Lindbladian dissipation of strongly-correlated quantum matter

Sá, Lucas (author), Ribeiro, Pedro (author), Prosen, Tomaž (author)

We propose the Sachdev-Ye-Kitaev Lindbladian as a paradigmatic solvable model of dissipative many-body quantum chaos. It describes N strongly coupled Majorana fermions with random all-to-all interactions, with unitary evolution given by a quartic Hamiltonian and the coupling to the environment described by M quadratic jump operators, rendering the full Lindbladian quartic in the Majorana operators. Analytical progress is possible by developing a dynamical mean-field theory for the Liouvillian time evolution on the Keldysh contour. By disorder-averaging the interactions, we derive an (exact) effective action for two collective fields (Green’s function and self-energy). In the large-N, large-M limit, we obtain the saddle-point equations satisfied by the collective fields, which determine the typical timescales of the dissipative evolution, particularly the spectral gap that rules the relaxation of the system to its steady state. We solve the saddle-point equations numerically and find that, for strong or intermediate dissipation, the system relaxes exponentially, with a spectral gap that can be computed analytically, while for weak dissipation, there are oscillatory corrections to the exponential relaxation. In this letter, we illustrate the feasibility of analytical calculations in strongly correlated dissipative quantum matter.

• Language: English
• Keywords: condensed matter physics, strongly-correlated systems, quantum chaos
• Work type: Scientific work
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 30.06.2022
• Year: 2022
• Number of pages: Str. L022068-1-L022068-8
• Numbering: Vol. 4, iss. 2
• PID: 20.500.12556/RUL-140002
• UDC: 538.9
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.4.L022068
• COBISS.SI-ID: 120644611
• Publication date in RUL: 09.09.2022

Record is a part of a journal

• Title: Physical review research
• Publisher: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

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: fizika kondenzirane snovi, močno korelirani sistemi, kvantni kaos

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES