Sampling reduced density matrix to extract fine levels of entanglement spectrum and restore entanglement Hamiltonian

Bin-Bin Mao, Yi-Ming Ding, Zhe Wang, Shijie Hu () and Zheng Yan ()
Additional contact information
Bin-Bin Mao: Westlake University
Yi-Ming Ding: Westlake University
Zhe Wang: Westlake University
Shijie Hu: Beijing Computational Science Research Center
Zheng Yan: Westlake University

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract The reduced density matrix (RDM) plays a key role in quantum entanglement and measurement, as it allows the extraction of almost all physical quantities related to the reduced degrees of freedom. However, restricted by the degrees of freedom in the environment, the total system size is often limited, let alone the subsystem. To address this challenge, we propose a quantum Monte Carlo scheme with a low technical barrier, enabling precise extraction of the RDM. To demonstrate the power of the method, we present the fine levels of the entanglement spectrum (ES), which is the logarithmic eigenvalues of the RDM. We clearly show the ES for a 1D ladder with a long entangled boundary, and that for the 2D Heisenberg model with a tower of states. Furthermore, we put forward an efficient way to restore the entanglement Hamiltonian in operator-form from the sampled RDM data. Our simulation results, utilizing unprecedentedly large system sizes, establish a practical computational framework for determining entanglement quantities based on the RDM, such as the ES, particularly in scenarios where the environment has a huge number of degrees of freedom.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/s41467-025-58058-0 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-58058-0

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-025-58058-0

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().