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Physical review. B, Condensed matter

Thermodynamic properties of the Δ-chain model in a uniform magnetic field

Hiromi Otsuka

Published Jan 1, 1995• 25 citations
Publisher

Abstract

A numerical approach for calculating an eigenvalue distribution function is developed and it is applied to the study on a fully frustrated spin system called the \ensuremath{\Delta}-chain model. We examine the magnetic-field dependence of the specific heat to clarify the relationship between the highly frustrated spins and the lower-temperature peak which has been extensively investigated by Kubo. Our numerical data show that with the increase of magnetic field, the peak width becomes broader and the height lower. This sensitive dependence should be caused by lowering the high degeneracy of states contributing to the peak formation. On the other hand, we also find that the higher-temperature peak observed commonly in antiferromagnetic quantum spin chains is almost unchanged.

DOI
10.1103/physrevb.51.305

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A numerical approach for calculating an eigenvalue distribution function is developed and it is applied to the study on a fully frustrated spin system called the \ensuremath{\Delta}-chain model. We examine the magnetic-field dependence of the specific heat to clarify the relationship between the highly frustrated spins and the lower-temperature peak which has been extensively investigated by Kubo. Our numerical data show that with the increase of magnetic field, the peak width becomes broader and the height lower. This sensitive dependence should be caused by lowering the high degeneracy of states contributing to the peak formation. On the other hand, we also find that the higher-temperature peak observed commonly in antiferromagnetic quantum spin chains is almost unchanged.
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A one-dimensional fully frustrated spin system called a \ensuremath{\Delta} chain is considered and its excited states and the specific heat are investigated. As in the Heisenberg antiferromagnet on the kagome$iaa--- lattice, the classical ground state of the system has infinite continuous degeneracies. Numerical studies of finite systems show that the low-lying excited states have an almost dispersionless spectrum near a small energy gap. As a result the specific heat exhibits a two-peak structure, one of which arises from these low-lying excited states.
The specific heat of the S = 1 transverse-crystal-field Ising model with an antiferro-magnetic exchange interaction J on a ∆-chain is studied by using the exact-diagonalization, quantum Monte Carlo and finite-temperature Lanczos methods. We find that when the strength of the transverse crystal field Γ is chosen to be sufficiently small, the specific heat exhibits a three-peak structure as a function of temperature, with peaks at T ∼ 0.05Γ, 0.2Γ and 0.7J. In addition to the two energy scales Γ and J, a new energy scale ∼ 0.1 × Γ appears due to the geometrical frustration and the existence of the Sz = 0 states in the present system. Geometrically frustrated spin systems have attracted considerable attention for a long time. It is expected that the introduction of quantum fluctuations into a clas-sically degenerate manifold leads to exotic properties of ground states and thermo-dynamics. From this point of view, S = 1/2 transverse-field Ising antiferromagnets
Thermodynamic properties of S =1 antiferromagnetic Heisenberg chains with free and periodic boundaries are investigated by means of a quantum Monte Carlo method. The specific heat is shown to have a peak at a temperature T peak ∼2Δ, where Δ is the energy gap of the present model, although global shape of the temperature dependence is very similar to the Schottky type specific heat. In open chains, due to the four-fold degeneracy of the ground state, the magnetic susceptibility shows a Curie-like divergence regardless of the number of spins. The extracted diverging part is consistent with the edge moment S =1/2.
Recently published methods used to examine the ground-state properties of the random-bond Ising chain in a uniform magnetic field are extended to describe the system at low temperatures. The entropy spikes broaden asymmetrically, and the excitation energy and specific heat become asymmetric double-peaked functions of the magnetic field with zero values between the peaks at B=2J/r for integer r. The magnetisation steps at B=2J/r are smoothed out asymmetrically. Both the ground-state and finite-temperature properties of a simple periodic frustrated Ising chain are investigated using the transfer-matrix method. The ground-state properties are similar to those of the random bond chain; the ground-state entropy, for instance, is finite for J<or=B<or=2J, with spikes at J and 2J.