Efficient representation of long-range interactions in tensor network algorithms

Abstract

We describe a practical and efficient approach to represent physically realistic long-range interactions in two-dimensional tensor network algorithms via projected entangled-pair operators (PEPOs). We express the long-range interaction as a linear combination of correlation functions of an auxiliary system with only nearest-neighbor interactions. To obtain a smooth and radially isotropic interaction across all length scales, we map the physical lattice to an auxiliary lattice of expanded size. Our construction yields a long-range PEPO as a sum of ancillary PEPOs, each of small, constant bond dimension. This representation enables efficient numerical simulations with long-range interactions using projected entangled pair states.

arXiv commentMain Document: 9 pages, 7 figures. Moved supplementary material into main text. Added more discussion of computational cost. Fixed minor errors in Figs 2c and 3a

References in corpus (37)

• The density-matrix renormalization group in the age of matrix product states
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Criticality, the area law, and the computational power of PEPS
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Corner Transfer Matrix Renormalization Group Method
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Matrix product operator representations
• Tensor Network Renormalization
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Variational optimization with infinite projected entangled-pair states
• Gradient methods for variational optimization of projected entangled-pair states
• Renormalization of tensor-network states
• Applying matrix product operators to model systems with long-range interactions
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Finite automata for caching in matrix product algorithms
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
• Spin-S Kagome quantum antiferromagnets in a field with tensor networks
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• Tensor operators: constructions and applications for long-range interaction systems
• Reference electronic structure calculations in one dimension
• The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain
• Optimized contraction scheme for tensor-network states
• Multigrid Algorithms for Tensor Network States
• Sliced Basis Density Matrix Renormalization Group for Electronic Structure
• Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field
• Lowering of the complexity of quantum chemistry methods by choice of representation

Cited by in corpus (13)

• The Shape of Full Configuration Interaction to Come
• Conversion of projected entangled pair states into a canonical form
• Multi-sliced Gausslet Basis Sets for Electronic Structure
• Generating Function for Tensor Network Diagrammatic Summation
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices
• On the generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions
• A simplified and improved approach to tensor network operators in two dimensions
• Numerical continuum tensor networks in two dimensions
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Quantum Phase Transitions in Long-Range Interacting Hyperuniform Spin Chains in a Transverse Field
• Efficient optimization of variational tensor-network approach to three-dimensional statistical systems
• Emergence of Gaussianity in the thermodynamic limit of interacting fermions
• Low-rank representation of tensor network operators with long-range pairwise interactions