Gauge-covariant projected entangled paired states for interacting systems in a magnetic field

TL;DR

This paper introduces a gauge-invariant PEPS wavefunction for 2D lattice systems in magnetic fields, enabling translation-invariant simulations regardless of gauge choice.

Contribution

The authors develop a PEPS framework with virtual flux tensors that maintains translation invariance and allows gauge-independent simulation of magnetic systems.

Findings

Physical observables remain translation invariant with the new PEPS construction.

The method allows continuous variation of magnetic flux per plaquette in tensor contractions.

It bypasses the need for extended magnetic unit cells in simulations.

Abstract

The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, because of the need to choose a particular gauge for the vector potential. Nonetheless, in many situations all physical observables of the ground state remain entirely translation invariant. In this work, we introduce a projected entangled-pair state (PEPS) wavefunction with a pattern of virtual flux tensors, for which all physical expectation values are translation invariant by construction, possibly within an enlarged unit cell reflecting any symmetry breaking in the target state. Moreover, we show that the usual contraction and optimization methods for translation-invariant PEPS can be used, with the magnetic flux per plaquette only entering as a continuous parameter in the tensor network contractions. Therefore, our approach provides a method for simulating an interacting many-body system in a uniform magnetic field independently of the gauge choice for the vector potential and bypassing the need to consider extended magnetic unit cells.