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Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions | | Gabriel Petrica
; Bo-Xiao Zheng
; Garnet Kin-Lic Chan
; Bryan K. Clark
; | | Date: |
31 Aug 2020 | | 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. | | Source: | arXiv, 2009.00064 | | Services: | Forum | Review | PDF | Favorites | |
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