Ballistic-to-diffusive transition in spin chains with broken integrability

Abstract

We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundarydriven XXZ spin chain. Studying the evolution of the spin current density J s as a function of the system size L, we show that, accounting for boundary effects, the transition has a nontrivial universal behavior close to the XX limit. It is controlled by the scattering length L * ∝ V −2 , where V is the strength of the integrability-breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasiballistic" regime at length scales much shorter than L *. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on matrix product operator numerical simulations and agree with perturbative analytical calculations.

Generic transport formula for a system driven by Markovian reservoirs

“…This situation is described by the Lindblad operator [36,[49][50][51]54,60,61,64,65,[68][69][70][71][72][73][74][75]…”

“…Beyond experimental interest, for which the Lindblad coupling is the proper microscopic description, on the theory side, this approach has allowed to unveil nontrivial properties of highly excited and correlated systems: Integrable structures, traditionally restrained to closed systems in the quantum realm [49][50][51][52][53][54][55][56]; the existence of ballistics spin transport [36,57,58] and anomalous diffusion [59][60][61] in the integrable XXZ model, thus allowing for the discovery of Kardar-Parisi-Zhang correlations [62,63] in the quantum realm [64][65][66][67]. Additionally, it has allowed to characterize the anomalous transport properties of disordered [68,69] and quasiperiodic [70] interacting systems, the persistence of ballistic transport in the presence of level repulsion induced by single impurities [71][72][73], and ballistic-to-diffusive transition induced by integrability breaking in finite-sized systems [74,75].…”

Efficient quantum information probes of non-equilibrium quantum criticality

“…To achieve this, we followed a similar recipe to the one described in Appendix A of Ref. [60]. For a set of parameters L, V , η and D:…”

Energy transport in Z3 chiral clock model

“…An extensive amount of work on high temperature transport focusing on spin-half models in one dimensional (1D) quantum systems [2][3][4][5][6][7][8][9][10][11] has shown that breaking integrability generally leads to diffusive energy transport. It has been analytically argued that integrability in clean systems typically leads to ballistic energy transport [7,12].…”

“…We aim to address the question of how energy transport is affected by the model parameters, in particular how integrability affects transport in this model. Transport through the chain is simulated using the Lindblad Master Equation (LME) approach implemented using Matrix Product State (MPS) techniques [11,13,15,25].…”