Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models

TL;DR

This paper analyzes the phase diagram of fermionic matrix quantum mechanics models, revealing a rich structure with phase transitions, critical points, and differences from traditional SYK models, especially in the large D limit.

Contribution

It provides a detailed numerical study of the phase transitions and critical behavior in tensor and matrix models, highlighting new nonmean field critical exponents and the absence of SYK-like IR solutions.

Findings

Identification of a first order phase transition line with a critical point.

Discovery of nonmean field critical exponents at the transition.

Absence of SYK-like IR solutions in the full theory.

Abstract

We compute the phase diagram of a $\text{U}(N)^{2}\times\text{O}(D)$ invariant fermionic planar matrix quantum mechanics [equivalently tensor or complex Sachdev-Ye-Kitaev (SYK) models] in the new large $D$ limit, dominated by melonic graphs. The Schwinger-Dyson equations can have two solutions describing either a high entropy, SYK black-hole-like phase, or a low entropy one with trivial IR behavior. In the strongly coupled region of the mass-temperature plane, there is a line of first order phase transitions between the high and low entropy phases. This line terminates at a new critical point which we study numerically in detail. The critical exponents are nonmean field and differ on the two sides of the transition. We also study purely bosonic unstable and stable melonic models. The former has a line of Kazakov critical points beyond which the Schwinger-Dyson equations do not have a consistent solution. Moreover, in both models the would-be SYK-like solution of the IR limit of the equations does not exist in the full theory.