Instability of the non-Fermi-liquid state of the Sachdev-Ye-Kitaev model

Abstract

We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the maximal chaotic non-Fermi liquid phase described by the ordinary q = 4 SYK model has marginally relevant/irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the SYKq model with a q−fermion interaction, similar perturbations can lead to a series of new fixed points with continuously varying exponents.

Model for continuous thermal metal to insulator transition

“…It is straightforward to show that, the renormalization group flow of the u term is almost identical to the single cluster case discussed in Ref. 37, i.e. when u < 0, it can be ignored in the infrared limit because it is marginally irrelevant; while when u > 0, it becomes marginally relevant.…”

“…37 and perform a Hubbard-Stratonovich transformation for the u-term. The action for the chain becomes:…”

“…But just like the model discussed in Ref. 37, a time-reversal symmetry breaking order parameter would increase continuously from the MIT. The MIT in our model is controlled by a tuning parameter in the Hamitonian, rather than the ratio between the sizes of two clusters of different nature, like the pase transition considered in a two-cluster model in Ref.…”

The bulk dual of SYK: cubic couplings

“…Or, one can consider a Lorentz invariant higher-dimensional bosonic SYK [30]. For other generalizations, see [19,[50][51][52][53][54][55][56][57][58][59]. In addition, in the study of AdS 2 /CFT 1 one must regulate the bulk, introducing a dilaton and turning it into "nearly" AdS 2 .…”

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

“…As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.…”