi–Zhang equation: boundary bound states and unbinding transitions

Delta-Bose gas on a half-line and the Kardar–Parisi–Zhang equation: boundary bound states and unbinding transitions

Spectrum statistics in the integrable Lieb-Liniger model

Adiabatic formation of bound states in the 1d Bose gas

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