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Annalen der Physik

Quantum spin chains with various defects

C. Schuster, Ulrich Eckern

Published Dec 1, 2002• 2 citations
Publisher

Abstract

Abstract Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one‐dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation‐invariant system a so‐called site‐impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so‐called bond‐impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site‐impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond‐impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.

DOI
10.1002/andp.20025141203

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Quantum spin chains with various defects

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Ground state properties of disordered and dimerized spin chains

C. Schuster, Ulrich Eckern

Concerning the question of the (spin-)Peierls mechanism in the presence of disorder we present a detailed analysis of the ground state phase diagram of the dimerized anisotropic Heisenberg-XXZ chain containing one impurity. It is obtained by studying the destruction of the quantum coherence by the perturbations. The stability of the Peierls phase, i. e. the occurence of a stable dimerization, is determined by the energy gain and gap due to the coupling to the static phonons. The extension of the paramagnetic phase, found already in the clean dimerized chain, grows by adding the impurity, because the distortions weaken each other. The Peierls phase is reduced for two reasons: First, the energy gain of the spin-system decreases, which leads to a smaller stable dimerization and second, the energy gap itself is reduced.

Annalen der Physik•Nov 1, 1999•2 citations
Abstract Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one‐dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation‐invariant system a so‐called site‐impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so‐called bond‐impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site‐impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond‐impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.
Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one-dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation-invariant system a so-called site-impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so-called bond-impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site-impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond-impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.
Using the density-matrix renormalization-group algorithm, we study the model of spinless fermions with nearest-neighbor interaction on a ring in the presence of disorder. We determine the spatial decay of the density induced by a defect (Friedel oscillations), and the phase sensitivity of the ground-state energy \ensuremath{\Delta}E=(-)N{)}^{\mathit{N}})N[E(\ensuremath{\varphi}=0)-E(\ensuremath{\varphi}=\ensuremath{\pi})], where \ensuremath{\varphi}=2\ensuremath{\pi}\ensuremath{\Phi}/${\mathrm{\ensuremath{\Phi}}}_{0}$ (N is the number of fermions, \ensuremath{\Phi} the magnetic flux, and ${\mathrm{\ensuremath{\Phi}}}_{0}$=h/e the flux quantum), for a disordered system versus the system size M. The quantity ln(M\ensuremath{\Delta}E) is found to have a normal distribution to a good approximation. The ``localization length'' decreases (increases) for a repulsive (attractive) interaction. \textcopyright{} 1996 The American Physical Society.
We study the effects of disorder on a system of two coupled chains of strongly correlated fermions (the ladder system), using a renormalization-group technique. The stability of the phases of the pure system has been investigated as a function of interactions both for fermions with spin and spinless fermions. For spinless fermions the repulsive side is strongly localized whereas the system with attractive interactions is stable with respect to disorder, at variance with the single-chain case. For fermions with spins, the repulsive side is also localized, and in particular the ddd-wave superconducting phase found for the pure system is totally destroyed by an arbitrarily small amount of disorder. On the other hand, the attractive side is again remarkably stable with respect to localization. We have also computed the charge stiffness, the localization length, and the temperature dependence of the conductivity for the various phases. In the parameter range where ddd-wave superconductivity would occur for the pure system the conductivity is found to decrease monotonically with temperature, even at high temperature, and we discuss this surprising result. For a model with one-site repulsion and nearest-neighbor attraction, the most stable phase is an orbital antiferromagnet. Although this phase has no divergent superconducting fluctuation it can have a divergent conductivity at low temperature. Finally, to make a comparison of our results with experimental ladder systems, we treated the interladder coupling in a mean-field approximation. We argue based on our results that the superconductivity observed in some of these compounds cannot be a simple stabilization of the ddd-wave phase found for a pure single ladder. The application of our results to systems such as quantum wires is also discussed. In particular, the corrections to conductance in a two-channel quantum wire have been obtained as a function of system length, temperature, and interactions.
Abstract The interplay between disorder and interaction, especially near metal insulator transitions, is a long‐standing question. We investigate in detail single impurities, in particular, the Friedel oscillations induced by them. We study the decay of the Friedel oscillations in the one‐dimensional Heisenberg and Hubbard model analytically using the bosonization technique and numerically using the density matrix renormalization group treatment (DMRG). For the Heisenberg chain, we confirm the predictions of conformal field theory and bosonization for small interaction, but near phase transitions deviations are found in form of vanishing or additional oscillations. For the Hubbard chain, we study the oscillations – in the density as well as in the magnetization – in the spin‐gap, charge‐gap, and Luttinger liquid phase. We find an exponential decay or a very slow algebraic decay of the oscillations in the gapped phases. In the Luttinger liquid phase, we concentrate on the question of logarithmic corrections (which occur also in the isotropic Heisenberg antiferromagnet). Differences in the behavior near a boundary compared to an impurity are pointed out. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract Concerning the question of the (spin‐)Peierls mechanism in the presence of disorder we present a detailed analysis of the ground state phase diagram of the dimerized anisotropic Heisenberg‐XXZ chain containing one impurity. It is obtained by studying the destruction of the quantum coherence by the perturbations. The stability of the Peierls phase, i. e. the occurence of a stable dimerization, is determined by the energy gain and gap due to the coupling to the static phonons. The extension of the paramagnetic phase, found already in the clean dimerized chain, grows by adding the impurity, because the distortions weaken each other. The Peierls phase is reduced for two reasons: First, the energy gain of the spin‐system decreases, which leads to a smaller stable dimerization and second, the energy gap itself is reduced.
Concerning the question of the (spin-)Peierls mechanism in the presence of disorder we present a detailed analysis of the ground state phase diagram of the dimerized anisotropic Heisenberg-XXZ chain containing one impurity. It is obtained by studying the destruction of the quantum coherence by the perturbations. The stability of the Peierls phase, i. e. the occurence of a stable dimerization, is determined by the energy gain and gap due to the coupling to the static phonons. The extension of the paramagnetic phase, found already in the clean dimerized chain, grows by adding the impurity, because the distortions weaken each other. The Peierls phase is reduced for two reasons: First, the energy gain of the spin-system decreases, which leads to a smaller stable dimerization and second, the energy gap itself is reduced.