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Journal of Physics Condensed Matter

Chiral quantum spin liquid on the repulsive Haldane–Hubbard model in square lattices

Ya-Jie Wu, Ning Li, Jing He, Su-Peng Kou

Published Sep 13, 2017• 1 citation
Publisher

Abstract

In this paper, we present a study on the repulsive Haldane-Hubbard model with spin-rotation symmetry in square lattices by deriving non-linear σ model for magnetic states. It is found that a chiral spin liquid state as the ground state of the correlated system exists in the [Formula: see text] topological spin-density wave proposed by Wu et al (2016 J. Phys.: Condens. Matter 28 115602), of which the low energy physics can be determined by the Chern-Simons-Hopf gauge field theory.

DOI
10.1088/1361-648x/aa8c65

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In this paper, we present a study on the repulsive Haldane-Hubbard model with spin-rotation symmetry in square lattices by deriving non-linear σ model for magnetic states. It is found that a chiral spin liquid state as the ground state of the correlated system exists in the [Formula: see text] topological spin-density wave proposed by Wu et al (2016 J. Phys.: Condens. Matter 28 115602), of which the low energy physics can be determined by the Chern-Simons-Hopf gauge field theory.
Motivated by cold atom experiments on Chern insulators, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-1/2 fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing the low energy spectrum, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid (CSL) with gapped semion excitations. We formulate and study the Chern-Simons-Higgs field theory of the exotic CSL-to-tetrahedral spin crystallization transition.
In this paper, we study the non-magnetic insulator state near Mott transition of 2D pi-flux Hubbard model on square lattice and find that such non-magnetic insulator state is quantum spin liquid state with nodal fermionic excitations - nodal spin liquid (NSL). When there exists small easy-plane anisotropic energy, the ground state becomes Z2 topological spin liquid (TSL) with full gapped excitations. The U(1)times U(1) mutual--Chern-Simons (MCS) theory is obtained to describe the low energy physics of NSL and TSL.
We study 1-dimension (1-d) and 2-dimensional (2-d) quantum anti-ferromagnets. Following AKLT's theory of valent bond solid (VBS) states, we find a family of topologically nontrivial 1-d VBS states for spin systems and provide a method to construct their parent Hamiltonians. Then we generalize the fermionic representation of S = 1/2 to arbitrary spin, and find an important difference between integer spins and half-odd-integer spins. Depending on different particle number constrains we develop different versions of mean field theory for spin models. We find that the mean field with restored particle-hole symmetry can reproduce Haldane's conjecture for 1-d Heisenberg models. Applying the mean field theory to 2-d anti-ferromagnetic models, we find that S = 1 spin liquids may exist in triangle lattice. Comparing with the experimental results of NiGa2S4, we argue that the antiferro-nematic f-wave spin liquid is a possible ground state. On the other hand, to check whether the material ZnCu3(OH)6Cl2 is really an U(1) Dirac spin liquid, we derive the Raman scattering operators of different symmetry channels for Hubbard model on Kagome lattice. Then we numerically calculate the Raman cross-section according to the mean field spin liquid state. The low energy continuum part of our results qualitatively match the experimental data.
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.
We revisit the challenging problem of identifying the quantum spin liquid candidate in the spin-1/2 J1J_1J1​-J2J_2J2​ Heisenberg antiferromagnet on the square lattice. By integrating the Gutzwiller-guided density matrix renormalization group method with analytical analyses, we present clear evidence that the ground state is a Z2_22​ Dirac spin liquid. This state can be efficiently described by a Gutzwiller-projected parton theory characterized by its projective symmetry group. To distinguish the difference between the projected Z2_22​ and U(1) parton state, we investigate the chiral spin liquid ground states as topological orders by incorporating a JχJ_χJχ​ term into the J1J_1J1​-J2J_2J2​ model and observe a transition from a Z2_22​ chiral spin liquid to a U(1)2_22​ chiral spin liquid as JχJ_χJχ​ increases.
We study the ground-state phase diagram of the half-filled extended Haldane-Hubbard model on the honeycomb lattice with sublattice-dependent on-site repulsion (UA/B{U}_{\text{A/B}}UA/B​) using the exact diagonalization (ED) and mean-field (MF) methods. The resulting phase diagram shows that there is a topologically nontrivial phase with the Chern number C=1C=1C=1, emerging via the development of the imbalance between UA{U}_{\text{A}}UA​ and UB{U}_{\text{B}}UB​. In this phase, the antiferromagnetic correlations are observed in the ED calculation, in line with the finite antiferromagnetic order obtained by the MF method. The spontaneous symmetry breaking of SU(2) spin rotation in the phase is also identified in the MF level. Distinct from previous studies in which the exotic C=1C=1C=1 phase relies on the interplay between sublattice-dependent potentials and electronic interactions, our paper presents an alternative way by solely tuning the on-site interactions.