Fermionic tensor network contraction for arbitrary geometries
arXiv:2410.02215 · doi:10.1103/PhysRevResearch.7.023193
Abstract
We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the quimb library. Using hyperoptimized approximate contraction strategies, we present benchmark fermionic projected entangled pair states simulations of finite Hubbard models defined on the three-dimensional diamond lattice and random regular graphs.
9 pages, 9 figures
References in corpus (40)
- The density-matrix renormalization group in the age of matrix product states
- Entanglement renormalization
- A class of quantum many-body states that can be efficiently simulated
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Stripe order in the underdoped region of the two-dimensional Hubbard model
- Tensor networks for complex quantum systems
- Competing states in the t-J model: uniform d-wave state versus stripe state
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
- Tensor network states and algorithms in the presence of a global U(1) symmetry
- Tensor network decompositions in the presence of a global symmetry
- Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
- Is there evidence for exponential quantum advantage in quantum chemistry?
- Fermionic Projected Entangled Pair States
- Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
- Hyper-optimized tensor network contraction
- Fermionic multi-scale entanglement renormalization ansatz
- Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
- Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond
- Tensor network states and algorithms in the presence of a global SU(2) symmetry
- Spin-S Kagome quantum antiferromagnets in a field with tensor networks
- Fermionic Matrix Product States and One-Dimensional Topological Phases
- Unitary circuits for strongly correlated fermions
- Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
- Low communication high performance ab initio density matrix renormalization group algorithms
- Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice
- Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations
- Fermionic Implementation of Projected Entangled Pair States Algorithm
- Efficient simulation of Grassmann Tensor Product States
- Fermionic projected entangled-pair states and topological phases
- Simulation of three-dimensional quantum systems with projected entangled-pair states
- Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field
- A universal tensor network algorithm for any infinite lattice
- A beginner's guide to non-abelian iPEPS for correlated fermions
- Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
- Fermionic tensor network methods
- Gradient optimization of fermionic projected entangled pair states on directed lattices
- Thermal bosons in 3d optical lattices via tensor networks
- Tensor Network Computations That Capture Strict Variationality, Volume Law Behavior, and the Efficient Representation of Neural Network States
- Projected Entangled Pair States with flexible geometry