Simulating both parity sectors of the Hubbard Model with Tensor Networks
arXiv:2106.13583 · doi:10.1103/PhysRevB.104.155118
Abstract
Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical potential is one such problem. Our method is based on projected entangled pair states (PEPS) using imaginary time evolution. We demonstrate that it provides accurate estimators for the ground state of the model, including cases where Monte Carlo simulations fail miserably. In particular it shows near to optimal, that is linear, scaling in lattice size. We also present a novel approach to directly simulate the subspace with an odd number of fermions. It allows to independently determine the ground state in both sectors. Without a chemical potential this corresponds to half filling and the lowest energy state with one additional electron or hole. We identify several stability issues, such as degenerate ground states and large single particle gaps, and provide possible fixes.
20 pages, 20 figures
References in corpus (12)
- The electronic properties of graphene
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Classical simulation of infinite-size quantum lattice systems in one spatial dimension
- Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
- Criticality, the area law, and the computational power of PEPS
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Valence Bond Solids for Quantum Computation
- Algorithms for finite Projected Entangled Pair States
- Tensor Networks for Lattice Gauge Theories with continuous groups
- Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
- Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
- Investigation of the chiral antiferromagnetic Heisenberg model using PEPS