In this paper we study the ground-state properties of a ladder Hamiltonian with chiral
SU(2)-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of
SU(2) symmetry in tensor network algorithms, specifically for infinite density matrix renormalization group. After a preliminary analysis with Kadanoff coarse graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agreement with our numerical findings. In particular, the scaling of the entanglement entropy as well as finite-entanglement scaling data show that the ground-state properties match those of the universality class of a
c=1 conformal field theory (CFT) in
(1+1) dimensions. We also study the algebraic decay of spin-spin and dimer-dimer correlation functions, as well as the algebraic convergence of the ground-state energy with the bond dimension, and the entanglement spectrum of half an infinite chain. Our results for the entanglement spectrum are remarkably similar to those of the spin-
21 Heisenberg chain, which we take as a strong indication that both systems are described by the same CFT at low energies, i.e., an
SU(2)1 Wess-Zumino-Witten theory. Moreover, we explain in detail how to construct matrix product operators for
SU(2)-invariant three-spin interactions, something that had not been addressed with sufficient depth in the literature.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground-state degeneracy on the torus signaling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field-theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.
We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground state degeneracy on the torus signalling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.
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.
Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.
The triangular-lattice Fermi-Hubbard model has been extensively investigated in the literature due to its connection to chiral spin states and unconventional superconductivity. Previous simulations of the ground state of the doped system rely on quasi-one-dimensional lattices where true long-range order is forbidden. Here we simulate two-dimensional and quasi-one-dimensional triangular lattices using state-of-the-art Auxiliary-Field Quantum Monte Carlo. Upon doping a non-magnetic chiral spin state, we observe evidence of chiral superconductivity supported by long-range order in Cooper-pair correlation and a finite value of the chiral order parameter. With this aim, we first locate the transition from the metallic to the non-magnetic insulating phase and the onset of magnetic order. Our results pave the way towards a better understanding of strongly correlated lattice systems with magnetic frustration.