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 the 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.
Highlights
The study of quantum many-body systems using tensor networks (TNs) has witnessed great success in the last three decades [1,2,3]
In this paper, inspired by the generating functional method in quantum field theory (QFT), we propose a set of generating functions for TNs, which encode TN diagrammatic summations as leading-order expansion coefficients
We find that, depending on the origins of diagrammatic summation, the generating functions can be divided into two classes, one for TN state and the other for TN operators, which we introduce separately
Summary
The study of quantum many-body systems using tensor networks (TNs) has witnessed great success in the last three decades [1,2,3]. Numerous progress has been made in various directions, including determining low-energy excited states [8], exploring dynamical and finite temperature properties [9], and finding valuable applications in long-range interacting systems [10,11]. These developments deepen our theoretical understanding of many-body systems [12] and bridge TN methods to real experiments [13].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
