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arXiv:1711.03679 · Physical Review Letters

Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice

Yan-Cheng Wang, Xue‐Feng Zhang, Frank Pollmann, Meng Cheng, Zi Yang Meng

Published Aug 2, 2018• 42 citations
arXivHTMLPDF

Abstract

Employing large-scale quantum Monte Carlo simulations, we study the extended XXZ model on the kagome lattice. A Z_{2} quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid, and ferromagnet. This Z_{2} spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the transition between the stripe solid and ferromagnet. However, the transition between a spin liquid and ferromagnet is found to be continuous and belongs to the 3D XY^{*} universality class associated with the condensation of spinons. The transition between a spin liquid and stripe solid appears to be continuous and associated with the condensation of visons.

DOI
10.1103/physrevlett.121.057202

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Employing large-scale quantum Monte Carlo simulations, we study the extended XXZ model on the kagome lattice. A Z_{2} quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid, and ferromagnet. This Z_{2} spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the transition between the stripe solid and ferromagnet. However, the transition between a spin liquid and ferromagnet is found to be continuous and belongs to the 3D XY^{*} universality class associated with the condensation of spinons. The transition between a spin liquid and stripe solid appears to be continuous and associated with the condensation of visons.
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Quantum spin liquids are exotic many-body states featured with long-range entanglement and fractional anyon quasiparticles. Quantum phase transitions of spin liquids are particularly interesting problems related with novel phenomena of anyon condensation and anyon confinement. Here we study a quantum dimer model, which implements a transition between a Z 2 spin liquid ( Z 2 SL ) and a valence bond solid (VBS) on the kagome lattice. The transition is driven by the condensation of vison excitation of the Z 2 spin liquid, which impacts on other anyon excitations especially leading to the confinement of spinon excitations. By numerical exact diagonalization of the dimer model, we directly measure the vison condensation using vison string operators, and explicitly check a confining potential acting on spinon excitations in the VBS state. It is observed that topological degeneracy of the spin-liquid state is lifted concomitantly with the vison condensation. The dimer ordering pattern of the VBS state is identified by investigating dimer structure factor. Furthermore, we find an interesting state that exhibits features of spin liquid and VBS simultaneously. We discuss the origin of the mixed behaviors and possible scenarios expected in thermodynamic limit. This work complements the previous analytical studies on the dimer model [ and ] by providing numerical evidences on the vison condensation and the spinon confinement in the Z 2 SL -to-VBS transition. Published by the American Physical Society 2024
We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2 XYXYXY model (JJJ) with a four-site ring-exchange interaction (KKK) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ring exchange, undergoes a direct transition to a Z2{\mathbb{Z}}_{2}Z2​ quantum spin liquid phase at ${(K/J)}_{c}\ensuremath{\approx}22$, which is related to the phase proposed by L. Balents, M. P. A. Fisher, and S. M. Girvin [Phys. Rev. B 65, 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents zzz and $\ensuremath{\nu}$ falling in the three-dimensional XYXYXY universality class, making it a candidate for an exotic XYXYXY* quantum critical point, mediated by the condensation of bosonic spinons.
Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice spin-1/2 model, which is known to harbor an extended Z_{2} quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the Z_{2} quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.
We investigate the properties in finite magnetic field of an extended anisotropic XXZXXZXXZ spin-1/2 model on the kagome lattice, originally introduced by Balents, Fisher, and Girvin [Phys. Rev. B 65, 224412 (2002)]. The magnetization curve displays plateaus at magnetization m=1/6m=1/6m=1/6 and 1/31/31/3 when the anisotropy is large. Using low-energy effective constrained models (quantum loop and quantum dimer models), we discuss the nature of the plateau phases, found to be crystals that break discrete rotation and/or translation symmetries. Large-scale quantum Monte Carlo simulations were carried out in particular for the m=1/6m=1/6m=1/6 plateau. We first map out the phase diagram of the effective quantum loop model with an additional loop-loop interaction to find stripe order around the point relevant for the original model as well as a topological Z2{\mathbb{Z}}_{2}Z2​ spin liquid. The existence of a stripe crystalline phase is further evidenced by measuring both standard structure factor and entanglement entropy of the original microscopic model.
We study the quantum-spin-liquid phase in a variant of the Kitaev model where the bonds of the honeycomb lattice are distributed in a Kekul\'e pattern. The system supports gapped and gapless Z2{Z}_{2}Z2​ quantum spin liquids with interesting differences from the original Kitaev model, the most notable being a gapped Z2{Z}_{2}Z2​ spin liquid on a kagome lattice. Perturbing the exactly solvable model with antiferromagnetic Heisenberg perturbations, we find a magnetically ordered phase stabilized by a quantum ``order by disorder'' mechanism, as well as an exotic continuous quantum phase transition between the topological spin liquid and this magnetically ordered phase. Using a combination of field theory and Monte Carlo simulations, we find that the transition likely belongs to the $3D\text{\ensuremath{-}}XY\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ universality class.