Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models

TL;DR

This paper introduces the Wishart SYK model, analyzes its integrability, degeneracy, and level statistics, and compares its information scrambling behavior with the original SYK model, revealing distinct dynamical features.

Contribution

The paper presents a new Wishart SYK variant, demonstrates its integrability and extensive residual entropy, and explores its level statistics and OTOC behavior, highlighting differences from the original SYK model.

Findings

Wishart SYK ground state is massively degenerate with extensive residual entropy.

Fermionic Wishart SYK is integrable and exhibits Poisson level statistics.

Fermionic Wishart SYK shows large temporal fluctuations in OTOC, unlike the original SYK.

Abstract

The Sachdev-Ye-Kitaev (SYK) model attracts attention in the context of information scrambling, which represents delocalization of quantum information and is quantified by the out-of-time-ordered correlators (OTOC). The SYK model contains $N$ fermions with disordered and four-body interactions. Here, we introduce a variant of the SYK model, which we refer to as the Wishart SYK model. We investigate the Wishart SYK model for complex fermions and that for hard-core bosons. We show that the ground state of the Wishart SYK model is massively degenerate and the residual entropy is extensive, and that the Wishart SYK model for complex fermions is integrable. In addition, we numerically investigate the OTOC and level statistics of the SYK models. At late times, the OTOC of the fermionic Wishart SYK model exhibits large temporal fluctuations, in contrast with smooth scrambling in the original SYK model. We argue that the large temporal fluctuations of the OTOC are a consequence of a small effective dimension of the initial state. We also show that the level statistics of the fermionic Wishart SYK model is in agreement with the Poisson distribution, while the bosonic Wishart SYK model obeys the GUE or the GOE distribution.