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Annalen der Physik

Ground state properties of disordered and dimerized spin chains

C. Schuster, Ulrich Eckern

Published Nov 1, 1999• 2 citations
Publisher

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.

DOI
10.1002/(sici)1521-3889(199911)8:7/9<585::aid-andp585>3.0.co;2-b

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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.
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.
Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.
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.
We investigate a one-dimensional S=1S=1S=1 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. Investigating the ground-state energy of the static bond-alternating chain, we find that the instability to a dimerized chain depends on the value of the spin-phonon coupling, unlike the case of S=12.S=\frac{1}{2}.S=21​. The spin state is the dimer state or the uniform Haldane state depending on whether the lattice distorts or not, respectively. At an intermediate value of the spin-phonon coupling, we find the first-order transition between the two states. We also find the coexistence of the two states.
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.
The spin-Peierls transition in the ground state of a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a spin-gapped Peierls state is explored in the parameter space spanned by the spatial anisotropy and the strength of spin-lattice coupling. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state occurs only when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D model, where adiabatic phonons lead to a dimerized ground state for any non-zero spin-phonon coupling. The phase diagram in the above parameter space is mapped out. No evidence is found for a region of co-existing long range magnetic order and dimerization. The vanishing of the Neel order occurs simultaneously with the setting in of the dimerization.