Quantum melting on a lattice and a delocalization transition

TL;DR

This paper investigates the quantum melting transition of a 2D lattice gas of spinless fermions with Coulomb interactions, revealing a transition from a periodic structure to a delocalized state at low hopping amplitudes.

Contribution

It provides computational evidence linking the melting transition to dielectric-metal and dielectric-superconductor transitions in a lattice fermion system.

Findings

Periodic structure melts at J=0.02--0.03 for ν=1/6

Transition associated with increased electron delocalization

Simultaneous measurement of current and structure confirms transition

Abstract

We consider 2d gas of spinless fermions with the Coulomb interaction on a lattice at T=0 and at different values of the hopping amplitude J. At small J electrons form a periodic structure. At filling factor \nu=1/6 this structure melts at J as low as 0.02--0.03 in units of the nearest-neighbor Coulomb energy. We argue that this transition is connected to the dielectric-metal and dielectric-superconductor transitions. To demonstrate this point we perform computer modeling of the systems 6x6 with 6 and 7 electrons and 6x12 with 12 electrons. By sweeping J we compute simultaneously persistent current and structural characteristics of the electron distribution.