Stationary State After a Quench to the Lieb–Liniger from Rotating BECs

It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-1 2 XXZ Heisenberg chain. These charges have been proven to be essential for properly describing stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-occupation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of quasilocal lattice charges are therefore necessary. As a concrete example, we find the complete set of charges needed in the sine-Gordon model, by using the fact that this field theory is recovered as the continuum limit of a spatially inhomogeneous version of the XXZ chain. The set of quasilocal charges of the lattice theory are shown to become a set local charges with fractional spin in the field theory.

Section: Quasilocal Lattice Chargessupporting

confidence: 79%

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Vernier¹,

Cubero²

2017

“…where the functions a n,m , b n,m and ε n (λ) are defined in (24), (25) and (35) respectively, while g (r)…”

Section: The Quench Action Methodsmentioning

confidence: 99%

Integrable quenches in nested spin chains I: the exact steady states

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

101

We consider quantum quenches in the integrable SU (3)-invariant spin chain (Lai-Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable "soliton non-preserving" boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a Quantum Transfer Matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the Quench Action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states. arXiv:1811.00432v4 [cond-mat.stat-mech]

“…with a driving term w(λ) which keeps into account all the relevant conservation laws, besides energy and number of particles. It is interesting to note that in a few cases the solution to (14) could be determined analytically [81,[95][96][97].…”

Section: The Lieb-liniger Modelmentioning

confidence: 99%

From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics

Bastianello

Piroli

2018

We derive exact formulas for the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions (Lieb-Liniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinh-Gordon field theory, we derive explicit analytic expressions for the one-point K-body correlation functions (Ψ † ) K (Ψ) K in the Lieb-Liniger gas, for arbitrary integer K. These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particle-number fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multi-point correlation functions at the Eulerian scale in non-homogeneous settings. Our results complement previous studies in the literature and provide a full solution to the problem of computing one-point functions in the Lieb-Liniger model. I. INTRODUCTIONCorrelation functions encode all of the information which can be experimentally extracted from a many-body quantum system. At the same time, the problem of their computation is extremely complicated from the theoretical point of view, restricting us, in general, to rely uniquely on perturbative or purely numerical methods.An outstanding exception to this picture are integrable systems [1], characterized by the existence of an extensive number of local conservation laws, which provide an ideal theoretical laboratory to deepen our knowledge of many-body physics. This is especially true due to the possibility of obtaining exact, unambiguous predictions for several quantities of interest, allowing us, for instance, to test the validity of approximate or numerical methods which can be applied to more general cases. While integrability directly provides the tools for diagonalizing the Hamiltonian, the computation of correlation functions constitute a remarkable challenge, which has attracted a constant theoretical effort over the past fifty years [2][3][4][5]. Classical studies have in particular focused on ground-state and thermal correlations, and joint efforts have led to spectacular results, for example in the case of prototypical interacting spin models such as the well-known Heisenberg chain [6][7][8][9][10][11][12].More recently, new energy has been pumped into the study of integrable models, also due to the new experimental possibilities offered by cold-atom physics. Nearly ideal integrable systems can now be realized in cold-atom experiments both in and out equilibrium [13][14][15], elevating the relevance of existing works beyond the purely theoretical interest, and motivating further advances in the framework of non-equilibrium physics (see [16] for a collection of recent reviews on this topic).From the experimental point of vie...