Quantum and semi-classical dynamics of random spin chains: models and methods for quantum non-ergodic statistical physics

Cuny College Of Staten Island, Staten Island NY

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on fundamental aspects of how and whether descriptions of matter, such as fluid dynamics and thermodynamics presented in textbooks emerge from a system composed of many tiny interacting particles, such as atoms or electrons. Recent progress on a phenomenon known as many-body localization highlights the possibility of a breakdown of the conventional thermodynamic description. The PI will carry out a theoretical study of model systems to explore and quantify the degree of this breakdown and to investigate the possibility that interesting intermediate states of matter interpolate continuously between textbook thermodynamics and fully many-body localized phases. In a wave picture of particles that do not interact, scattering from random imperfections leads to destructive interference among the waves resulting in quantum mechanical states that are localized and do not conduct electricity. It is thought that turning on interactions among particles can lead to a dynamical form of localization, many-body localization, a conceptual ingredient in this research project. A significant offshoot of this work is the exploration and modelling of quantum control of localized states, novel experimental schemes for detecting many-body localization, and design of exotic models particularly favorable to numerical studies of these phenomena and novel approximation schemes to systematically extrapolate between classical and quantum mechanical simulations of matter. These theoretical studies will also complement and guide ongoing experimental efforts to "imitate" many-body localization using systems like ultracold atomic gases. This project will contribute to training undergraduate and graduate students in the field of condensed matter physics and many-body dynamics more generally. The PI will continue mentoring diverse students at the undergraduate, graduate levels and postdoctoral researchers. The PI will continue to organize conferences and a weekly seminar at the Graduate Center, serving the research community at the City University, New York and nearby institutions. The PI will also continue to seek opportunities to contribute to international condensed matter community including through organization of workshops. TECHNICAL SUMMARY This award supports theoretical research and education to investigate dynamical phenomena in excited but isolated many-body systems. The primary physical motivation here is the phenomenon of many-body localization which is broadly defined as stalled ergodicity of strongly excited many-body dynamics, effectively at finite temperature or, better, finite entropy per particle. In certain quantum models a sharp dynamical transition is expected to separate localized from diffusive phases. Existence of such a transition in spin models of classical many-body dynamics is an intriguing possibility previously explored numerically by the PI and collaborators and tentatively ruled out due to prevalence of localized classical chaos. There are two complementary parts to the research agenda. The first part will be focused on developing conceptual and numerical tools for studying models of many-body localization that overcome limitations of commonly used methods. The phenomenology of emergent integrability recently introduced by PI and others for fully many-body localized spectra will be streamlined but also extended to cases where a nearby mobility edge might exist. Efficient variational methods, using matrix-product states will be developed to compute excited eigenstates of very long spin chains, but also to approximate many-body dynamics near "classical" trajectories. In parallel, the second part of the research agenda will explore the notion of many-body localization in novel settings: many-body localization in traps, self-dual models of many-body localization, adiabatic annealing into the Hilbert glass phase inside many-body localization. Each of these three model specific studies is expected to produce general insights into the physics of these dynamical transitions. This project will contribute to training undergraduate and graduate students in the field of condensed matter physics and many-body dynamics more generally. The PI will continue mentoring diverse students at the undergraduate, graduate levels and postdoctoral researchers. The PI will continue to organize conferences and a weekly seminar at the Graduate Center, serving the research community at the City University, New York and nearby institutions. The PI will also continue to seek opportunities to contribute to international condensed matter community including through organization of workshops.