Professor Fabian Essler

Abstract:

We consider a Lindblad equation that for particular initial conditions reduces to an asymmetric simple exclusion process with additional loss and gain terms. The resulting Lindbladian exhibits operator-space fragmentation and each block is Yang–Baxter integrable. For particular loss/gain rates the model can be mapped to free fermions. We determine the full quantum dynamics for an initial product state in this case.

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.