Transfer matrix approach to quantum systems subject to certain Lindblad evolution

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

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.

• Jezik: Angleški jezik
• Ključne besede: quantum mechanics, quantum many-body systems, 1-dimensional spin chains, diffusion
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: Str. 174306-1-174306-11
• Številčenje: Vol. 111, iss. 17
• PID: 20.500.12556/RUL-182239
• UDK: 530.145
• ISSN pri članku: 2469-9950
• DOI: 10.1103/PhysRevB.111.174306
• COBISS.SI-ID: 276512515
• Datum objave v RUL: 05.05.2026

Gradivo je del revije

• Naslov: Physical review
• Založnik: American Physical Society
• ISSN: 2469-9950
• COBISS.SI-ID: 2997348

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: kvantna mehanika, kvantni večdelčni sistemi, enodimenzionalne spinske verige, difuzija

Projekti

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: J1-4385
• Naslov: Kvantna večdelčna fizika in nehermitskost