n the study of quantum physics, one of the most powerful organizing principles is that of symmetry classifications. Here, particles and systems are grouped together by some feature
that is unchanged after a transformation. For example, a movie of a quantum mechanical system in equilibrium looks the same when played forward or backward—such a system
is called time-reversal symmetric. But recent realizations of novel phases of quantum matter in experiments require a generalization of these symmetry classifications to
driven systems coupled to their environment, where the external drive does not allow these systems to thermally equilibrate. Here, we provide such a generalization for fermionic quantum matter.

Our approach to the classification problem is bottom up, starting from ten fundamental symmetry transformations in fermionic state space. We pay particular attention to certain symmetries
that, in equilibrium, are associated with time reversal. In systems that are out of equilibrium, time is not reversible, so such symmetries require a complete rethinking.

Building on this framework, we uncover a fundamental distinction between the incarnations of the ten state-space symmetry classes, depending on whether the dynamics
proceeds in or out of equilibrium. This gives rise to 20 dynamical symmetry classes: ten each for equilibrium and nonequilibrium dynamics. The transformation laws obtained out
of equilibrium are sharply distinct from the known ones at equilibrium. Using the example of an interacting quantum wire, we show how this new understanding may help to
engineer and manipulate a topological phase.

Our analysis provides a comprehensive description of symmetry classes, in and out of equilibrium, which expressly includes systems with interactions. From a more
applied perspective, the work offers a concrete transformation rule book for the building blocks of dynamical evolution subject to symmetry constraints.

Alexander Altland, Michael Fleischhauer, and Sebastian Diehl
Symmetry classes of open fermionic quantum matter
Phys. Rev. X 11,021037 (2021); https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.021037

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)

Recently an article on Topological Insulators was publisehd in Physik Konkret, the Outreach Publication by the German Physical Society (DPG) for the general public. The article was co-authored by TopDyn PI Mathias Kläui. A copy and more information can be found at:

https://www.dpg-physik.de/veroeffentlichungen/publikationen/physikkonkret/copy_of_arbeitsmarkt-fuer-physikerinnen-und-physiker