Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renormalization Group Study

Abstract

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.

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Plain Language Summary

A quantum spin liquid is an exotic phase of matter in which there is no magnetic ordering even at extremely low temperatures. Such a state may result from geometric frustration of antiferromagnetism: In an antiferromagnet, the magnetic moments of neighboring electrons tend to point in opposite directions, but this is impossible when the electrons are located at, for example, the vertices of a triangle. Indeed, the first experimental observation of a spin liquid, in 2003, was in a triangular lattice antiferromagnet; however, a full understanding of this system is still lacking. In this work, we use computer simulations to show that a simplified but realistic model realizes a state called a chiral spin liquid.

In a chiral spin liquid, neither heat nor electricity can be conducted through the bulk of the material, but there is a quantized heat conductance around the edge. The state is called chiral because at low temperatures the edge conduction will spontaneously go clockwise or counterclockwise and flow only in that direction. Additionally, the collective motion of electrons in the material forms so-called quasiparticles; each one, despite being formed by many electrons acting together, acts as if it were half an electron. This strange behavior, called fractionalization, is a hallmark of so-called topological phases of matter.

Our results answer a long-standing question about the nature of spin liquids in triangular lattice materials and provide the first clear demonstration of a chiral spin liquid in a model of electrons that is not intentionally biased toward such a state.