Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice

TL;DR

This paper develops a symmetric PEPS numerical method to study the ground state of the kagome antiferromagnetic Heisenberg model, providing evidence for a U(1) Dirac spin liquid over a Z2 spin liquid.

Contribution

It introduces a symmetric PEPS approach applicable to 2D strongly correlated systems and applies it to clarify the nature of the kagome Heisenberg model's ground state.

Findings

Ground state is consistent with a U(1) Dirac spin liquid.

Method applicable to strongly correlated 2D systems.

Supports the absence of Z2 topological order in this model.

Abstract

The properties of ground state of spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and $Z_2$ topological order leads to different types of $Z_2$ spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a $U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.