Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential

TL;DR

This paper investigates a quantum particle in a random potential with a harmonic trap, revealing a phase diagram with glassy behavior and quantum transitions, using variational and replica methods.

Contribution

It extends previous work by solving the model's phase diagram in the quantum regime using advanced analytical techniques.

Findings

Identifies a phase diagram similar to quantum spin glasses.

Characterizes the glassy phase with replica-symmetry-breaking.

Discusses quantum phase transition at zero temperature.

Abstract

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ``toy'' model for an interface in a random medium. It also applies to a single quantum particle like an an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use the replica method, and are able to solve the model and obtain its phase diagram in the $T - (\hbar^2/m)$ plane, where $m$ is the particle's mass. The phase diagram is similar to that of a quantum spin-glass in a transverse field, where the variable $\hbar^2/m$ plays the role of the transverse field. The glassy phase is characterized by replica-symmetry-breaking. The quantum transition at zero temperature is also discussed.