Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model

Abstract

We consider the time evolution of local observables after an interaction quench in the repulsive Lieb-Liniger model. The system is initialized in the ground state for vanishing interaction and then time-evolved with the Lieb-Liniger Hamiltonian for large, finite interacting strength c. We employ the Quench Action approach to express the full time evolution of local observables in terms of sums over energy eigenstates and then derive the leading terms of a 1/c expansion for several one and two-point functions as a function of time t>0 after the quantum quench. We observe delicate cancellations of contributions to the spectral sums that depend on the details of the choice of representative state in the Quench Action approach and our final results are independent of this choice. Our results provide a highly non-trivial confirmation of the typicality assumptions underlying the Quench Action approach.

Duality between Weak and Strong Interactions in Quantum Gases

“…On physical grounds, we expect a drastic change of potential from small positive to small negative β as it corresponds to going from a Tonks-Girardeau to a Super-Tonks-Girardeau gas. Applying our results to a strong coupling expansion in the LL model is particularly appealing due to the recent accounts of uniform convergence-in space and time-of the perturbative series for correlation functions both in [64] and out of equilibrium [65]. For instance, this opens the door to a systematic investigation of quantum quenches, explicitly accessing the late time regime where homogeneous systems are expected to locally relax [66] and inhomogeneous ones to follow the predictions of generalised hydrodynamics [67][68][69].…”

Regularization of a strong-weak duality between pointlike interactions in one dimension

“…We now wish to prove that the limit lim a→0 ψa,β (x) (44) exists. Let us consider f β (x) satisfying (20).…”

“…Our potential allows for a well-behaved perturbative expansion of the energy levels of the Cheon-Shigehara model at small coupling, and we show that we recover indeed the energy levels of the Lieb-Liniger model at strong coupling. This duality should prove useful to study expansions of the Lieb-Liniger model at large coupling [38][39][40][41][42][43][44].…”

Out-of-equilibrium dynamics of the XY spin chain from form factor expansion

“…The standard approach to these problems [2] consists in expressing such correlation functions as form factor sums over the full Hilbert space. In interacting models, this task has been achieved only in certain parameter regimes, such as ground state correlations at late times and large distances [3][4][5][6], equal-time finite temperature correlations at short or large distances [7][8][9][10][11][12][13][14][15][16], full correlations in systematic strong coupling expansions [17,18] or expansions in low densities of excitations [19][20][21], and also in some particularly simple interacting models or settings [22][23][24][25]. A number of numerical, approximate, field theory and other approaches aimed at facilitating form factor summations have been developed over the last decade and a half [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”