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

Abstract

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.

Keywords

fizika kondenzirane snovi;močno korelirani sistemi;kvantni kaos;condensed matter physics;strongly-correlated systems;quantum chaos;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 538.9
COBISS: 120644611 Link will open in a new window
ISSN: 2643-1564
Views: 23
Downloads: 19
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Other data

Secondary language: Slovenian
Secondary keywords: fizika kondenzirane snovi;močno korelirani sistemi;kvantni kaos;
Type (COBISS): Scientific work
Pages: str. L022068-1-L022068-8
Volume: ǂVol. ǂ4
Issue: ǂiss. ǂ2
Chronology: 2022
DOI: 10.1103/PhysRevResearch.4.L022068
ID: 16411114