Thermal Hall transport has emerged as a valuable tool for probing the fractionalized excitations in chiral quantum spin liquids. Observing quantized thermal Hall response, expected at temperatures below the spectral gap, has been challenging and controversial. The finite-temperature behavior, especially in the quantum critical regime above the spectral gap, can provide useful signatures of the underlying topological order. In this context, we study the spin-
1/2 Heisenberg antiferromagnet on a kagome lattice that is believed to be a
U(1) Dirac spin liquid over a wide intermediate energy range. Scalar spin chirality perturbations turn this into a gapped Abelian chiral spin liquid with semionic topological order. Using a recently developed large-
N technique [Guo et al., Phys. Rev. B 101, 195126 (2020)], we obtain explicit expressions for the thermal Hall conductivity ${\ensuremath{\kappa}}_{xy}$ at finite temperatures, taking into account both matter and gauge fluctuations. At low temperatures below the spectral gap, the quantized thermal Hall response agrees with that expected from conformal field theory and gravitational anomaly arguments. Our main finding is that in a large temperature window spanning the spectral gap and the Curie temperature scales where quantum critical fluctuations dominate, ${\ensuremath{\kappa}}_{xy}/T$ obeys a power law with logarithmic corrections. Our analysis also provides a route to understanding the thermal Hall response at higher temperatures in the quantum critical regime.
The chiral spin liquid is a canonical state of quantum spins combining topological and symmetry-breaking order, and possible experimental realizations have attracted growing interest. We examine the physics at interfaces between chiral spin liquid domains of opposite chirality. We show that a self-consistent mean-field description of spinons remains possible in the vicinity of a domain wall and use this to formulate a Ginzburg-Landau theory of the domain wall. The bulk of a chiral spin liquid contains gapped spinon excitations and gauge fluctuations, set by a finite spinon mass and a nonzero spinon Chern number. A third class of excitations consists of amplitude fluctuations of the spinon hoppings, which admit a geometric interpretation in terms of effective vielbein fields. These fluctuations are usually neglected because they are irrelevant for a homogeneous chiral spin liquid and are suppressed in standard large-[Formula: see text] treatments. Going beyond the purely topological Chern-Simons limit, we incorporate these fluctuations into an effective field theoretic framework and show that they generate momentum-dependent corrections, including Chern-Simons-like linear terms and higher-order contributions, beyond the universal topological limit. We then analyze nontopological properties, including domain wall tension and edge velocity, and explain how they modify observables relative to the uniform case. These results connect measurable, nonuniversal quantities such as domain wall width, domain wall tension, and edge velocity to microscopic parameters and provide concrete targets for experiments.
In this work we study the crystal symmetry fractionalization in chiral spin liquids with the chiral-semion topological order. We show that if such a chiral spin liquid is realized in a two-dimensional lattice model with odd number of spin-
21 per unit cell and the state preserves spin rotation symmetry and translation symmetries, the semion excitation must carry both half-integer spin and fractional crystal quantum numbers. As a result, only a unique symmetry enriched topological phase can be realized in chiral spin liquids in a spin-
21 kagome lattice model. These fractional symmetry quantum numbers are confirmed numerically using ground state wave functions obtained with the density matrix renormalization group method.
We perform an exact-diagonalization study of the spin-
21 XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization
m=32 with an emphasis on the
XY point
(Jz=0) and in the presence of a small chiral term. Recent analytic work by Kumar et al. [K. Kumar, K. Sun, and E. Fradkin, Phys. Rev. B 90, 174409 (2014)] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$. Such a state is topological in nature, has a ground-state degeneracy, and exhibits fractional excitations. We analyze the degeneracy structure in the low-energy manifold, identify the candidate topological states, and use them to compute the modular matrices and Chern numbers, all of which strongly agree with expected theoretical behavior for the ${\ensuremath{\sigma}}_{xy}=\frac{1}{2}$ CSL. In the limit of zero chirality, we find on most (not all) clusters that the topological invariants are still those of a CSL.
We present a comprehensive analytical theory of quantum spin liquids (QSLs) on the kagome lattice with Heisenberg exchange J1, next-nearest-neighbor exchange J2, Dzyaloshinskii-Moriya interaction D, and scalar spin chirality interaction λ. The work contains three principal contributions. First, we derive new mean-field analytic relations connecting the chiral interaction λ to the spinon gap, low-temperature thermodynamics, and thermal Hall response, with explicit spin-S dependence and generalization across kagome, triangular, and honeycomb lattices. The central result is Δspinon ∝ S³λ/J12 with lattice-dependent prefactors derived from self-consistent mean-field equations. Second, we derive a controlled effective model by projecting the kagome Hamiltonian onto the triangle-doublet subspace, obtaining an effective spin-chirality model on the triangular lattice with complex-valued interactions arising from the C3 symmetry of the chirality eigenstates. We compute all matrix elements of the effective spin operator in the chirality basis and characterize the inter-chirality coupling mediated by shared lattice sites. Third, we provide a rigorous map of obstructions to exact analytical solutions, systematically examining eight classes of proof techniques and identifying the precise mathematical reason each fails for the kagome Hamiltonian. The Lieb-Schultz-Mattis theorem provides the single rigorous exact result: any gapped ground state on the kagome lattice with spin-1/2 per site must exhibit topological order. All other results are classified by derivation category with explicit uncertainty quantification. AI-Generated Content Statement: This manuscript was generated primarily with the assistance of artificial intelligence language models, including ChatGPT. The work represents an exploratory demonstration of AI-assisted knowledge generation and prompt engineering methods rather than traditional experimental research.
The square-hexagon-dodecagon (SHD) lattice hosts an exactly solvable Kitaev spin liquid, while further-neighbor couplings frustrate its Heisenberg magnet into classically degenerate lines where quantum fluctuations can melt the Néel order. To place this state among the lattice's spin liquids, we classify fermionic parton mean-field states with singlet and spin-orbit-coupled triplet amplitudes by their projective symmetry groups (PSGs). As SHD sites lack site symmetry, its
Z2 PSGs are the projective classes of
p6mm with time reversal, from which those of every single-orbit
p6mm lattice follow. In the idealized Kitaev model, where lattice operations do not rotate spins, these liquids carry a single
Z2 PSG descending from the
SU(2) Lieb-flux state, and their projections are exact eigenstates. The PSG's sixfold-rotation sign, fixed by the dodecagon flux, doubles all Majorana bands, and the mirrors exclude a chiral phase in any uniform field, so only a sublattice-staggered three-spin term drives the non-Abelian Ising phase. Beyond the Kitaev state, we find a critical semi-Dirac spin liquid, with mean-field correlations
∝r−3 along three directions and
r−6 otherwise, and extended Dirac phases with up to
48 fermion flavors, among them an
Nf=12 state whose PSG forbids every singlet mass. Out-of-plane Dzyaloshinskii-Moriya couplings gap the Dirac states of its
U(1) class into a mean-field spinon counterpart of the Kane-Mele quantum spin Hall insulator, with spin Chern number
1 or
3 and spin-carrying monopoles. Chiral states imply Kalmeyer-Laughlin, semion
×semion, and three-fermion orders, rotation-breaking ones show
q→−q asymmetric neutron spectra, and sign-alternating fluxes break time reversal alone. Masses and monopoles in these many-flavor phases and the energetics of frustrated SHD Heisenberg models are natural next steps.