Structural and insulator-metal quantum phase transitions on a lattice

TL;DR

This study investigates quantum phase transitions in a 2D lattice of spinless fermions, revealing how structural and insulator-metal transitions are driven by defect energy bands, using exact diagonalization on finite clusters.

Contribution

It provides a detailed analysis of the mechanisms behind structural and insulator-metal transitions in a lattice fermion system, highlighting the role of defect energy bands.

Findings

Transitions are driven by the defect energy band in the Wigner crystal.

The system transitions from a classical Wigner crystal to a nearly free fermion gas.

Exact diagonalization reveals the low-energy spectrum across different phases.

Abstract

We consider 2D gas of spinless fermions with the Coulomb and the short range interactions on a square lattice at T=0. Using exact diagonalization technique we study finite clusters up to 16 particles at filling factors $\nu=1/2$ and 1/6. By increasing the hopping amplitude we obtain the low-energy spectrum of the system in a wide range from the classical Wigner crystal to almost free gas of fermions. The most efforts are made to study the mechanism of the structural and insulator-metal transitions. We show that both transitions are determined by the energy band of the defect with the lowest energy in the Wigner crystal.