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arXiv:cond-mat/0002288

Quantum Phase Transition in Extended Attractive Hubbard Model

S. Saito, H. Yoshimoto, Y. Y. Suzuki, Susumu Kurihara

Published Feb 18, 2000• 0 citations
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Abstract

We have made a variational analysis on an evolution of superconductivity from weak to strong coupling regime. In contrast to a crossover without thermodynamic anomaly found in a dilute system, we show the existence of a quantum phase transition near half filling. The transition is driven by charge density waves instabilities. We have found that superconductivity and charge density waves coexist in the presence of a weak intersite repulsion. The ground state phase diagram is determined and the quantum phase transition is an attractive version of the Mott transition.

DOI
10.48550/arxiv.cond-mat/0002288

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We have made a variational analysis on an evolution of superconductivity from weak to strong coupling regime. In contrast to a crossover without thermodynamic anomaly found in a dilute system, we show the existence of a quantum phase transition near half filling. The transition is driven by charge density waves instabilities. We have found that superconductivity and charge density waves coexist in the presence of a weak intersite repulsion. The ground state phase diagram is determined and the quantum phase transition is an attractive version of the Mott transition.
We have performed a variational analysis on the evolution of superconductivity from weak to strong coupling regime. We have improved the Bardeen Cooper Schrieffer (BCS) wave function, and show that the electronic correlations are important in obtaining the correct behavior of superconducting condensation energy. In contrast to a crossover without thermodynamic anomaly discussed in a dilute system, we show the existence of a quantum phase transition near half filling, which suggests that an evolution is not always continuous. The transition is driven by charge density waves instabilities. We have found that superconductivity and charge density waves coexist in the presence of a weak intersite repulsion. The ground state phase diagram is determined by varying both interactions and filling.
At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U,V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V, the attractive P may give rise to the superconducting phases for 2V≤min{2|P|;4|P|−U}.
Cooperation and competition between the antiferromagnetic, ddd-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength UUU below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.
We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state.For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v 2Zt, |UD <2Zt) and strong coupling (v > 2Zt) limits.The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit.In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coułomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-frlling.The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined.It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction.Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.
We have obtained the quantum phase diagram of one dimensional extended Bose-Hubbard model using the density-matrix renormalization group and Abelian bosonization methods for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from Mott insulating phase to superconducting phase for integer band fillings of bosons. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, apart from the charge density wave and superconducting phases for half-integer band fillings. Our study reveals that extended range interactions are necessary to get the correct phase boundary of an one-dimensional interacting bosons system.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.