Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians

Abstract

In a recent contribution [Phys. Rev. B 81, 165104 (2010)] fermionic Projected Entangled-Pair States (PEPS) were used to approximate the ground state of free and interacting spinless fermion models, as well as the $t$-$J$ model. This paper revisits these three models in the presence of an additional next-nearest hopping amplitude in the Hamiltonian. First we explain how to account for next-nearest neighbor Hamiltonian terms in the context of fermionic PEPS algorithms based on simulating time evolution. Then we present benchmark calculations for the three models of fermions, and compare our results against analytical, mean-field, and variational Monte Carlo results, respectively. Consistent with previous computations restricted to nearest-neighbor Hamiltonians, we systematically obtain more accurate (or better converged) results for gapped phases than for gapless ones.

10 pages, 11 figures, minor changes

References in corpus (17)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Simulation of anyons with tensor network algorithms
• Magnetism and superconductivity in the $t-t^{\prime }-J$ model
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Anyonic entanglement renormalization
• Finite compressibility in the low-doping region of the two-dimensional $t-J$ model
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States