Simulating Bulk Gap in Chiral Projected Entangled-Pair States

TL;DR

This paper demonstrates that PEPS can reliably describe gapped bulk excitations in chiral topological phases, even with long-range correlation tails, by using a variational excited state approach validated on Kitaev models.

Contribution

It introduces a variational principle for excited states in PEPS that clarifies the relationship between correlation decay and bulk gaps in chiral topological phases.

Findings

PEPS accurately captures excitation gaps in the Kitaev model with a chiral term.

Correlation functions decaying faster than r^{-2} do not imply gapless modes.

Evidence supports the existence of a gapped chiral ground state in the $ ext{Z}_3$ Kitaev model.

Abstract

Projected entangled-pair states (PEPS) have proven effective in capturing chiral spin liquid ground states, yet the presence of long-range ``gossamer'' correlation tails raises concerns about their ability to accurately describe bulk gaps. Here, we address this challenge and demonstrate that PEPS can reliably characterize gapped bulk excitations in chiral topological phases. Using a variational principle for excited states within a local mode approximation, we establish that correlation functions decaying faster than $r^{-2}$ are not necessarily related to gapless modes and thus long-range ``gossamer'' correlation tails in chiral PEPS do not contradict the presence of a bulk gap. This framework is validated in the spin-$\frac{1}{2}$ Kitaev model with a chiral term, where PEPS yields excitation gaps that agree well with exact solutions. Extending our approach to the $\mathbb{Z}_3$ Kitaev model, we present compelling evidence for its chiral ground state and accurately resolve its gapped excitations. These findings thus solidify PEPS as a powerful tool for studying both ground and excited states in chiral topological systems, thereby bridging a key gap in the understanding of their bulk properties.