A simplified and improved approach to tensor network operators in two dimensions

Abstract

Matrix product states (MPS) and matrix product operators (MPOs) are one dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality and wide range of applicability of DMRG. However, current algorithms for two dimensional (2D) tensor network states, known as projected entangled-pair states (PEPS), rarely employ the associated 2D tensor network operators, projected entangled-pair operators (PEPOs), due to their computational cost and conceptual complexity. To lower these two barriers, we describe how to reformulate a PEPO into a set of tensor network operators that resemble MPOs by considering the different sets of local operators that are generated from sequential bipartitions of the 2D system. The expectation value of a PEPO can then be evaluated on-the-fly using only the action of MPOs and generalized MPOs at each step of the approximate contraction of the 2D tensor network. This technique allows for the simpler construction and more efficient energy evaluation of 2D Hamiltonians that contain finite-range interactions, and provides an improved strategy to encode long-range interactions that is orders of magnitude more accurate and efficient than existing schemes.

16 pages, 7 figures

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• Simulation methods for open quantum many-body systems
• The Shape of Full Configuration Interaction to Come
• Dynamical Phase Transitions in a 2D Classical Nonequilibrium Model via 2D Tensor Networks
• Optimal sampling of dynamical large deviations via matrix product states
• Generating Function for Tensor Network Diagrammatic Summation
• Entanglement in the quantum phases of an unfrustrated Rydberg atom array
• Numerical continuum tensor networks in two dimensions
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States