Soh Koike

Variational Monte Carlo study on the superconductivity in the two-dimensional Hubbard model

Abstract The possibility of superconductivity (SC) in the ground state of the two-dimensional (2D) Hubbard model was investigated by means of the variational Monte Carlo method. The energy gain of the d-wave SC state, obtained as the difference of the minimum energy with a finite gap and that with zero gap, was examined with respect to dependences on U, electron density ρ and next nearest neighbor transfer t′ mainly on the 10×10 lattice. It was found to be maximized around U=8 (the energy unit is nearest neighbor transfer t). It was shown to sharply increase for negative values of t′ and have a broad peak for t′∼−0.10. For these value of t′ the energy gain was a smooth increasing function of ρ almost independent of the shell structure in the region starting from ∼0.76 up to the upper bound of investigation 0.92. This clearly indicates that the result is already close to the value in the bulk limit. For t′=0, the energy gain depended on the electronic shell state. This suggests the 10×10 lattice is not sufficiently large for this case, although it is highly plausible that the bulk limit value is finite. Competition between the SC and the commensurate SDW states was also investigated. When t′=0, the ground state is SDW in the range of ρ≥∼0.84. The SC region slightly extends up to ∼0.87 for t′∼−0.10. Consequently the present results strongly support an assertion that the 2D Hubbard model with t′∼−0.1 drives SC by itself in the ρ region from ∼0.76 to ∼0.87. The above features are in a fair agreement with the phase diagram of the optimally and overly hole-doped cuprates. The energy gain in the SC state with suitable parameters is found to be in reasonable agreement with the condensation energy in the SC state of YBa2Cu3O7. The corresponding t–J model proves to give an order-of-magnitude larger energy gain, which questions its validity.

Uniaxial-Pressure Induced Ferromagnetism of Enhanced Paramagnetic Sr3Ru2O7

We report a uniaxial pressure-dependence of magnetism in layered perovskite strontium ruthenate Sr 3 Ru 2 O 7 . By applying a relatively small uniaxial pressure, greater than 0.1 GPa normal to the RuO 2 layer, ferromagnetic ordering manifests below 80 K from the enhanced-paramagnet. Magnetization at 1 kOe and 2 K becomes 100 times larger than that under ambient condition. Uniaxial pressure dependence of Curie temperature T C suggests the first order magnetic transition. Origin of this uniaxial-pressure induced ferromagnetism is discussed in terms of the rotation of RuO 6 octahedra within the RuO 2 plane.

Bulk limit of superconducting condensation energy in 2D Hubbard model

Abstract We have studied the possibility of superconductivity (SC) in the titled model by computing the SC condensation energy per site as the energy gain in the d-pairing SC state using the variational Monte Carlo method. Its bulk limit was obtained by finite-size scaling with approximately fixed electron density ρ. This value survived finite for ρ⩾0.84 when next n.n. transfer energy t′ satisfied −0.25t⩽t′⩽−0.10t with on-site Coulomb energy U=8t; here t is the n.n. transfer energy. The obtained values are of the order of the experimental one for YBCO.

Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model I.

We propose a Monte Carlo method, which is a hybrid method of the quantum Monte Carlo method and variational Monte Carlo theory, to study the Hubbard model. The theory is based on the off-diagonal and the Gutzwiller type correlation factors which are taken into account by a Monte Carlo algorithm. In the 4×4 system our method is able to reproduce the exact results obtained by the diagonalization. An application is given to investigate the half-filled band case of two-dimensional square lattice. The energy is favorably compared with quantum Monte Carlo data.

Effect of the Medium-Range Transfer Energies to the Superconductivity in the Two-Chain Hubbard Model

We investigate the two-chain Hubbard model including the next nearest-neighbor transfer energies both in the interchain and intrachain directions by use of the exact-diagonalization and the variational Monte Carlo methods. We find that superconducting correlation functions are enhanced in such a situation where the density of states of the antibonding band in the neighborhood of the Fermi level enlarges due to the above-mentioned transfer energies, especially, in the situation where the Fermi level is located a little above the bottom of the antibonding band. In such a situation we find from the calculated momentum distribution function that this system is in almost one-band situation close to the two-band one. The relevance to ladder-type superconductor Sr 14- x Ca x Cu 24 O 41 is asserted.

Phase diagram of the Cu}O model in the oxide superconductors: Variational Monte Carlo study

Abstract A variational Monte Carlo method is formulated to study the ground state of the model for the Cu–O plane in the oxide superconductors. The possibility of superconductivity is investigated employing the Gutzwiller-projected BCS and SDW wave functions with respect to dependences on electron density ρ and transfer tpp between neighboring oxygen orbitals. Near half-filling the SDW state is most stable for both the hole and electron doping cases. Away from half-filling when hole doping ratio δ∼0.2, the d-wave superconducting state turns out to be more favorable than the SDW state. The superconducting condensation energy is in reasonable agreement with the experimental value obtained from the critical magnetic field Hc.

Superconducting Condensation Energy of the Two-Chain Hubbard Model in the Bulk Limit

We have studied on the possibility of superconductivity in the two-chain Hubbard model by using the variational Monte Carlo method changing the interchain transfer energy t d . The energy gain per site Δ E in the variational BCS state in reference to the normal state energy, which is nothing but the superconducting condensation energy, was computed. We have fitted Δ E as a function of the inverse of the lattice size by a power-law function and found that in the bulk limit Δ E remains finite in a certain narrow range of t d . Calculated momentum distribution functions reveal that the superconductivity is most stable in the case where the electron distribution in k -space is in a one-band-like situation, on the brink of transition to a two-band-like one. The SDW-type trial wave function was also examined but we did not obtain any energy gain with it in the above-mentioned superconducting region.

Variational Monte Carlo study of the two-chain Hubbard model

Abstract We have calculated the ground state energy of the two-chain Hubbard model by using the Variational Monte Carlo method in which we employed the Gutzwiller-projected BCS superconducting wave function as the trial wave function. A clear energy minimum was obtained with two different gaps having opposite signs for the bonding and antibonding bands. The energy gain per site ΔE of the variational BCS state against the normal state was found to be fitted for the number of the sites N up to 144 by ΔE 0 + αN − β with Δ E ∼ 0.00103 and β ∼ 2 in a certain case, leading to a finite energy gain per site in the bulk limit.

Exact-diagonalization study on the effect of the long-range Coulomb interaction to the superconducting ground state in the two-chain Hubbard model

We present exact-diagonalization results clearly indicating that the long-range part of Coulomb interaction does not sweep away the superconducting region of the two-chain Hubbard model driven by the short-range part. When the model contains the nearest-neighbor Coulomb interaction both for the interchain and the intrachain directions, the region of developed superconducting correlations in the ground state is reduced. The CDW correlation is found to increase, intervening with the competition between superconductivity and CDW. When we include the long-range Coulomb interaction of the type of 1/r, the instability to the CDW state weakens with the superconducting region recovered to some extent compared with the above case.

Variational Monte Carlo study of the ground state of the two-dimensional d-p model

Abstract Variational Monte Carlo calculations are carried out to study the ground state of the two-dimensional d-p model which is the most basic one for CuO 2 plane in the cupratesuperconductors. The possibility of superconductivity is investigated using the Gutzwiller-projected BCS and SDW wave functions for the 6 × 6 and 8 × 8 lattices. Near half-filling the SDW state is most stable in a wide range for both hole and electron doping cases. The d -wave superconducting state turns out to be more favorable than the SDW state when the hole doping ratio is more than or almost equal to 0.2. The transfer energy between neighboring O orbitals is found to extend the region of the d -wave state near half filling.