Generating Function for Tensor Network Diagrammatic Summation

Abstract

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by computing variational excited states and dynamical structure factor of a quantum spin chain, and further investigating entanglement properties of excited states. Extensions to infinite size systems and higher dimension are outlined.

arXiv commentv1: 6 pages, 2 figures. v2: published version

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• The ITensor Software Library for Tensor Network Calculations
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Variational methods for contracting projected entangled-pair states
• Universal Rényi Entropy of Quasiparticle Excitations
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Generating function for projected entangled-pair states
• Automatic Differentiable Numerical Renormalization Group
• Projector formalism for kept and discarded spaces of matrix product states
• 2D excitation information by MPS method on infinite helixes
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS