Involved numerical simulations performed by a team of theoretical physicists from Kaiserslautern and the University of Manitoba in Canada have provided evidence that a peculiar quantum phase of matter, termed many-body localized, which was believed to remain in a nonequilibrium state forever, may eventually thermalize on extremely long time scales. These findings obtained mainly on the high-performance cluster "Elwetritsch" at the University of Kaiserslautern were recently published in the journal Physical Review Letters as Editors suggestion and covered in a Synopsis article in Physics.
Whether or not a small partition of an isolated quantum many-body system approaches thermal equilibrium is a long-standing question in physics. While equilibration in classical systems is more or less understood the same is not true in the quantum world where interference phenomena dominate the time evolution of particles. In the late 50th Nobel laurate Phillip Anderson showed that non-interacting electrons in a disordered material could stay localized, i.e. remain in a small spatial region of the material forever rather than diffusing through the whole system. This phenomenon of Anderson localization was initially thought to break down when interactions between particles are present until a peculiar new state of matter was discovered termed many-body localized (MBL). Similarly to Anderson localization, MBL phases are not expected to show any kind of particle diffusion and so should not thermalize. The long-time dynamics of interacting disordered systems is notoriously difficult to describe theoretically or to simulate numerically and until today there is no comprehensive understanding of MBL. Now a team of theorists from Kaiserslautern and the University of Manitoba in Canada including Maximilian Kiefer-Emmanouilidis, Dr. Razmik Unanyan, Prof. Jesko Sirker and Prof. Michael Fleischhauer found that particles in an MBL system actually continue to diffuse through it. They show this by numerically calculating the contribution to a subsystem’s entropy arizing from fluctuations in the numbers of particles moving between the system’s different regions, known as number entropy. If the system was truly localized the number fluctuations and thus the number entropy should quickly reach a small constant value. Instead the simulations showed that the number entropy continues to grow in time proportional to ln(ln(t)). This indicated that particles continued to diffuse throughout the system, albeit extremely slowly. The unexpected result suggests that either an unknown effect makes the system take much longer than previously thought to become localized, or that true MBL may actually not exist.
Publication:
M. Kiefer-Emmanouilidis, R. Unanyan, M. Fleischhauer, J. Sirker
Evidence for unbounded growth of the number entropy in many-body localized phases
Phys. Rev. Lett. 124 243601 (2020); https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.243601
see also:
Erika K. Carlson: Many-Body Localized States Inch Toward Equilibrium, Physics 13, s80 (2020)