We numerically study Heisenberg models on modified triangular lattices, and show that a weak nextnearest-neighbor exchange interaction added to a simple triangular lattice, namely, the equilateral triangular lattice with only the nearest-neighbor exchange is sufficient to stabilize a quantum spin liquid against the antiferromagnetic order widely accepted as the ground state of the simple triangular model. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic and spin-liquid phases as well as inside the spin-liquid phase, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents z + η ∼ 1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.KEYWORDS: triangular lattice, next nearest neighbor interaction, J1-J2 Heisenberg model, many-variable variational Monte Carlo method, gapless quantum spin liquid, spin gap, spinon Fermi surface
The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearestneighbor sites, J 1 , and those between next-nearest-neighbor sites, J 2 . We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra.We obtain the nonmagnetic phase in the region 0.4 < J 2 /J 1 ≤ 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J 2 /J 1 ≤ 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J 2 /J 1 ≤ 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C 4v symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation S(0)S(r) ∝ 1/r z+η at a long distance r appears to increase from z + η ∼ 1 at J 2 /J 1 ∼ 0.4 toward the continuous transition to the VBC phase at J 1 /J 1 ∼ 0.5. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality. *
Recent discovery of the half-quantized thermal Hall conductivity in α-RuCl3, a candidate material for the Kitaev spin liquid, suggests the presence of a highly-entangled quantum state in external magnetic fields. This field-induced phase appears between the low-field zig-zag magnetic order and the high-field polarized state. Motivated by this experiment, we study possible field-induced quantum phases in theoretical models of the Kitaev magnets, using the two-dimensional tensor network approach or infinite tensor product states (iTPS). More specifically, we map out the magnetic-field phase diagram of the K-Γ-Γ model, where K is the ferromagnetic Kitaev interaction and Γ, Γ are additional bond-dependent anisotropic interactions between spin-1/2 moments. We find various novel quantum ground states in addition to the chiral Kitaev spin liquid occupying a small area in the phase diagram. They form a band of emergent quantum phases in an intermediate window of external magnetic fields, somewhat reminiscent of the experiment. We discuss the implications of these results in view of the experiment and previous theoretical studies. arXiv:1908.07671v1 [cond-mat.str-el]
There has been a great interest in magnetic field induced quantum spin liquids in Kitaev magnets after the discovery of neutron scattering continuum and half-quantized thermal Hall conductivity in the material α-RuCl 3. In this work, we provide a semiclassical analysis of the relevant theoretical models, which enable us to treat large system sizes approximating the thermodynamic limit. We find a series of competing magnetic orders with fairly large unit cells at intermediate magnetic fields, which are mostly missed by previous studies. We show that quantum fluctuations are typically strong in these large unit cell orders, while the magnetic excitations, magnons, have a dispersion that resembles a scattering continuum. The huge quantity of magnon bands with finite Chern numbers also gives rise to an unusually large thermal Hall conductivity. Given the highly frustrated nature of the spin model, the large unit cell orders are likely to melt into the putative spin liquid in the quantum limit. Our work provides an important basis for a thorough investigation of emergent spin liquids and competing phases in Kitaev magnets.
We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the language of tensor network (TN). Without introducing Majorana fermion, most of the features of the KSL including the symmetries, gauge structure, criticality and vortex-freeness are explained in a compact TN representation. Our construction reveals a hidden string gas structure of the KSL. With only two variational parameters to adjust, we obtain an accurate KSL ansatz with the bond dimension D = 8 in a compact form, where the energy is about 0.007% higher than the exact one. arXiv:1901.05786v3 [cond-mat.str-el]
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.