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Journal of the Physical Society of Japan

Spin Dimer State Model andSpin-Phonon Coupling Model of Superconductivity

Masatoshi Imada

Published Jun 15, 1991• 50 citations
Publisher

Abstract

A mechanism of superconductivity coming from the doping of mobile fermions into the spin dimerized insulator such as spin Peierls state, valence bond glass, Heisenberg spins with next nearest neighbor exchange coupling and the Haldane gap state is discussed. The doping of fermions with narrow band into a Mott insulator with a spin gap results in the superconducting long range order in two- and three-dimensions, while results in the power law divergence of the pairing susceptibility with Tomonaga-Luttinger liquid character of charge in one-dimension. An example of numerical calculation in one-dimension is shown. The possible relevance of this mechanism to high-temperature superconductivity, where dynamical coupling of lattice distortion to spin may play a crucial role, is discussed. A relevant model Hamiltonian with spin-phonon coupling and dynamical spin-Peierls fluctuation is proposed.

DOI
10.1143/jpsj.60.1877

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•Jan 1, 2000•13 citations
A mechanism of superconductivity coming from the doping of mobile fermions into the spin dimerized insulator such as spin Peierls state, valence bond glass, Heisenberg spins with next nearest neighbor exchange coupling and the Haldane gap state is discussed. The doping of fermions with narrow band into a Mott insulator with a spin gap results in the superconducting long range order in two- and three-dimensions, while results in the power law divergence of the pairing susceptibility with Tomonaga-Luttinger liquid character of charge in one-dimension. An example of numerical calculation in one-dimension is shown. The possible relevance of this mechanism to high-temperature superconductivity, where dynamical coupling of lattice distortion to spin may play a crucial role, is discussed. A relevant model Hamiltonian with spin-phonon coupling and dynamical spin-Peierls fluctuation is proposed.
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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.
"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of ""operator-loop"" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling."
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-12\frac{1}{2}21​ Heisenberg model coupled to adiabatic bond phonons is investigated using the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless N\'eel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the N\'eel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature Tc{T}_{c}Tc​ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc{T}_{c}Tc​, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.
Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1