Approximating strongly correlated spin and fermion wavefunctions with correlator product states

TL;DR

This paper investigates correlator product states as a versatile method for approximating complex wavefunctions in various dimensions, demonstrating their ability to capture key quantum correlations and their relation to other variational approaches.

Contribution

It introduces correlator product states as a unifying framework that includes many important quantum states and compares their effectiveness to existing methods like matrix product states.

Findings

Correlator product states can represent Laughlin, spin, and toric code states.

They effectively capture 2D correlations regardless of system width.

They are competitive with matrix product states in 1D simulations.

Abstract

We explore correlator product states for the approximation of correlated wavefunctions in arbitrary dimensions. We show that they encompass many interesting states including Laughlin's quantum Hall wavefunction, Huse and Elser's frustrated spin states, and Kitaev's toric code. We further establish their relation to common families of variational wavefunctions, such as matrix and tensor product states and resonating valence bond states. Calculations on the Heisenberg and spinless Hubbard models show that correlator product states capture both two-dimensional correlations (independent of system width) as well as non-trivial fermionic correlations (without sign problems). In one-dimensional simulations, correlator product states appear competitive with matrix product states with a comparable number of variational parameters, suggesting they may eventually provide a route to practically generalise the density matrix renormalisation group to higher dimensions.