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Journal of the Physical Society of Japan

Direct Calculation of Dynamical Susceptibility in Strongly Fluctuating Quantum Spin Systems

Seiji Miyashita, Taro Yoshino, Akira Ogasahara

Published Feb 15, 1999• 43 citations
Publisher

Abstract

We propose a direct numerical method to calculate the dynamical susceptibility, χ''(ω), in strongly fluctuating quantum systems, where the system is nonmagnetic but the exchange effect is very strong. We demonstrate this method by calculating ESR line shape χ''(ω) of the one dimensional antiferromagnetic Heisenberg model ( S =1/2) and comparing the results with those obtained by other methods and experiments.

DOI
10.1143/jpsj.68.655

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We propose a direct numerical method to calculate the dynamical susceptibility, χ''(ω), in strongly fluctuating quantum systems, where the system is nonmagnetic but the exchange effect is very strong. We demonstrate this method by calculating ESR line shape χ''(ω) of the one dimensional antiferromagnetic Heisenberg model ( S =1/2) and comparing the results with those obtained by other methods and experiments.
The field and temperature dependence of the line shape of ESR for strongly interacting quantum spin systems would provide various important informations for the magnetic interaction. We have introduced a method of direct numerical estimation of the dynamical susceptibility with the Kubo formula and applied it to spin systems of various lattice structures. There the ESR line shape shows significant dependence on the strength of the field, and also on the geometrical situation among the directions of the fields and lattice axes.
(1) The wave number dependence of the static spin susceptibility χ( q ) and (2) the effective interaction between quasiparticles mediated by spin fluctuations in the dilute two dimensional Hubbard model are investigated. The quantum Monte Carlo method (QMC) and the fluctuation exchange approximation (FLEX) are applied to this model. It is found that a maximum at wave number q =0 emerges and develops in χ( q ) as the interaction U gets strong. It is also found that the most attractive component of the effective interaction mediated by spin fluctuations is the p -wave component in the strong coupling region where a maximum at q =0 devolops in χ( q ).
(1) The wave number dependence of the static spin susceptibility χ( q ) and (2) the effective interaction between quasiparticles mediated by spin fluctuations in the dilute two dimensional Hubbard model are investigated. The quantum Monte Carlo method (QMC) and the fluctuation exchange approximation (FLEX) are applied to this model. It is found that a maximum at wave number q =0 emerges and develops in χ( q ) as the interaction U gets strong. It is also found that the most attractive component of the effective interaction mediated by spin fluctuations is the p -wave component in the strong coupling region where a maximum at q =0 devolops in χ( q ).
Dynamical spin correlation functions in (q, omega )-space are calculated numerically for linear quantum-mechanical Heisenberg systems containing up to ten spins with s= 1 / 2 and s=1. The authors consider ferro- and antiferromagnets including single-site and exchange anisotropies. They compare their results with various other theoretical treatments and draw conclusions for the dynamics of infinite chains. In the case of the s=1 planar Heisenberg ferromagnet direct comparison is made with inelastic neutron scattering cross sections of CsNiF 3 . The theoretical and experimental results are in good agreement.
We develop a simple and unbiased numerical method to obtain the uniform susceptibility of quantum many-body systems. When a Hamiltonian is spatially deformed by multiplying it with a sine-square function that smoothly decreases from the system center toward the edges, the size-scaling law of the excitation energy is drastically transformed to a rapidly converging one. Then, the local magnetization at the system center becomes nearly size independent; the one obtained for the deformed Hamiltonian of a system length as small as $L\ensuremath{\sim}10$ provides the value obtained for the original uniform Hamiltonian of $L\ensuremath{\sim}100$. This allows us to evaluate a bulk magnetic susceptibility by using the magnetization at the center by existing numerical solvers without any approximation, parameter tuning, or size-scaling analysis. We demonstrate that the susceptibilities of the spin-1/2 antiferromagnetic Heisenberg chain and square lattice obtained by our scheme at $L\ensuremath{\sim}10$ agree within ${10}^{\ensuremath{-}3}$ with exact analytical and numerical solutions for $L=\ensuremath{\infty}$ down to temperatures of 0.1 times the coupling constant. We apply this method to the spin-1/2 kagome lattice Heisenberg antiferromagnet which is of prime interest in the search for spin liquids.