Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential

TL;DR

This study investigates phase transitions in finite-temperature matrix quantum mechanics with a chemical potential, revealing a GWW-type transition in the bosonic case and exploring phase behavior with fermions using non-lattice simulations.

Contribution

It provides the first Monte Carlo evidence of GWW-type phase transition in bosonic matrix models and extends analysis to fermionic models with non-lattice methods.

Findings

Existence of GWW-type third-order phase transition in bosonic model

Phase transition between gapped and ungapped phases in fermionic model

Comparison of phase diagrams between bosonic and fermionic cases

Abstract

In this paper, we study the finite-temperature matrix quantum mechanics with chemical potential term linear in the single trace of U(N) matrices, via Monte Carlo simulation. In the bosonic case, we exhibit the existence of the Gross-Witten-Wadia (GWW) type third-order phase transition. We also extend our studies to the model with the fermionic degrees of freedom employing the non-lattice simulation via Fourier expansion, and explore the possibilities that there is a phase transition between the gapped and ungapped phase both in the absence and presence of the chemical potential term. We make a comparison of the phase diagram between the bosonic and fermionic cases.