Jacob Robertson (Oxford)
Abhi Prakash, abhishodh.prakash@physics.ox.ac.uk
Quantum quenches in gapped spin-chains: mean-field theory and beyond
I will discuss the out of equilibrium dynamics following a shallow quantum quench in two spin chains. First, I will focus on the ANNNI model, a transverse field Ising chain with next-nearest neighbour interactions. The intermediate time dynamics of this model were explored in [1] which investigated the possibility of using quench dynamics to detect equilibrium quantum phase transitions. A simple mean-field study reproduces this result and allows for an easy criterion for the cutoff energy below which low-energy scaling behaviour is observed; it also allows us to estimate the correlation length at different times and show that it grows following the quench [2].
An unusual feature of the mean-field dynamics is that local observables do not relax to stationary values at late time. I will argue that this is a mean-field artefact by considering a second model, a staggered XXZ chain, and showing that a similar mean-field analysis gives similar long-lived oscillations and that these are damped when going one order perturbatively beyond mean-field theory [3]. This gives strong numerical evidence towards an open question of whether similar oscillations will decay in the tilted field Ising model.
[1] Haldar, Mallayya, Heyl, Pollmann, Rigol, Das, Phys. Rev. X 11, 031062 (2021)
[2] JR, Senese, Essler, SciPost Phys. 15, 032 (2023)
[3] JR, Senese, Essler, arxiv.org/abs/2307.04466