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Chinese Physics Letters

Phase Transition of Spin-Peierls Systems with Impurities

Xu Bo-wei, Guo-Hui Ding, Fei Ye

Published Aug 1, 2000• 4 citations
Publisher

Abstract

The quasi-one-dimensional spin-Peierls (SP) systems with impurities are studied in their bosonized form. The spins of the dimerized state are bounded into singlets with an SP gap, while the impurities of doped systems will induce fluctuations of the coupling strength between the spins at different sites and break some pairs of spin singlets. The doping suppresses the dimerized SP state and induces a Kosterlitz-Thouless phase transition from the dimerized state into the undimerized one.

DOI
10.1088/0256-307x/17/8/003

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The quasi-one-dimensional spin-Peierls (SP) systems with impurities are studied in their bosonized form. The spins of the dimerized state are bounded into singlets with an SP gap, while the impurities of doped systems will induce fluctuations of the coupling strength between the spins at different sites and break some pairs of spin singlets. The doping suppresses the dimerized SP state and induces a Kosterlitz-Thouless phase transition from the dimerized state into the undimerized one.
The role of the spin-phonon coupling in spin-Peierls chains doped with spin-0 or spin-1 impurities is investigated by various numerical methods such as exact diagonalization, quantum Monte Carlo simulations and Density Matrix Renormalization Group. Various treatments of the lattice, in a fully quantum mechanical way, classically in the adiabatic approximation or using a fixed three-dimensional dimerization pattern are compared. For an isolated chain, strong bonds form between the two spin-1/2 sites next to the impurity site, leading to the appearance of magneto-elastic solitons. We also show that these excitations do not bind to spin-0 impurities but are weakly attracted by spin-1 impurities. However, the interchain elastic coupling generates an effective confining potential at the non-magnetic impurity site which can lead to the formation of soliton-impurity bound states. We also predict that a soliton and an antisoliton bound to two impurities on the same chain can annihilate each other when the separation between the impurities is smaller than a critical value depending on the interchain elastic constant.
The effects of spin-1 impurities introduced in dimerized antiferromagnetic spin chains are studied using Lanczos diagonalization and quantum Monte Carlo simulations. First, the magnitude of the interaction between a Ni ion replacing a Cu ion is derived for the case study system Cu-O-Cu. Then, it is shown that the introduction of S=1S=1S=1 impurities leads to the suppression of the original spin gap of the dimerized system and to the enhancement of the antiferromagnetic correlations close to the impurity. These features are interpreted in terms of a valence bond picture of the ground state of both the pure and the doped system. The similitudes and differences between the underlying mechanisms that produce these effects in the cases of nonmagnetic and S=1S=1S=1 impurities are analyzed. It is stressed that a singlet formed between the spin-1 impurity site and the two spin-1/2 neighbors spins behaves as an effective nonmagnetic vacancy which may be partially responsible for the enhancement of the antiferromagnetic correlations on the whole system. Implications of these results for experiment are also discussed.
Effects of spin-Peierls fluctuation are examined in models of one-dimensional conductors. One-dimensional strongly correlated systems coupled to dynamical lattice distortion or polarization are examined by quantum Monte Carlo studies. Excitations are given by spinless charge solitons and neutral spin solitons when the system is doped away from a Mott insulator. A pairing mechanism due to a dynamical spin-Peierls fluctuation is discussed. Numerical results on the spin gap formation and the enhancement of pairing correlations in a dimerized t-J model and doped spin-1 Heisenberg model in one dimension are summarized.
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.
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.