Universal two-time correlations, out-of-time-ordered correlators, and Leggett-Garg inequality violation by edge Majorana fermion qubits

Abstract

In the present work we propose that two-time correlations of Majorana edge localized fermions constitute a novel and versatile toolbox for assessing the topological phases of 1D open lattices. Using analytical and numerical calculations on the Kitaev model, we uncover universal relationships between the decay of the short-time correlations and a particular family of out-of-time-ordered correlators, which provide direct experimental alternatives to the quantitative analysis of the system regime, either normal or topological. Furthermore we show that the saturation of two-time correlations possesses features of an order parameter. Finally, we find that violations of Leggett-Garg inequalities can indicate the topological-normal phase transition by looking at different qubits formed by pairing local and non-local edge Majorana fermions.

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

“…in the topologically non-trivial phase; W αβ Eα=E β = 0 otherwise. Here f (h) is a smooth function of magnetic field h, that can be extracted numerically for finite size systems, whereas by usingC 36 we can determine an analytical expression f (h) = 2(1 − h 2 )/2 in the thermodynamic limit. Hence F diag = (1 − h 2 ) 2 can be written, whileC = 1 − h 236 .…”

“…13 is calculated asC = 1 − h 2 for h < J andC = 0 for h > J in Ref. 36 . We substitute this analytical result into Eq.…”

“…The dynamical detection of topological order has been under intensive investigation 29,30,[35][36][37] . Furthermore, the topological insulators and superconductors have been studied [38][39][40][41][42] and classified 43 according to their nonequilibrium dynamics rather in an analogy to the classification tables for topological states of matter 44 superposed with the notion of dynamical quantum phase transitions [45][46][47] .…”

Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence

“…As a result, the direction and magnitude of the overall maximal violation can be controlled by ∆, being enhanced in the strongly-interacting regime. This also shows that the LGI violation indicates the nonequilibrium critical point, a property that it also features in equilibrium [57,58].…”

Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling

“…An interesting choice to study next would be the Sachdev-Ye-Kitaev (SYK) model [7,63]. The SYK model consists of Majorana fermions, whose experimental realizations are being pursued assiduously [64][65][66][67][68][69][70]. As the SYK model scrambles maximally quickly, like black holes, it has been hoped to shed light on quantum gravity.…”