Optimized multi-determinant trial wavefunctions for Constrained Path Monte Carlo

Two of the most successful types of methods for strongly-correlated models are quantum Monte Carlo and renormalization group methods. Both however suffer from limitations that make large calculations difficult except in special cases, for example one dimension (1D). The Density Matrix Renormalization Group method suffers from poor scaling beyond 1D. The Path Integral Renormalization Group (PIRG) method expands the wavefunction in Slater Determinants and is not limited by dimension, but by the strength of interactions. Quantum Monte Carlo calculations are severely limited by the Fermion sign problem. The Constrained Path Monte Carlo (CPMC) method prevents the exponential loss of precision from the sign problem through the use of a trial wavefunction. However, the trial wavefunction is an uncontrolled approximation with an unknown error. We demonstrate a way to combine the advantages of a renormalization method (PIRG) with those of a quantum Monte Carlo (CPMC), by using PIRG wavefunctions as CPMC trial wavefunctions. The advantage of PIRG wavefunctions as trial
wavefunctions is that they can be systematically improved. We present results for PIRG-CPMC calculations on frustrated Hubbard models, comparing energies, spin correlations, and superconducting pair-pair correlations.