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arXiv:1305.4151 · Physical Review B

Monte Carlo simulations of two-dimensional fermion systems with string-bond states

Jeong-Pil Song, Rudolf Torsten Clay

Published Feb 3, 2014• 8 citations
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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.

DOI
10.1103/physrevb.89.075101

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Simulating frustrated quantum magnets is among the most challenging tasks in computational physics. We apply string-bond states, a recently introduced Ansatz which combines tensor networks with Monte Carlo based methods to the simulation of frustrated quantum systems in both two and three dimensions. We compare our results with existing results for unfrustrated and two-dimensional systems with open boundary conditions and demonstrate that the method applies equally well to the simulation of frustrated systems with periodic boundaries in both two and three dimensions.
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