Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath

Abstract

The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with N Majorana fermion modes coupled to another SYK model with N 2 Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from 2π/β (β = 1/(k B T ), T is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a √ T -dependence at relatively high temperature to a linear T -dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.

Spread of entanglement in a Sachdev-Ye-Kitaev chain

“…In this paper, we will focus on the generalized Sachdev-Ye-Kitaev (SYK) models [19][20][21][22]] as a solvable model of a chaotic system. The solvability of this model, and various generalizations of it [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], allows for detailed studies of quantum chaos and thermalization.…”

Conformality of 1/N corrections in Sachdev-Ye-Kitaev-like models

“…The disordered and tensor SYK models have been extended in several directions: higher dimensions and lattices [30][31][32][33][34][35][36][37][38], N = 1, 2 supersymmetry [39,40] (see [41] for a related system with N = 4), non-quenched disorder [42][43][44]. Various properties have been studied in the last year: spectrum and thermodynamical properties [45][46][47][48][49][50][51][52][53][54][55], correlation functions [45,[56][57][58][59][60][61], dynamics of the Goldstone bosons [4,60,62,63], relation with matrix models (for both the disordered and tensor versions) [46,51,[64][65][66][67][68], transport properties [30,69,70], renormalization and phases…”

A new class of SYK-like models with maximal chaos

“…The model has been intensively studied the past few years. There exists many generalizations including higher dimensions [13][14][15][16][17], flavours [18,19], tunable chaos [20] and supersymmetry [16,21].…”