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Spin correlations and impurities in one-dimensional gapped spin systems

Guangyong Xu

Published May 1, 2000• 0 citations
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We consider the one-dimensional gas of electrons interacting via an attractive δ-function potential. The attractive potential leads to the formation of Cooper-pair-like bound states with a spin gap. Without destroying the integrability, we introduce a finite concentration of mixed-valence impurities with two magnetic configurations of spin S and S + {{1}/{2}}, which hybridize with the conduction states of the host. We derive the Bethe ansatz equations diagonalizing the system for the correlated host with impurities and discuss the ground-state properties as functions of the concentration of impurities and the Kondo coupling. For a sufficiently large density of electrons the spin gap is reduced by the impurities and is closed at a critical concentration which depends on the impurity spin and the coupling strength. A ferromagnetic phase of unpaired spin-polarized itinerant electrons is induced for impurity concentrations larger than the critical one. The critical behaviour of the correlation functions is studied in the gapped and gapless regions using the mesoscopic energy spectrum and conformal field theory.
In spin‐gapped quasi‐one‐dimensional antiferromagnets that do not show phase transitions down to zero temperature, impurities cause phase transitions by inducing local magnetic moments around them between which long‐range correlation is mediated by weak interchain couplings. We investigate the difference between the effects of non‐magnetic impurities and those of spin‐1/2 magnetic ones in the impurity‐induced transition temperatures and the staggered magnetization in the impurity‐induced ordered phase by the quantum Monte Carlo method. We find that the staggered correlation induced by spin‐1/2 impurities grows slower than that done by non‐magnetic ones as the system is cooled and approaches the ground state, while the transition temperature induced by the former is higher than that done by the latter. We argue that this is one of the characteristic aspects of the order‐by‐disorder phenomena in quantum systems.