# Spin liquids in graphene - Condensed Matter > Strongly Correlated Electrons

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Abstract: We reveal that local interactions in graphene allow novel spin liquidsbetween the semi-metal and antiferromagnetic Mott insulating phases, identifiedwith algebraic spin liquid and Z$ {2}$ spin liquid, respectively. We argue thatthe algebraic spin liquid can be regarded as the two dimensional realization ofone dimensional spin dynamics, where antiferromagnetic correlations showexactly the same power-law dependence as valence bond correlations. Nature ofthe Z$ {2}$ spin liquid turns out to be $d + i d-$ singlet pairing, but timereversal 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 anessential feature of this gapped spin liquid state. Quantum phase transitionsamong the semi-metal, algebraic spin liquid, and Z$ {2}$ spin liquid are shownto be continuous while the transition from the Z$ {2}$ spin liquid to theantiferromagnetic Mott insulator turns out to be the first order. We emphasizethat both algebraic spin liquid and $d \pm id-$ Z$ {2}$ spin liquid can beverified by the quantum Monte Carlo simulation, showing the enhanced symmetryin the algebraic spin liquid and the quantized thermal valley Hall effect inthe Z$ {2}$ spin liquid.

Author: ** Minh-Tien Tran, Ki-Seok Kim**

Source: https://arxiv.org/