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Physical review. B, Condensed matter

Optimal phonon approach to the spin Peierls model with nonadiabatic spin-phonon coupling

Barry Friedman

Published Mar 1, 2000• 17 citations
Publisher

Abstract

We have investigated the spin Peierls model treating the lattice quantum mechanically using an optimal phonon method. For small systems, the optimal phonon method is compared to truncation techniques. There is good agreement between the two methods; however, the optimal phonon method is superior in that it achieves greater basis reduction and the optimal phonons are relatively insensitive to system size. Using the optimal phonons from small systems and the density matrix renormalization group, a soliton-antisoliton pair is studied. Our calculation resolves a factor of 4 discrepancy between adiabatic theories and experiment.

DOI
10.1103/physrevb.61.6701

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We have investigated the spin Peierls model treating the lattice quantum mechanically using an optimal phonon method. For small systems, the optimal phonon method is compared to truncation techniques. There is good agreement between the two methods; however, the optimal phonon method is superior in that it achieves greater basis reduction and the optimal phonons are relatively insensitive to system size. Using the optimal phonons from small systems and the density matrix renormalization group, a soliton-antisoliton pair is studied. Our calculation resolves a factor of 4 discrepancy between adiabatic theories and experiment.
The one-dimensional spin-Peierls model with quantum phonons is studied with an optimal phonon method combined with the density matrix renormalization group. By calculating the ground state in the sector Sz = 1 I obtain a soliton-antisoliton pair. The soliton is compared to nuclear magnetic resonance experiments which image the soliton lattice present in CuGeO3 under a high magnetic field. Reasonable agreement with experiment can be achieved by choosing a large value of the phonon frequency and the spin phonon coupling constant. This indicates that CuGeO3 is in a non-adiabatic strongly coupled parameter regime. A robust feature of the calculations is an attraction between solitons even without interchain coupling.
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.
An optimized phonon approach for the numerical diagonalization of interacting electron-phonon systems is proposed. The variational method is based on an expansion in coherent states that leads to a dramatic truncation in the phonon space. The reliability of the approach is demonstrated for the extended Holstein model showing that different types of lattice distortions are present at intermediate electron-phonon couplings as observed in strongly correlated systems. The connection with the density matrix renormalization group is discussed.
We propose a density matrix renormalization group approach to tackle a two-state system coupled to a bosonic bath with continuous spectrum. In this approach, the optimized phonon scheme is applied to several hundred phonon modes that are linearly divided among the spectra. Although density matrix renormalization group cannot resolve very small energy scales, the delocalized-localized transition points of the two-state system are extracted by the extrapolation of the flow diagram results. The phase diagram is compared to the numerical renormalization group results and shows a good agreement in both Ohmic and sub-Ohmic cases.
The density-matrix renormalization-group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein) limit to a gapless, dispersive (Debye) limit. A variety of theoretical probes are used to determine the quantum phase transition, including energy gap crossing, a finite-size scaling analysis, bond-order autocorrelation functions, and bipartite quantum entanglement. All these probes indicate that in the antiadiabatic phonon limit a quantum phase transition of the Berezinskii-Kosterlitz-Thouless type is observed at a nonzero spin-phonon coupling, gc{g}_{\text{c}}gc​. An extrapolation from the Einstein limit to the Debye limit is accompanied by an increase in gc{g}_{\text{c}}gc​ for a fixed optical $(q=\ensuremath{\pi})$ phonon gap. We therefore conclude that the dimerized ground state is more unstable with respect to Debye phonons with the introduction of phonon-dispersion renormalizing the effective spin-lattice coupling for the Peierls-active mode. We also show that the staggered spin-spin and phonon displacement order parameters are unreliable means of determining the transition.
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.