Finite and infinite matrix product states for Gutzwiller projected meanfield wave functions
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 method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic meanfield 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 meanfield states that arise from the variational slavefermion approach to the S =1 bilinearbiquadratic quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate groundstate 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 slavefermion states, exploring their qualitative features and finding good qualitative agreement with the respective exact groundstate spectra found from density matrix renormalization group.
 Publication:

Physical Review B
 Pub Date:
 March 2021
 DOI:
 10.1103/PhysRevB.103.125161
 arXiv:
 arXiv:2009.00064
 Bibcode:
 2021PhRvB.103l5161P
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 Phys. Rev. B 103, 125161 (2021)