Monte Carlo Simulations of Two-dimensional Fermion Systems with String-bond States

Song, J. P., & Clay, R. T. (2014). Monte Carlo Simulations of Two-dimensional Fermion Systems with String-bond States. Physical Review B. 89, 075101. DOI:10.1103/PhysRevB.89.075101.

Abstract

We describe an application of variational Monte Carlo to two-dimensional fermionic systems within the recently developed tensor-network string-bond state ansatz. We use a combination of variational Monte Carlo and stochastic optimization to optimize the matrix-product state matrices representing the ground state. We present results for a two-dimensional spinless fermion model including nearest-neighbor Coulomb interactions and determine using finite-size scaling the phase boundary between charge-ordered insulating and metallic phases. This approach can treat frustrated systems and be easily extended to fermion models with spin.