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Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions

Petrica, Gabriel and Zheng, Bo-Xiao and Chan, Garnet Kin-Lic and Clark, Bryan K. (2021) Finite and infinite matrix product states for Gutzwiller projected mean-field wave functions. Physical Review B, 103 (12). Art. No. 125161. ISSN 2469-9950. doi:10.1103/PhysRevB.103.125161.

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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 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 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 an 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 density matrix renormalization group.

Item Type:Article
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URLURL TypeDescription Paper
Petrica, Gabriel0000-0001-9607-4802
Chan, Garnet Kin-Lic0000-0001-8009-6038
Alternate Title:Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
Additional Information:© 2021 American Physical Society. Received 18 January 2021; revised 15 March 2021; accepted 17 March 2021; published 31 March 2021. B.K.C. acknowledges support from the Department of Energy Grant No. DOE de-sc0020165. This project is part of the Blue Waters sustained petascale computing project, which is supported by the National Science Foundation (Awards No. OCI-0725070 and No. ACI-1238993) and the State of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. G.K.-L.C. was supported by the US National Science Foundation via Grant No. 1839204. G.K.-L.C. also acknowledges support from the Simons Foundation via the Investigator Award and the Many-Electron Collaboration.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0020165
State of IllinoisUNSPECIFIED
Simons FoundationUNSPECIFIED
Issue or Number:12
Record Number:CaltechAUTHORS:20201027-094309674
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106297
Deposited By: Tony Diaz
Deposited On:27 Oct 2020 16:57
Last Modified:08 Apr 2021 21:08

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