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

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.

4 pages, 1 figure

References in corpus (4)

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• Fluctuations of g-factors in metal nanoparticles: Effects of electron-electron interaction and spin-orbit scattering
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• A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots
• Level Spacings in Random Matrix Theory and Coulomb Blockade Peaks in Quantum Dots
• Large spin-orbit effects in small quantum dots
• Interactions, superconducting $T_c$, and fluctuation magnetization for two coupled dots in the crossover between the Gaussian Orthogonal and Unitary ensembles
• Diamagnetic persistent currents for electrons in ballistic billiards subject to a point flux
• The renormalization group for interacting fermions: from Fermi liquids to quantum dots