Simulating fermionic fractional Chern insulators with infinite projected entangled-pair states

TL;DR

This paper extends the iPEPS variational method to simulate fermionic fractional Chern insulators, demonstrating the approach's effectiveness and introducing a compression scheme for entanglement spectrum calculations.

Contribution

It develops a fermionic iPEPS framework for FCIs, identifies a critical bond dimension for accurate phase representation, and introduces a new compression scheme for entanglement spectra.

Findings

Evidence of a critical bond dimension for faithful FCI representation

Successful characterization of FCI states using bulk observables

Efficient entanglement spectrum calculation with a new compression scheme

Abstract

Infinite projected entangled-pair states (iPEPS) provide a powerful variational framework for two-dimensional quantum matter and have been widely used to capture bosonic topological order, including chiral spin liquids. Here we extend this approach to \emph{fermionic} topological order by variationally optimizing $U(1)$-symmetric fermionic iPEPS for a fractional Chern insulator (FCI), with bond dimensions up to $D=9$. We find evidence for a critical bond dimension, above which the ansatz faithfully represents the FCI phase. The FCI state is characterized using bulk observables, including the equal-time single-particle Green's function and the pair-correlation function, as well as the momentum-resolved edge entanglement spectrum. To enable entanglement-spectrum calculations for large iPEPS unit cells, we introduce a compression scheme and show that the low-lying part of the spectrum is already well converged at relatively small cutoff dimensions.