Phase structure of matrix quantum mechanics at finite temperature

TL;DR

This paper investigates the phase structure of matrix quantum mechanics at finite temperature using Monte Carlo simulations, revealing a non-uniform phase and characterizing the order of phase transitions relevant to gauge/gravity duality.

Contribution

It provides the first detailed numerical evidence for a non-uniform phase and the order of phase transitions in the finite-temperature matrix quantum mechanics model.

Findings

Existence of a non-uniform eigenvalue distribution phase.

Second order transition from non-uniform to gapped phase.

Third order transition between uniform and non-uniform phases.

Abstract

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N=32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.