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

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• Gradient methods for variational optimization of projected entangled-pair states
• Tensor network study of the Shastry-Sutherland model in zero magnetic field
• Lecture Notes of Tensor Network Contractions
• Loop optimization for tensor network renormalization
• Faster Methods for Contracting Infinite 2D Tensor Networks
• Unifying Projected Entangled Pair States contractions
• Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Excitations and the tangent space of projected entangled-pair states
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• Real-time simulation of the Schwinger effect with Matrix Product States
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
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• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Efficient simulation of Grassmann Tensor Product States
• Renormalization group contraction of tensor networks in three dimensions
• Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
• Spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks
• A universal tensor network algorithm for any infinite lattice
• Conversion of projected entangled pair states into a canonical form
• A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
• Simulating 2+1d ${\mathbb{Z}}_3$ lattice gauge theory with iPEPS
• Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
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• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
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• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices
• Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study
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• Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State
• Ground state properties of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ determined from $\text{ab initio}$ Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions
• Tensor networks for quantum computing
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• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
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• Finite Projected Entangled Pair States for the Hubbard model
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• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
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• Functional Tensor Network Solving Many-body Schrödinger Equation
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• Thermal bosons in 3d optical lattices via tensor networks
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• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Monte Carlo simulations of two-dimensional fermion systems with string-bond states
• Frustration-Induced Superconductivity in the $t$-$t^{\prime }$ Hubbard Model
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Optimization of infinite projected entangled pair states: The role of multiplets and their breaking
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• Finite-size scaling on the torus with periodic projected entangled-pair states
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