First order Quantum Hall to Wigner crystal phase transition on a triangular lattice: an iDMRG study

TL;DR

This study uses iDMRG to investigate a phase transition from an Integer Quantum Hall state to a Wigner crystal in a fermionic system on a triangular lattice under magnetic field, revealing a first-order transition.

Contribution

First to identify and characterize a first-order quantum phase transition between Quantum Hall and Wigner crystal phases on a triangular lattice using iDMRG.

Findings

First-order transition between Quantum Hall and Wigner crystal phases.

Transition consistent with Ginzburg-Landau theory.

Relevance to moiré heterostructures of 2D materials.

Abstract

In this work we study a system of interacting fermions on a triangular lattice in the presence of an external magnetic field. We neglect spin and fix a density of one third, with one unit of magnetic flux per particle. The infinite density matrix renormalization group algorithm is used to compute the ground state of this generalized Fermi-Hubbard model. Increasing the strength of the nearest-neighbor repulsion, we find a first order transition between an Integer Quantum Hall phase and a crystalline, generalized Wigner crystal state. The first-order nature of the phase transition is consistent with a Ginzburg-Landau argument. We expect our results to be relevant for moir\'e heterostructures of two-dimensional materials.