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Journal of the Physical Society of Japan

Chirality and Flux in Two-Dimensional Spin-1/2 Antiferromagnets –Exact Diagonalization Study–

Masatoshi Imada

Published Aug 15, 1989• 26 citations
Publisher

Abstract

The possibility of chiral symmetry breaking in quantum spin systems is examined by the extrapolation of exactly diagonalized results on finite lattices in the ground state. Both on the triangular and the square lattice, linear dependence of squared chirality on the inverse linear size in the free boundary condition strongly suggests that the correlation of chirality defined by S 1 ·( S 2 × S 3 ) is short-ranged in the thermodynamic limit, which also leads to the absence of the flux state.

DOI
10.1143/jpsj.58.2650

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The possibility of chiral symmetry breaking in quantum spin systems is examined by the extrapolation of exactly diagonalized results on finite lattices in the ground state. Both on the triangular and the square lattice, linear dependence of squared chirality on the inverse linear size in the free boundary condition strongly suggests that the correlation of chirality defined by S 1 ·( S 2 × S 3 ) is short-ranged in the thermodynamic limit, which also leads to the absence of the flux state.
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The ground-state properties of the periodic Anderson model on one-dimensional chains from three to six sites are studied by exact diagonalization. An appropriate average over boundary conditions is found to be necessary in order to eliminate finite-size oscillations. In the weak-coupling limit, the results for the short-range correlations suggest a smooth transition from a ferromagnetic state at low electron concentration to an antiferromagnetic state at half-filling, rather than a sudden jump at a critical concentration.
We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1
We consider the low-energy spectrum of spin-12\frac{1}{2}21​ two-dimensional triangular lattice models subject to a ferromagnetic Heisenberg interaction and a three spin chiral interaction of variable strength. Initially, we consider quasi-one-dimensional ladder systems of various geometries. Analytical results are derived that yield the behavior of the ground states, their energies, and the transition points. The entanglement properties of the ground state of these models are examined and we find that the entanglement depends on the lattice geometry due to frustration effects. To this end, the chirality of a given quantum state is used as a witness of tripartite entanglement. Finally, the two-dimensional model is investigated numerically by means of exact diagonalization and indications are presented that the low energy sector is a chiral spin liquid.
We have studied the pseudoscalar chiral long-range order, based on the local operator ${\mathrm{\ensuremath{\chi}}}_{\mathrm{\ensuremath{\psi}}}$=S1{\mathbf{S}}_{1}S1​\ensuremath{\cdot}(S2{\mathbf{S}}_{2}S2​\ifmmode\times\else\texttimes\fi{}S3{\mathbf{S}}_{3}S3​), of the S=1/2 XY antiferromagnet on the triangular lattice. At finite temperature the chirality has been studied via a seventh-order high temperature series expansion of the square of the fluctuation in the pseudoscalar chiral long-range order. An exact diagonalization study on small finite lattices has been used to investigate the chirality long-range order parameter at T=0. While Pad\'e approximant analysis of the series suggests the possibility of a finite-temperature phase transition to a low temperature phase with pseudoscalar chiral long-range order, exact diagonalization results indicate that no such order exists at zero temperature.
Recent advances in moiré engineering motivate the study of lattice models of strongly-correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120∘^\circ∘ antiferromagnetic phases. We use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.