Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice

TL;DR

This paper investigates how four-spin interactions in the triangular-lattice Hubbard model lead to the stabilization of a chiral spin liquid, providing insights into its physical origin and connection to the Kalmeyer-Laughlin state.

Contribution

It demonstrates that four-spin interactions naturally arising in Mott insulators can stabilize a chiral spin-liquid state, clarifying its microscopic origin.

Findings

Four-spin interactions stabilize a chiral spin-liquid (CSL) of Kalmeyer-Laughlin type.

Numerical methods show the CSL state at relevant parameters.

Mean-field analysis links the CSL to the parent Hamiltonian of the Kalmeyer-Laughlin state.

Abstract

At strong repulsion, the triangular-lattice Hubbard model is described by $s=1/2$ spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120$^\circ$ order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that at physically relevant parameters, they stabilize a chiral spin-liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.