Many-BOdy Localization and Quantum Thermalization
Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration; when equilibration fails, so does much of our understanding. In isolated quantum systems, this breakdown is captured by the phenomenon known as many-body localization. Many-body localized phases violate Ohm's law and Fourier's law as they conduct neither charge nor heat; they can exhibit symmetry breaking and/or topological orders in dimensions normally forbidden by Mermin-Wagner arguments; and they hold potential as strongly interacting quantum computers due to weak logarithmic dephasing. We are actively exploring a number of questions in this field, ranging from the effect of power-law interactions to coherent quantum control in the MBL phase.
While MBL systems fail to thermalize, there has also been recent excitement about exploring systems that reach thermal equilibrium extremely rapidly. In fact, as rapidly as nature allows! The approach to thermal equilibrium is typically characterized by the spreading of entanglement and the “scrambling” of quantum information. More precisely, scrambling describes the delocalization of quantum information over all of a system’s degrees of freedom. That there might exist fundamental limits on the rate of scrambling/thermalization has a long and storied history. At one extreme are strongly disordered MBL systems, where thermalization is absent and quantum information spreads slowly. At the other extreme, certain gauge theories appear to spread quantum information very quickly. However, these gauge theories are special—their thermal states are “holographically dual” to black holes in Einstein gravity. They are also highly symmetrical, display scale invariant physics, and do not order at low temperatures despite strong interactions. The key question that my group is focused on at the moment is: Where do typical interacting systems fall between these two extremes?
Interferometric Approach to Probing Fast Scrambling. Norman Y. Yao, Fabian Grusdt, Brian Swingle, Mikhail D. Lukin, Dan M. Stamper-Kurn, Joel E. Moore and Eugene A. Demler, arXiv:1607.01801.
Quasi Many-body Localization in Translation Invariant Systems. Norman Y. Yao, Chris R. Laumann, J. Ignacio Cirac, Mikhail D. Lukin, Joel E. Moore, Phys. Rev. Lett. 117, 240601 (2016).
Spin transport of weakly disordered Heisenberg chain at infinite temperature. Ilia Khait, Snir Gazit, Norman Y. Yao and Assa Auerbach, Phys. Rev. B 93, 224205 (2016).
Many-body Localization with Dipoles. Norman Y. Yao, Chris R. Laumann, Sarang Gopalakrishnan, Michael Knap, Markus Mueller, Eugene A. Demler and Mikhail D. Lukin, Phys. Rev. Lett. 113, 243002 (2014).