Exact density matrix of the Gutzwiller wave function: II. Minority spin component

TL;DR

This paper derives the exact density matrix for the Gutzwiller wave function's minority spin component in one dimension, providing comprehensive results for all magnetizations and densities, and linking it to the t-J model's ground state.

Contribution

It extends previous work by analytically deriving the density matrix for the minority spin component, completing the characterization for all magnetizations in the Gutzwiller wave function.

Findings

Exact density matrix for all magnetizations obtained

Discontinuities and singularities in momentum distribution identified

Numerical Fourier transform matches analytical results

Abstract

The density matrix, i.e. the Fourier transform of the momentum distribution, is obtained analytically for all magnetization of the Gutzwiller wave function in one dimension with exclusion of double occupancy per site. The present result complements the previous analytic derivation of the density matrix for the majority spin. The derivation makes use of a determinantal form of the squared wave function, and multiple integrals over particle coordinates are performed with the help of a diagrammatic representation. In the thermodynamic limit, the density matrix at distance x is completely characterized by quantities v_c x and v_s x, where v_s and v_c are spin and charge velocities in the supersymmetric t-J model for which the Gutzwiller wave function gives the exact ground state. The present result then gives the exact density matrix of the t-J model for all densities and all magnetization at zero temperature. Discontinuity, slope, and curvature singularities in the momentum distribution are identified. The momentum distribution obtained by numerical Fourier transform is in excellent agreement with existing result.