Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit

TL;DR

This paper presents an exactly solvable model for interacting electrons in a quantum dot with chaotic boundaries in the large-g limit, revealing phase transitions and universal behaviors relevant to Coulomb blockade and Fermi liquid properties.

Contribution

It introduces a solvable large-g limit framework for quantum dots with interactions and disorder, connecting quantum critical points to observable phenomena.

Findings

Exact solution for the large-g limit of quantum dots with interactions

Identification of a quantum critical point controlling phase behavior

Predictions for Coulomb blockade peak spacing and quasiparticle properties

Abstract

We show that problem of interacting electrons in a quantum dot with chaotic boundary conditions is solvable in the large-g limit, where g is the dimensionless conductance of the dot. The critical point of the $g=\infty$ theory (whose location and exponent are known exactly) that separates strong and weak-coupling phases also controls a wider fan-shaped region in the coupling-1/g plane, just as a quantum critical point controls the fan in at T>0. The weak-coupling phase is governed by the Universal Hamiltonian and the strong-coupling phase is a disordered version of the Pomeranchuk transition in a clean Fermi liquid. Predictions are made in the various regimes for the Coulomb Blockade peak spacing distributions and Fock-space delocalization (reflected in the quasiparticle width and ground state wavefunction).