BCS-type Wave Function Research Articles

Variational Monte Carlo analysis of singlet-pairing state in a system with inhomogeneous potential

We investigate the singlet-pairing superfluid state of two-component correlated fermions with repulsive interactions in a one-dimensional harmonic potential. By introducing a BCS-type wave function with spatially modulated order parameter, we show how the spin-singlet pairs are formed in the inhomogeneous potential. We then perform variational calculations with particular emphasis on the effect of particle correlations in order to examine the stability of the superfluid state.

Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field [Eur. Phys. J. C 20 (2001) 723]. The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes [Eur. Phys. J. C 24 (2002) 653]. This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode [hep-th/0212226]. We argue that the obtained result is not a counterexample to the Mermin–Wagner–Hohenberg and Coleman theorems.

Odd-parity singlet pairing in the positive-UHubbard model

We consider the possibility of an odd-parity singlet pairing in the positive-U Hubbard model, which naturally incorporates short-ranged antiferromagnetic correlations in the ground state. In a quantum Monte Carlo simulation of a nearly half-filled Hubbard model, we find that the repulsive U enhances the tendency for this type of pairing more strongly than for other pairing channels considered earlier. We propose a BCS-type wave function for this pairing where the gap has no nodes over the Fermi surface, and discuss various experimental consequences in connection to high-${\mathit{T}}_{\mathit{c}}$ superconductivity.

Factorizability of the BCS wave function.

A BCS-type wave function for an ordinary superconductor is discussed that incorporates a new variational parameter that allows writing the wave function as a product of singlets that is more general than the standard BCS form using Cooper pairs. In spite of the extra variational freedom, it is shown that the minimum-energy state reduces to the ordinary BCS ground state for the ordinary BCS Hamiltonian. However, in the presence of higher-order terms generically present in a Hamiltonian, the factorization symmetry of the wave function is broken.

Possible mechanism of superconductivity in electron superconducting cuprates

Based on the recent result of cluster calculations for electron doped superconductor that electrons are accommodated in the 4s level of Cu atoms, we propose a unified treatment of electron- and hole-doped superconductivities, i.e. the spin-polaron pairing mechanism developed by Kamimura et al.. For this purpose we perform a computer simulation of a 2D quantum spin system with two impurity spins and show that the long-ranged attractive interaction exists between two spin-polarons. Thus a spin-polaron system forms Cooper pairs and condensates to a usual BCS type wave function. Our mechanism can explain the observed doping concentration and pressure dependences of Tc.

Generator coordinate method applied to nuclei in the transition region

The generator coordinate method is applied to the transition region nuclei. Using the de deformation parameter as a generator coordinate, the trial wave function is constructed by superposing shell-model wave functions with various varues of the deformation parameter. For simplicity the deformation is restricted to be axially symmetric, and the pairing correlation is taken into account by using a BCS type shell-model wave function. The generator wave function which serves as a weight function may be obtained by solving an integral equation derived through the variational principle. In the integral equation there appear overlap and energy kernels, which are matrix elements between shell-model wave functions with different values of the deformation parameter. In calculating the kernels a new method is presented. The BCS type wave function is expressed in a more suitable form to practical calculations and the matrix elements are obtained in a simple and compact form without any approximation.