Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model

TL;DR

This study uses large-scale DMRG simulations on the kagome Heisenberg model to identify signatures of a gapless Dirac spin liquid, including Dirac cones in the excitation spectrum and a very small spin gap.

Contribution

It provides strong numerical evidence for a U(1) Dirac spin liquid ground state in the kagome Heisenberg model, highlighting the presence of Dirac cones and a smaller spin gap than previously estimated.

Findings

Identification of Dirac cones in the excitation spectrum

Demonstration of a very small spin gap via flux insertion

Evidence supporting a U(1) Dirac spin liquid ground state

Abstract

The antiferromagnetic spin-$1/2$ Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large scale density matrix normalization group simulations (DMRG) on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a $\pi$-flux free fermion model (the parton mean-field ansatz of a $U(1)$ Dirac spin liquid)