Random Matrix Crossovers and Quantum Critical Crossovers for Interacting Electrons in Quantum Dots

TL;DR

This paper investigates quantum critical behavior in large quantum dots with crossover ensembles, revealing how a new tunable energy scale enables access to the quantum critical regime through nonperturbative large-N methods.

Contribution

It introduces a novel approach to study quantum criticality in quantum dots with crossover ensembles using large-N techniques, highlighting a new energy scale for experimental access.

Findings

Quantum critical regime accessible at a new energy scale

Large-N approach effectively describes collective critical fluctuations

Crossover ensembles reveal tunable quantum phase transition behavior

Abstract

Quantum dots with large Thouless number $g$ embody a regime where both disorder and interactions can be treated nonperturbatively using large-N techniques (with $N=g$) and quantum phase transitions can be studied. Here we focus on dots where the noninteracting Hamiltonian is drawn from a crossover ensemble between two symmetry classes, where the crossover parameter introduces a new, tunable energy scale independent of and much smaller than the Thouless energy. We show that the quantum critical regime, dominated by collective critical fluctuations, can be accessed at the new energy scale. The nonperturbative physics of this regime can only be described by the large-N approach, as we illustrate with two experimentally relevant examples.