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Journal of Physics Conference Series

Bound states of spinons in spatially anisotropic frustrated XXZ models in the Ising limit

Masanori Kohno

Published Mar 1, 2009• 0 citations
Publisher

Abstract

Dynamical properties of frustrated XXZ models in the Ising limit on spatially anisotropic two-dimensional lattices are investigated by a weak-coupling approach from the one-dimensional limit. Restricting the Hilbert space to that spanned by exact eigenstates of XXZ chains in the Ising limit, we calculate dynamical structure factor 5 -+ (k,ω) in spatially anisotropic two-dimensional systems. As in the case of frustrated Heisenberg models [M.Kohno, et al. , Nat. Phys. 3, 790 (2007)], spinons form bound states through hopping process between chains. We calculate the density-density correlation function of spinons in the Ising limit, and show that spinons in the bound state hop together as a pair, although those in a continuous spectrum behave almost independently. We discuss possible implications of the present results on fractionalization of bosonic and fermionic particles in spatially anisotropic frustrated systems with strong repulsion.

DOI
10.1088/1742-6596/150/4/042097

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Dynamical properties of frustrated XXZ models in the Ising limit on spatially anisotropic two-dimensional lattices are investigated by a weak-coupling approach from the one-dimensional limit. Restricting the Hilbert space to that spanned by exact eigenstates of XXZ chains in the Ising limit, we calculate dynamical structure factor 5 -+ (k,ω) in spatially anisotropic two-dimensional systems. As in the case of frustrated Heisenberg models [M.Kohno, et al. , Nat. Phys. 3, 790 (2007)], spinons form bound states through hopping process between chains. We calculate the density-density correlation function of spinons in the Ising limit, and show that spinons in the bound state hop together as a pair, although those in a continuous spectrum behave almost independently. We discuss possible implications of the present results on fractionalization of bosonic and fermionic particles in spatially anisotropic frustrated systems with strong repulsion.
We investigate spectral features of spatially anisotropic spin-1/2 frustrated antiferromagnets in a magnetic field by a weak-coupling approach from the one-dimensional (1D) limit. Using exact results of the Heisenberg chain, we calculate dynamical structure factors of spatially anisotropic frustrated antiferromagnets in two dimensions. We obtain rich peak structures depending on the momentum and the strength of magnetic fields. We identify the sharp peaks as bound and antibound states between particles carrying fractional Sz in 1D in a magnetic field, psinons and antipsinons, and those originating from 2-string solutions. We compare these spectral features with available experimental results on Cs2CuCl4, and suggest that the dynamical properties of Cs2CuCl4 in a magnetic field can be interpreted in terms of particles in 1D in a magnetic field.
We investigate spectral features of spatially anisotropic spin-1/2 frustrated antiferromagnets in a magnetic field by a weak-coupling approach from the one-dimensional (1D) limit. Using exact results of the Heisenberg chain, we calculate dynamical structure factors of spatially anisotropic frustrated antiferromagnets in two dimensions. We obtain rich peak structures depending on the momentum and the strength of magnetic fields. We identify the sharp peaks as bound and antibound states between particles carrying fractional Sz in 1D in a magnetic field, psinons and antipsinons, and those originating from 2-string solutions. We compare these spectral features with available experimental results on Cs2CuCl4, and suggest that the dynamical properties of Cs2CuCl4 in a magnetic field can be interpreted in terms of particles in 1D in a magnetic field.
Using large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at T=0T=0T=0. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.
Dynamics of one-dimensional Ising-like (strongly anisotropic) antiferromagnets is studied by the perturbation theory from the pure Ising limit and by an exact calculation for finite chains. Both calculations show that the des Cloizeaux-Gaudin (dC-G) “spin-wave” spectrum corresponds neither to a lower bound of excitation continuum nor to the peak position of the transverse response Sxx(Q, ω). A new interpretation is given of the spin-wave spectrum of CsCoCl3 without relying on the dC-G theory. It is also shown that at elevated temperatures Sxx(Q, ω) has a three-peak structure. The longitudinal response Sxx(Q, ω) at low temperatures has a weak peak at the position of spin wave peak, while with increasing temperature Sxx(Q, ω) is dominated by the central peak due to thermally activated solitons, which was predicted by Villain.
Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit, N→∞, in terms of the N spin-1/2 physical spins of the spin-1/2XXZ chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies Δ>1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin-1/2XXZ chain's continuous SUq(2) symmetry parameterized by q=Δ+Δ2-1∈]1,∞] and associated with q-spin Sq. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length n that have no spinon representation, contribute to the dynamical properties of the spin-1/2XXZ chain with anisotropy Δ>1 and for n=1,2,3 were experimentally identified and realized in the zigzag materials SrCo2V2O8 and BaCo2V2O8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous SUq(2) symmetry reveals that for anisotropy Δ>1 the Bethe strings of length n=1,2,3,… describe a number n of physical-spins Sq=0 singlet pairs that for n>1 are bound within a Sq=0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin-1/2XXZ chain in a longitudinal magnetic field and the spin chains in SrCo2V2O8 is one of the issues addressed in this paper. In addition, the SUq(2) symmetry imposes that only 2Sq out of the N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento ["Diffusive spin transport of the spin-1/2 XXZ chain in the Ising regime at zero magnetic field and finite temperature," (submitted) (2024)] concerning the vanishing of the contributions to finite-temperature ballistic spin transport at zero magnetic field. Within the physical-spins representation, this merely follows from the absolute value of the elementary spin currents carried by the M=2Sq spin carriers of all finite-Sq states that contribute to the spin stiffness being finite. Finally, we discuss deviations of the zigzag materials BaCo2V2O8 and SrCo2V2O8 from the one-dimensional physics described the spin-1/2XXZ chain due to selective interchain couplings.
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.