Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
Tong Shen, Hatem Barghathi, Adrian Del Maestro, Brenda M. Rubenstein
The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states, like the entanglement entropy, can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resources for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive Auxiliary Field Quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear - and unique - signatures of the underlying electronic behavior even when those features are less pronounced in more conventional correlation functions.
This repository includes links, code, scripts, and data to generate the figures in a paper.
The data for this project was generated using the source code SwapQMC. Everything included in the data directory was processed from the raw data on Zenodo 
The creation of these materials was supported in part by the NSF CTMC CAREER Award 2046744 and the NSF under Grant No. DMR-2041995.