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

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.

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• Real time evolution of Anderson impurity models via tensor network influence functionals
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Density matrix renormalization group boosted by Gutzwiller projected wave functions
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Unveiling a critical stripy state in the triangular-lattice SU(4) spin-orbital model
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Twisting the Dirac cones of the SU(4) spin-orbital liquid on the honeycomb lattice
• Variational adiabatic transport of tensor networks
• U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
• Projected d-wave superconducting state: a fermionic projected entangled pair state study
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Kinetic Ferromagnetism and Topological Magnons of the Hole-Doped Kitaev Spin Liquid
• Finite-Entanglement Scaling of 2D Metals
• Efficient conversion from fermionic Gaussian states to matrix product states
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Non-Abelian topological order with SO(5)${}_1$ chiral edge states
• Partons from stabilizer codes
• Process Tensor Approaches to Non-Markovian Quantum Dynamics