Generating Function for Tensor Network Diagrammatic Summation

TL;DR

This paper introduces a generating function approach combined with automatic differentiation to efficiently perform tensor network diagrammatic summations, enabling advanced analysis of quantum many-body systems.

Contribution

The paper presents a novel generating function method for tensor network diagrammatic summation, improving computational efficiency and enabling new analyses of quantum systems.

Findings

Successfully computed variational excited states

Analyzed dynamical structure factors

Investigated entanglement properties of excited states

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.