Projected entangled-pair states can describe chiral topological states

TL;DR

This paper demonstrates that PEPS can effectively describe chiral topological states, including those with non-trivial Chern numbers, by constructing explicit examples and analyzing their properties.

Contribution

The authors explicitly construct PEPS for chiral topological states and analyze their properties, showing they can approximate topological insulators even if not exact ground states of local Hamiltonians.

Findings

PEPS can describe chiral topological states with non-trivial Chern numbers.

Constructed PEPS are ground states of both local gapless and long-range gapped free-fermion Hamiltonians.

Numerical evidence shows PEPS can approximate topological insulators at arbitrary temperatures.

Abstract

We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We derive general conditions on topological free fermionic PEPS which show that they cannot correspond to exact ground states of gapped, local parent Hamiltonians, and provide numerical evidence demonstrating that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.