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arXiv:2306.16466 · Physical review. B./Physical review. B

Chiral spin liquid phase in an optical lattice at mean-field level

Jian Yang, Xiong-Jun Liu

Published Apr 2, 2024• 3 citations
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Abstract

We study an optical Raman square lattice with $\mathrm{U}(1)$ synthetic gauge flux to show a chiral spin liquid (CSL) phase for cold atoms based on slave-rotor and spinon mean-field theories, respectively. An effective U(1) gauge flux generated by Raman potentials plays a major role in realizing the CSL phase. By using slave-rotor techniques we find the CSL phase at a strong on-site Fermi Hubbard interacting regime. For large value of Hubbard interaction, we derive an effective spin model including up to the four spin interactions. By spinon mean-field analysis it is shown that the CSL phase is stabilized in the case of strong magnetic frustration. Two mean-field approximation methods give consistent phase diagrams and provide qualitative numerical evidence of the CSL phase.

DOI
10.1103/physrevb.109.165108

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A chiral spin liquid (CSL) is an analog of the fractional quantum Hall state in spin systems. Recently, an interesting topic has been the coexistence of CSL and magnetic order, which is beyond the conventional understanding of the spin liquid. Here, the authors examine possible phase coexistence in the spin-\textonehalf{} square-lattice J1{J}_{1}J1​-J2{J}_{2}J2​-${J}_{\ensuremath{\chi}}$ model, by using unbiased density matrix renormalization group calculations. The numerical data identify the CSL but find no evidence for the phase coexistence that was conjectured by mean-field calculations.
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° 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 a 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.
Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-1/2 fermions. A slave rotor mean field theory suggests the appearance of gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-1/2 bosons.
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