Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions

TL;DR

This paper introduces a novel method to represent and analyze Gutzwiller projected mean-field wavefunctions as matrix product states (MPS), enabling detailed study of their entanglement properties and ground-state energies in quantum spin systems.

Contribution

The authors develop a new approach to obtain finite and infinite MPS representations of fermionic mean-field states, including products of states, and apply it to Gutzwiller projected states in spin chains.

Findings

Accurate MPS and iMPS representations of mean-field states

Close match between variational and MPS energies

Qualitative agreement of entanglement spectra with exact ground states

Abstract

Matrix product states (MPS) and `dressed' ground states of quadratic mean fields (e.g. Gutzwiller projected Slater Determinants) are both important classes of variational wave-functions. This latter class has played important roles in understanding superconductivity and quantum spin-liquids. We present a novel method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian, (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g. determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the $S=1$ Bilinear-Biquadratic (BLBQ) quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely indicating the method is accurate and there is minimal loss due to truncation error. We then present the first exploration of the entanglement spectra of projected slave-fermion states exploring their qualitative features and finding good qualitative agreement with the respective exact ground state spectra found from DMRG.