Spin liquids in graphene

TL;DR

This paper predicts novel spin liquid phases in graphene, including algebraic and Z2 spin liquids, characterized by unique correlations, pairing symmetries, and thermal Hall effects, with potential verification via quantum Monte Carlo simulations.

Contribution

It identifies and characterizes two new spin liquid states in graphene, detailing their properties, phase transitions, and experimental signatures.

Findings

Algebraic spin liquid exhibits power-law correlations similar to 1D spin dynamics.

Z2 spin liquid features d+id' singlet pairing with preserved time-reversal symmetry.

Quantized thermal valley Hall effect is proposed as a key signature.

Abstract

We reveal that local interactions in graphene allow novel spin liquids between the semi-metal and antiferromagnetic Mott insulating phases, identified with algebraic spin liquid and Z$_{2}$ spin liquid, respectively. We argue that the algebraic spin liquid can be regarded as the two dimensional realization of one dimensional spin dynamics, where antiferromagnetic correlations show exactly the same power-law dependence as valence bond correlations. Nature of the Z$_{2}$ spin liquid turns out to be $d + i d'$ singlet pairing, but time reversal symmetry is preserved, taking $d + i d'$ in one valley and $d - i d'$ in the other valley. We propose the quantized thermal valley Hall effect as an essential feature of this gapped spin liquid state. Quantum phase transitions among the semi-metal, algebraic spin liquid, and Z$_{2}$ spin liquid are shown to be continuous while the transition from the Z$_{2}$ spin liquid to the antiferromagnetic Mott insulator turns out to be the first order. We emphasize that both algebraic spin liquid and $d \pm id'$ Z$_{2}$ spin liquid can be verified by the quantum Monte Carlo simulation, showing the enhanced symmetry in the algebraic spin liquid and the quantized thermal valley Hall effect in the Z$_{2}$ spin liquid.