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Journal of Physics Condensed Matter

Quantum solitons in CuGeO3: a density matrix renormalization group study

Barry Friedman

Published Apr 18, 2002• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0953-8984/14/17/331

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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.
We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​. A variant of the finite temperature density matrix renormalization group (DMRG) allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ such as magnetic dimerization, critical temperature, susceptibility, and entropy.
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 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.
We report results from a systematic strong-coupling expansion of a spin-½ Heisenberg chain coupled to Einstein phonons and a frustrating next-nearest-neighbor spin interaction. It is not obvious which interaction dominates in the regime of small coupling constants. In the non-adiabatic regime (ℏΩ ≈ J ) this model is used to describe the zero-temperature properties of CuGeO 3 . The linked cluster expansion allows the determination of observables in the thermodynamic limit preserving the full lattice dynamics without a truncation of the phononic Hilbert space. We show that the spin-phonon coupling leads to a renormalization of the elementary triplet dispersion. Surprisingly, in the non-adiabatic regime a substantial renormalization of the spin gap only sets in at much larger couplings than those proposed for CuGeO 3 . The ground-state magnetic correlations are found to be hardly affected by the spin-phonon coupling, but dominated by the frustrating magnetic interaction in the parameter regime relevant for CuGeO 3 .
Spin dynamics as well as static properties of the one-dimensional J-J' model (S=1/2, J>0 and 0\le α=J'/J\le 0.5) are studied by the exact diagonalization and the recursion method of finite systems up to 26 sites. Especially, the dynamical structure factor S(q,ω) is investigated carefully for various values of α. As αincreases beyond the gapless-gapful critical value α_c=0.2411, there appear features definitely different from the Heisenberg model but the same with the Majumdar-Ghosh model. Some of these features depend only on the value of αand not on δ: a parameter introduced for the coupling alternation. By comparing these results with a recent inelastic neutron scattering spectrum of an inorganic spin-Peierls compound CuGeO_3 [M. Arai et al.: Phys. Rev. Lett. 77 (1996) 3649], it is found that the frustration by J' in CuGeO_3 is unexpectedly strong (α=0.4-0.45), and at least αmust be larger than α_c to some extent. The value of J is evaluated at \sim 180K consistent with other estimations. The coupling alternation is extremely small. This large frustration is a primary origin of the various anomalous properties CuGeO_3 possesses. For comparison we refer also to α'-NaV_2O_5.