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CRC Press eBooks

Magnetic properties of quasi-one-dimensional strongly correlated systems

Pierre Pujol

Published Nov 30, 2003• 0 citations
Publisher

Abstract

The present article contains a brief review of theoretical work on magnetization properties of strongly correlated systems in 1 D. We will focus on the study of the magnetization curves of quantum spin chains and ladders, and generalizations such as the presence of charge carriers or impurities. W⅛ show that plateaux appear in these curves and give the conditions under which such plateaux are expected to appear.

DOI
10.1201/9781482269079-55

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The present article contains a brief review of theoretical work on magnetization properties of strongly correlated systems in 1 D. We will focus on the study of the magnetization curves of quantum spin chains and ladders, and generalizations such as the presence of charge carriers or impurities. W⅛ show that plateaux appear in these curves and give the conditions under which such plateaux are expected to appear.
We investigate the magnetic properties of quasi-one-dimensional quantum spin-SSS antiferromagnets. We use a combination of analytical and numerical techniques to study the presence of plateaux in the magnetization curve. The analytical technique consists in a path integral formulation in terms of coherent states. This technique can be extended to the presence of doping and has the advantage of a much better control for large spins than the usual bosonization technique. We discuss the appearance of doping-dependent plateaux in the magnetization curves for spin-SSS chains and ladders. The analytical results are complemented by a density matrix renormalization group (DMRG) study for a trimerized spin-1/21/21/2 and anisotropic spin-3/23/23/2 doped chains.
We report results of theoretical investigations on the effect of doping and quenched disorder on the occurrence of plateaux in the magnetization curve of 1D systems with periodic modulations in the couplings.For single q-merized Hubbard chains, doping is shown to affect the position at which plateaux appear, leading to the emergence of plateaux at irrational values of the magnetization.For random bond antiferromagnetic Heisenberg chains with periodically modulated bond distributions, disorder generically removes the plateau structure, except in the case of discrete probability distributions.In the latter case, wide plateaux emerge at values of the magnetization dependent on the strength of disorder.
We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.
In this paper we continue and extend a systematic study of plateaux in magnetization curves of antiferromagnetic Heisenberg spin-1/2 ladders. We first review a bosonic field-theoretical formulation of a single XXZ\mathrm{XXZ}XXZ chain in the presence of a magnetic field, which is then used for an Abelian bosonization analysis of NNN weakly coupled chains. Predictions for the universality classes of the phase transitions at the plateaux boundaries are obtained in addition to a quantization condition for the value of the magnetization on a plateau. These results are complemented by and checked against strong-coupling expansions. Finally, we analyze the strong-coupling effective Hamiltonian for an odd number NNN of cylindrically coupled chains numerically. For N=3N=3N=3 we explicitly observe a spin gap with a massive spinon-type fundamental excitation and obtain indications that this gap probably survives the limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing U/tU/tU/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U/tU/tU/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.