Approximating strongly correlated spin and fermion wavefunctions with correlator product states

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.

Table 1 expanded, Table 2 updated, optimization method discussed, discussions expanded in some sections, earlier work on similar wavefunctions included in text and references, see also (arXiv:0905.3898). 5 pages, 1 figure, 2 tables, submitted to Phys. Rev. B

References in corpus (9)

• The ALPS project release 1.3: open source software for strongly correlated systems
• Area laws in quantum systems: mutual information and correlations
• Criticality, the area law, and the computational power of PEPS
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Tensor-product representations for string-net condensed states

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