Topological and Entanglement Properties of Resonating Valence Bond wavefunctions

TL;DR

This paper explores the topological and entanglement characteristics of resonating valence bond wavefunctions using PEPS on kagome and square lattices, revealing insights into topological order, edge states, and entanglement spectra.

Contribution

It explicitly constructs minimally entangled PEPS RVB states, analyzes their topological sectors, and links boundary Hamiltonians to topological properties, advancing understanding of topological quantum spin liquids.

Findings

Identified two vanishing energy scales related to vison lines and spin freezing.

Demonstrated the boundary Hamiltonian as a product of a non-local projector and a local superfluid Hamiltonian.

Showed the entanglement spectrum reflects edge modes and explains the topological entanglement entropy.

Abstract

We examine in details the connections between topological and entanglement properties of short-range resonating valence bond (RVB) wave functions using Projected Entangled Pair States (PEPS) on kagome and square lattices on (quasi-)infinite cylinders with generalized boundary conditions (and perimeters with up to 20 lattice spacings). Making use of disconnected topological sectors in the space of dimer lattice coverings, we explicitly derive (orthogonal) "minimally entangled" PEPS RVB states. For the kagome lattice, we obtain, using the quantum Heisenberg antiferromagnet as a reference model, the finite size scaling of the energy separations between these states. In particular, we extract two separate (vanishing) energy scales corresponding (i) to insert a vison line between the two ends of the cylinder and (ii) to pull out and freeze a spin at either end. We also investigate the relations between bulk and boundary properties and show that, for a bipartition of the cylinder, the boundary Hamiltonian defined on the edge can be written as a product of a highly non-local projector with an emergent (local) su(2)-invariant one-dimensional (superfluid) t--J Hamiltonian, which arises due to the symmetry properties of the auxiliary spins at the edge. This multiplicative structure, a consequence of the disconnected topological sectors in the space of dimer lattice coverings, is characteristic of the topological nature of the states. For minimally entangled RVB states, it is shown that the entanglement spectrum, which reflects the properties of the edge modes, is a subset (half for kagome RVB) of the spectrum of the local Hamiltonian, providing e.g. a simple argument on the origin of the topological entanglement entropy S0=-ln 2 of Z2 spin liquids. We propose to use these features to probe topological phases in microscopic Hamiltonians and some results are compared to existing DMRG data.