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Modern Physics Letters B

ENERGY GAP IN HEISENBERG ANTIFERROMAGNETIC HALF-INTEGER SPIN CHAINS WITH LONG-RANGE INTERACTIONS

J. Rodrigo Parreira, Oscar Bolina, J. FERNANDO PEREZ

Published Jan 20, 1996• 2 citations
Publisher

Abstract

We show that there is no gap in the excitation spectrum of antiferromagnetic chains with half-integer spins and long-range interactions provided the exchange function has a sufficiently rapid decay.
DOI
10.1142/s0217984996000080

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We present evidence for the absence of a gap in a class of S = 1 antiferromagnetic exchange models. The spin exchange is long ranged, of the type where . We have shown previously that without the alternating factor the model for (the S = 1 Haldane - Shastry model) has a gap, exponentially decaying correlation functions and exponentially small susceptibility at very low temperatures. In the case of the alternating interaction the stabilizing next-nearest-neighbour ferromagnetic interaction changes the behaviour of the system qualitatively. We have studied the ground state and first excited state using a modified Lanczos algorithm for system sizes up to 16 sites. Also, we performed exact diagonalization for systems up to 8 sites and obtained the thermodynamics. The correlation functions decay with distance like a power law. These models define a new class of integer spin chains that do not show a Haldane gap. The results may be relevant for describing impurity spins coupled by a RKKY interaction through a half-filled conduction electron band.
According to Haldane’s conjecture, there is a spin gap of the excitation spectrum in integer Heisenberg spin chains whereas half-integer spin chains have a gapless excitation spectrum. In an earlier publication (Hung and Gong 2005 Phys. Rev. B 71 054413), the Haldane gap and other properties of the spin-1 system are explained using a spin-1/2 alternating bond chain model. The ferromagnetic–ferromagnetic–antiferromagnetic Heisenberg spin-1/2 chain is expected to behave similarly to the uniform spin-3/2 Heisenberg chain for strong ferromagnetic coupling. And the general nonuniform spin-1/2 chain may be used to explain the properties of the integer and half-integer high spin- S chains, consistently. In this paper, we provide a detailed numerical verification for the above problems.
Integer-spin Heisenberg antiferromagnetic chains are expected to have a singlet groundstate and a gap to the first excited state, as first argued by Haldane. We review rigorous results on this conjecture and discuss experimental realizations. Theoretical and experimental aspects of three recent developments in this field are then reviewed: chainend excitations and the non-local order parameter, a field theory mapping and behavior near zero wave-vector, high-field behavior and one-dimensional Bose condensation.
Ground state properties of finite anisotropic antiferromagnetic Heisenberg chains are studied for odd half-integer spins S= 1 / 2 , 3 / 2 ... as well as integer spins S=1, 2 .... Finite size scaling analysis of the results clearly distinguishes the half-integer (S= 1 / 2 , 3 / 2 ) from the integer (S=1) spin situation. It gives strong support to a recent conjecture which postulates that the T=0 phase structure is very different in the two cases. According to this idea there exists a new phase between the planar and the antiferromagnetic region, for integer spins only. This phase, which includes the isotropic point, has a finite energy gap and no long range order.
The double chain Heisenberg antiferromagnet with anisotropy is studied using the mapping onto the coupled anisotropic nonlinear σ model. This model consists of two anisotropic antiferromagnetic quantum Heisenberg chains with half-integer spin coupled with each other via the ferromagnetic interchain coupling J '. For small J ', our analysis suggests that J ' is an irrelevant parameter and consequently the two chains behave independently and no gap is generated. On the other hand, for large enough J ', the two chains behave as a single Heisenberg chain with integer spin which has a gap in the excitation spectrum. The expected behavior in the isotropic limit is also discussed.