Probing the entanglement of operator growth

TL;DR

This paper investigates operator growth and entanglement in systems with Lie symmetries using quantum information tools, revealing universal features and simplifying calculations through symmetry-based methods.

Contribution

It introduces a symmetry-based approach to study operator growth, bypassing the Lanczos algorithm, and demonstrates universal entanglement features in systems with SU(1,1) and SU(2) symmetries.

Findings

Quantities exhibit universal features consistent with the operator growth hypothesis.

Symmetry-based methods simplify the calculation of operator growth measures.

Operator entanglement properties can be studied directly from symmetry considerations.

Abstract

In this work we probe the operator growth for systems with Lie symmetry using tools from quantum information. Namely, we investigate the Krylov complexity, entanglement negativity, von Neumann entropy and capacity of entanglement for systems with SU(1,1) and SU(2) symmetry. Our main tools are two-mode coherent states, whose properties allow us to study the operator growth and its entanglement structure for any system in a discrete series representation of the groups under consideration. Our results verify that the quantities of interest exhibit certain universal features in agreement with the universal operator growth hypothesis. Moreover, we illustrate the utility of this approach relying on symmetry as it significantly facilitates the calculation of quantities probing operator growth. In particular, we argue that the use of the Lanczos algorithm, which has been the most important tool in the study of operator growth so far, can be circumvented and all the essential information can be extracted directly from symmetry arguments.