Simulating chiral spin liquids with projected entangled-pair states

TL;DR

This paper demonstrates that projected entangled-pair states (PEPS) can effectively represent chiral spin liquids with topological order, showing promising results for simulating such complex quantum phases.

Contribution

It provides the first evidence that a generic PEPS can accurately model a chiral spin liquid phase, overcoming previous doubts about PEPS representations.

Findings

Faithful PEPS representation of chiral spin liquids achieved.

Observation of a gapless chiral edge mode and short-range correlations.

Faster convergence of ground state energy with increasing bond dimension.

Abstract

Doubts have been raised on the representation of chiral spin liquids exhibiting topological order in terms of projected entangled pair states (PEPSs). Here, starting from a simple spin-1/2 chiral frustrated Heisenberg model, we show that a faithful representation of the chiral spin liquid phase is in fact possible in terms of a generic PEPS upon variational optimization. We find a perfectly chiral gapless edge mode and a rapid decay of correlation functions at short distances consistent with a bulk gap, concomitant with a gossamer long-range tail originating from a PEPS bulk-edge correspondence. For increasing bond dimension, (i) the rapid decrease of spurious features -- SU(2) symmetry breaking and long-range tails in correlations -- together with (ii) a faster convergence of the ground state energy as compared to state-of-the-art cylinder matrix-product state simulations involving far more variational parameters, prove the fundamental relevance of the PEPS ansatz for simulating systems with chiral topological order.