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Physical review. B, Condensed matter

Excited states and the thermodynamics of a fully frustrated quantum spin chain

Kenn Kubo

Published Oct 1, 1993• 61 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.48.10552

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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.
A one-dimensional fully frustrated quantum spin system called the Δ -chain is investigated, particularly with respect to the low-temperature structure of the specific heat, by quantum Monte Carlo simulations using the restructuring method. Sizes of the systems we considered are N =32,48 and 64. The simulation results together with the diagonalization results for N =10 and 16 show that the size dependence of the data is very weak, and thus the second peak of the specific heat stably exists at T <0.1, which corresponds to less than half the spin gap. Locality of excitations is seen in the Monte Carlo snapshot. We consider that the low-temperature properties of this system are governed by the local elementary excitations which generate the Schottky-type specific heat peak in the background of the ordinary thermal specific heat.
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.
The one-dimensional spin-1 Heisenberg antiferromagnetic chains are studied by a generalized two-time Green's-function method at finite temperature. 〈Siz{\mathit{S}}_{\mathit{i}}^{\mathit{z}}Siz​〉 is set to zero at each site to guarantee the lack of the long-range order in the one-dimensional Heisenberg system. The Green's functions are decoupled in terms of the correlation functions of spin operators. A set of self-consistent equations of the correlation functions are derived and solved numerically. Correlation functions of spin operators, thermodynamic properties such as the internal energy, and specific heat in the entire temperature region are obtained. The Haldane gap in the excitation spectrum appears naturally in the analytical result. When k is zero, there is a gap 2\ensuremath{\Delta}, which is 1.0J and close to the theoretical result of White and Huse. And there is a broad maximum in the temperature dependence of the specific heat. The properties of the thermodynamic quantities are consistent with the numerical results on the finite chains. \textcopyright{} 1996 The American Physical Society.
We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.
We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a kagom\'e-strip chain (KSC), a one-dimensional analog of the kagom\'e lattice, and construct its phase diagram in an extended exchange-parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-3/23/23/2 state as well as spin-1/21/21/2 states with and without additional degeneracies. We explore the ground-state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.
We investigate the quantum phases of a frustrated antiferromagnetic Heisenberg spin-1/2 model Hamiltonian on a Kagome-strip chain (KSC), a one-dimensional analogue of the Kagome lattice, and construct its phase diagram in an extended exchange parameter space. The isolated unit cell of this lattice comprises of five spin-1/2 particles, giving rise to several types of magnetic ground states in a unit cell: a spin-3/23/23/2 state as well as spin-1/21/21/2 states with and without additional degeneracies. We explore the ground state properties of the fully connected thermodynamic system using exact diagonalization and density matrix renormalization group methods, identifying several distinct quantum phases. All but one of the phases exhibit gapless spin excitations. The exception is a dimerized spin-gapped phase that covers a large part of the phase diagram and includes the uniformly exchange coupled system. We argue that this phase can be understood by perturbing around the limit of decoupled unit cells where each unit cell has six degenerate ground states. We use degenerate perturbation theory to obtain an effective Hamiltonian, a Kugel-Khomskii model with an anisotropic spin-one orbital degree of freedom, which helps explain the origin of dimerization.