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.
Highlights
We consider the case of a quantum quench to the repulsive Lieb-Liniger model, and bring to bear strong-coupling expansion methods we recently developed in the context of equilibrium response functions [64]
In this work we have combined the Quench Action approach with our recently developed 1/c-expansion method for form factor sums in the Lieb-Liniger model to analyze a number of different observables after a quantum quench starting in the ground state of a non-interacting Bose gas
Our work uncovered a novel aspect regarding the application of typicality ideas to the analysis of quantum quenches in integrable models
Summary
The non-equilibrium dynamics in isolated many-particle quantum systems has attracted a great deal of attention over the last decade [1,2,3,4,5,6]. It was realized early on that conservation laws play a crucial role in the late time relaxational behaviour of isolated systems [9, 19] This implies in particular that in the thermodynamic limit integrable systems with extensive numbers of conservation laws will typically relax to non-thermal stationary states [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]. The method of choice for studying the time evolution of local operators in interacting integrable models is the so-called Quench-Action approach [24, 53]. Determining the time evolution requires carrying out spectral sums like (3) Given that these generally involve an exponentially (in system size) large number of terms this is a formidable challenge. We consider the case of a quantum quench to the repulsive Lieb-Liniger model, and bring to bear strong-coupling expansion methods we recently developed in the context of equilibrium response functions [64]
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