Variational methods for contracting projected entangled-pair states

Abstract

The norms or expectation values of infinite projected entangled-pair states (PEPS) cannot be computed exactly, and approximation algorithms have to be applied. In the last years, many efficient algorithms have been devised -- the corner transfer matrix renormalization group (CTMRG) and variational uniform matrix product state (VUMPS) algorithm are the most common -- but it remains unclear whether they always lead to the same results. In this paper, we identify a subclass of PEPS for which we can reformulate the contraction as a variational problem that is algorithm independent. We use this variational feature to assess and compare the accuracy of CTMRG and VUMPS contractions. Moreover, we devise a new variational contraction scheme, which we can extend to compute general N-point correlation functions.

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Cited by in corpus (25)

• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Fermionic tensor network methods
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Generating function for projected entangled-pair states
• Ground state search by local and sequential updates of neural network quantum states
• Extracting the Speed of Light from Matrix Product States
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
• Matrix product state fixed points of non-Hermitian transfer matrices
• Differentiable programming tensor networks for Kitaev magnets
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Simulating chiral spin liquids with projected entangled-pair states
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Scalable projected entangled-pair state representation of random quantum circuit states
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Les Houches Lecture Notes on Tensor Networks
• Competing pair density wave orders in the square lattice $t$-$J$ model
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS