Transfer matrix approach to quantum systems subject to certain Lindblad evolution

Bhat, Junaid Majeed (author), Žnidarič, Marko (author)

Solving for the time evolution of a many particle system whose dynamics is governed by Lindblad equation is hard. We extend the use of the transfer matrix approach to a class of Lindblad equations that admit a closed hierarchy of two point correlators. An example that we treat is the XX spin chain, i.e., free fermions, subject to the local onsite dephasing, but can be extended to other Hermitian dissipators, e.g., nonlocal dephasing. We find a simple expression of the Green's function in the Laplace domain. The method can be used to get analytical results in the thermodynamic limit, for instance, to get the evolution of the magnetization density and to explicitly see the crossover between ballistic and diffusive behavior, or to show that the correlations between operators at distance l decay with time as $1/t^{[l/2]+1/2}$. It also provides a fast numerical method to determine the evolution of the density with a complexity scaling with the system size more favorably than in previous methods, easily allowing one to study systems with $\sim 10^6$ spins.

• Language: English
• Keywords: quantum mechanics, quantum many-body systems, 1-dimensional spin chains, diffusion
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 174306-1-174306-11
• Numbering: Vol. 111, iss. 17
• PID: 20.500.12556/RUL-182239
• UDC: 530.145
• ISSN on article: 2469-9950
• DOI: 10.1103/PhysRevB.111.174306
• COBISS.SI-ID: 276512515
• Publication date in RUL: 05.05.2026

Record is a part of a journal

• Title: Physical review
• Publisher: American Physical Society
• ISSN: 2469-9950
• COBISS.SI-ID: 2997348

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, kvantni večdelčni sistemi, enodimenzionalne spinske verige, difuzija

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J1-4385
• Name: Kvantna večdelčna fizika in nehermitskost