Bloch Electron on a Triangular Lattice and Quantum Ising Model in a Transverse Field

TL;DR

This paper investigates the phase transitions of an electron on a triangular lattice under a magnetic field and relates these to quantum Ising models, revealing universality classes and critical points.

Contribution

It introduces a decimation scheme to analyze the tight binding model and establishes a connection between electron phases and quantum Ising chain universality classes.

Findings

Identification of critical, localized, and transition phases in the electron model.

Description of phase diagram with three nontrivial renormalization fixed points.

Relation of electron phases to universality classes of the quantum Ising chain.

Abstract

The tight binding model for an electron on an anisotropic triangular lattice in a uniform magnetic field is studied using a decimation scheme. The model exhibits a transition from critical to localized phase and the phase diagram is described in terms of three nontrivial renormalization fixed points for the band edges. These subcritical, critical, and supercritical universality classes also describe the corresponding states of the quantum Ising chain in a modulating transverse field. The only exception is the conformally invariant point of the Ising model which has no analog in the electron problem.