Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature

Abstract

We report a numerical observation where the infinite-temperature out-of-time-order correlators (OTOCs) directly probe quantum phase transitions at zero temperature, in contrast to common intuition where low energy quantum effects are washed away by strong thermal fluctuations at high temperature. By comparing numerical simulations with exact analytic results, we determine that this phenomenon has a topological origin and is highly generic, as long as the underlying system can be mapped to a 1D Majorana chain. Using the Majorana basis, we show that the infinite-temperature OTOCs probe zero-temperature quantum phases via detecting the presence of Majorana zero modes at the ends of the chain that is associated with 1D Z2 topological order. Hence, we show that strong zero modes also affect OTOCs and scrambling dynamics. Our results demonstrate an intriguing interplay between information scrambling and topological order, which leads to a new phenomenon in the scrambling of generic non-integrable models: topological order induced pre-scrambling, paralleling the notion of prethermalization of two-time correlators, that defines a time-scale for the restricted scrambling of topologically-protected quantum information.

DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

“…Furthermore, our 2 Hamiltonian may open up a pathway toward testing recently proposed connections between 2 topological order, thermalization [57], and information scrambling [58] in two-dimensions. As shown in a previous work [58] authored by one of us, the degeneracy structure of a spectrum has profound effects in dynamics of information scrambling probed by out-of-time-order correlators (OTOC).…”

“…Furthermore, our 2 Hamiltonian may open up a pathway toward testing recently proposed connections between 2 topological order, thermalization [57], and information scrambling [58] in two-dimensions. As shown in a previous work [58] authored by one of us, the degeneracy structure of a spectrum has profound effects in dynamics of information scrambling probed by out-of-time-order correlators (OTOC). Because the ferromagnetic regime of the 1D transverse-field Ising model (TFIM) is dual to a 1D topological superconductor (the Kitaev chain), the presence of edge states results in a topological degeneracy which exists throughout the spectrum, and such a degeneracy inhibits information scrambling of edge operators, even at infinite temperature.…”

Out-of-time-ordered correlation in the anisotropic Dicke model

“…There have been flourishing works on Bose-Hubbard model [19], Ising model [20] and XXZ model [21]. Even in topological phase transition, OTOC has a substantial footprint [22].…”

Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions

“…Different from the normal time-order correla-tion function characterizing classical and quantum statistics [39][40][41][42][43][44], the OTOC can quantify the temporal and spatial correlations throughout many-body quantum systems, which is closely related to information scrambling. Thus, it is a widely used tool for diagnosing chaotic behavior [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63], many-body localization [64][65][66][67][68][69][70][71], entanglement [72][73][74][75][76], and quantum phase transitions [77][78][79][80][81][82][83][84].…”