Insights into the structure of many-electron wave functions of Mott-insulating antiferromagnets: The three-band Hubbard model in full configuration interaction quantum Monte Carlo

Abstract

We investigate the ground-state wave function of a prototypical strongly correlated system, a three-band (p-d) Hubbard model of cuprates, using full configuration interaction quantum Monte Carlo. We show that the configuration interaction description of the exact ground state wave function is profoundly affected by the choice of single-particle representation, in a counterintuitive manner. Thus a broken-symmetry unrestricted Hartree-Fock basis, which at a single configuration level produces a qualitatively correct description of the antiferromagnet, results in a highly entangled exact solution consisting of high particle-hole excitations of the reference. This wave function is found to be very difficult to approximate using subspace diagonalizations. Conversely, a restricted Hartree-Fock basis, which yields at a single configuration level a qualitatively incorrect paramagnetic metal, results in a relatively rapidly converging configuration interaction expansion. Convergence can be further accelerated by adopting a natural orbital representation. Our results suggest that with the correct single-particle basis, such strongly correlated systems may be described by relatively compact wave functions.

Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

“…Changes of basis set do in general affect the sign problem in a more nontrivial way in other systems, and this has been studied elsewhere. [34,37] C. Discussion…”

“…The drawback is that the simulation must now be converged much more stringently with walker number, and analysis of this is performed elsewhere and beyond the scope of this paper. [22,27,29,30] In practice, the initiator approach enables systems of far larger sizes to be investigated, [31][32][33][34] further increased by a semistochastic adaptation. [22,35] C. The DOCI Hamiltonian…”

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

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Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

“…The FCIQMC method was originally developed for fermionic many-body problems. It has been applied to the electronic structure of molecules and solids [60][61][62] and the Hubbard model [63][64][65]. Recently, it was used to study the yrast states in a superfluid of spin- 1 2 fermions [66].…”