Single-Particle Spectral Function Formulated and Calculated by Variational Monte Carlo Method with Application to d -Wave Superconducting State

Abstract

A method to calculate the one-body Green's function for ground states of correlated electron materials is formulated by extending the variational Monte Carlo method. We benchmark against the exact diagonalization (ED) for the one-and two-dimensional Hubbard models of 16-site lattices, which proves high accuracy of the method. The application of the method to a larger-sized Hubbard model on the square lattice correctly reproduces the Mott insulating behavior at half-filling and gap structures of the d-wave superconducting state of the hole-doped Hubbard model in the ground state optimized by enforcing the charge uniformity, evidencing a wide applicability to strongly correlated electron systems. From the obtained d-wave superconducting gap of the charge-uniform state, we find that the gap amplitude at the antinodal point is several times larger than the experimental value when we employ a realistic parameter as a model of the cuprate superconductors. The effective attractive interaction of carriers in the d-wave superconducting state inferred for an optimized state of the Hubbard model is as large as the order of the nearest-neighbor transfer, which is far beyond the former expectation in the cuprates. We discuss the nature of the superconducting state of the Hubbard model in terms of the overestimate of the gap and the attractive interaction in comparison to the cuprates.

Two-Hole Ground State: Dichotomy in Pairing Symmetry

“…The single-hole problem has been a focus of intensive study with a history almost as long as the high-T c problem. It had been believed for a long time that the single hole injected into the AF spin background would behave like a Landau-like quasiparticle with translational symmetry and a finite spectral weight, known as a spin polaron [41][42][43][44][45][46][47][48]. Namely, the spin distortion of the AF background in response to the motion of the hole was expected to merely dress the bare hole's effective mass.…”

The Hubbard model: A computational perspective

“…More finite temperature results in other parameter regimes as well as excitation spectra (17,258,199,257) from tensor network approaches can be expected in future. Progress in computing dynamical quantities has also recently been achieved by dynamical variational Monte Carlo approaches (62,28), with a first application to the 2D Hubbard model in Ref. (28).…”

“…Progress in computing dynamical quantities has also recently been achieved by dynamical variational Monte Carlo approaches (62,28), with a first application to the 2D Hubbard model in Ref. (28). Moreover, diagrammatic approaches based on the two-particle vertex are being extended to real frequencies (147).…”

Why the Schwinger Boson mean field theory fails to describe the spin dynamics of the triangular lattice antiferromagnetic Heisenberg model?

“…While such a Bosonic rigidity is beyond the reach of any mean field treatment, it can be treated faithfully by the Gutzwiller projection technique. In recent years, such a technique has been generalized to the study of the dynamical properties of strongly correlated electron mod-els and received much success 26,39,[45][46][47][48][49][50][51] . In such a variational treatment, one adopt the Gutzwiller projected mean field eigenstates(all those that can be reached by operating the spin density operator S i µ (q) on the mean field ground state |MFG ) to form a variational subspace, within which the dynamical behavior of the system is computed.…”