Approximating strongly correlated wave functions with correlator product states
We describe correlator product states, a class of numerically efficient many-body wave functions to describe strongly correlated wave functions in any dimension. Correlator product states introduce direct correlations between physical degrees of freedom in a simple way, yet provide the flexibility to describe a wide variety of systems. We show that many interesting wave functions can be mapped exactly onto correlator product states, including Laughlin's quantum Hall wave function, Kitaev's toric code states, and Huse and Elser's frustrated spin states. We also outline the relationship between correlator product states and other common families of variational wave functions such as matrix product states, tensor product states, and resonating valence-bond states. Variational calculations for the Heisenberg and spinless Hubbard models demonstrate the promise of correlator product states for describing both two-dimensional and fermion correlations. Even in one-dimensional systems, correlator product states are competitive with matrix product states for a fixed number of variational parameters.
© 2009 American Physical Society. Received 26 July 2009; revised manuscript received 28 October 2009; published 22 December 2009. We thank C. L. Henley for bringing the work of Huse and Elser to our attention, T. Nishino for pointing out the long history of CPS, and S. R. White for helpful discussions. This work was supported by the National Science Foundation through Grant No. CHE-0645380 and CHE-1004603, the David and Lucile Packard Foundation, the Alfred P. Sloan Foundation, and the Camille and Henry Dreyfus Foundation. Supplemental funding for C. J. Unrigar was provided through the DOE-CMSN program through Grant No. DE-FG02-07ER46365.
Accepted Version - 0907.4646.pdf
Published - PhysRevB.80.245116.pdf