Date:
Thu, 29/11/201812:00-13:30
Location:
Danciger B building, Seminar room
Lecturer: Yuval Baum, Institute of Quantum Information and Matter, Caltech
Abstract:
The many body localized phase provides the rst and only example of a generic quantum inter-acting system that does not reach thermal equilibrium, and thereby violates the most fundamental
principles of statistical physics. In the last decade, an enormous theoretical eort was invested in
understanding the nature of this phase. It has attracted a similar deal of attention also within the
experimental community, as it has the potential of storing information about initial states for long
times and it allows the application of driving protocols without heating the system to an innite
temperature.
A key ingredient for achieving the MBL phase is randomness. The roots of this phase lie within the
phenomenon of Anderson localization, where non-interacting particles form a localized non-ergodic phase. It is the question regarding the fate of Anderson localization in the presence of interactions that plants the seed for the discovery of the MBL phase.
We pose the question whether randomness is indeed an essential ingredient in achieving generic non-ergodic interacting phases. We propose the idea that the essential ingredient for MBL is localization, which does not necessarily mean disorder. We analyze the spectral and the dynamical properties of one-dimensional interacting fermions and spins in the presence of both disorder and linear potential.
We show that by considering these two dierent localizing mechanisms, i.e., disorder and linear elds, one may construct a two-dimensional phase diagram which hosts a connected non-ergodic (MBL) phase.
We also examine the eect of periodic driving on the dynamics of many-body systems and show
how such driving provides a general framework for controlling the transport properties in the system, as well establish mobile composite particles. We demonstrate that by including successive driving terms, it is possible to completely suppress the motion of particles, and eectively localize the many-body system, without the presence of disorder.
While at this point we can not make conclusive statements about the nature of this phase in
higher dimensions, the lack of randomness and the low sensitivity to dimensionality may render
these systems more accessible to a theoretical investigation in dimensions larger than one.
Furthermore, we make steps towards employing well studiedmachine learning techniques to address the issue of nite size. Although we don't show explicitly if it is possible to use such techniques to numerically solve larger system sizes, we show that a mapping of the disorder realization to the level statistics is easily learned.
1. Y. Baum, Evert P. L. van Nieuwenburg and Gil Refael, "From Dynamical Localization to
Bunching in interacting Floquet Systems", SciPost Phys. 5, 017 (2018).
2. Y. Baum, Evert P. L. van Nieuwenburg and Gil Refael, "From Bloch Oscillations to Many
Body Localization in Clean Interacting Systems", arXiv:1808.00471 (2018).
Abstract:
The many body localized phase provides the rst and only example of a generic quantum inter-acting system that does not reach thermal equilibrium, and thereby violates the most fundamental
principles of statistical physics. In the last decade, an enormous theoretical eort was invested in
understanding the nature of this phase. It has attracted a similar deal of attention also within the
experimental community, as it has the potential of storing information about initial states for long
times and it allows the application of driving protocols without heating the system to an innite
temperature.
A key ingredient for achieving the MBL phase is randomness. The roots of this phase lie within the
phenomenon of Anderson localization, where non-interacting particles form a localized non-ergodic phase. It is the question regarding the fate of Anderson localization in the presence of interactions that plants the seed for the discovery of the MBL phase.
We pose the question whether randomness is indeed an essential ingredient in achieving generic non-ergodic interacting phases. We propose the idea that the essential ingredient for MBL is localization, which does not necessarily mean disorder. We analyze the spectral and the dynamical properties of one-dimensional interacting fermions and spins in the presence of both disorder and linear potential.
We show that by considering these two dierent localizing mechanisms, i.e., disorder and linear elds, one may construct a two-dimensional phase diagram which hosts a connected non-ergodic (MBL) phase.
We also examine the eect of periodic driving on the dynamics of many-body systems and show
how such driving provides a general framework for controlling the transport properties in the system, as well establish mobile composite particles. We demonstrate that by including successive driving terms, it is possible to completely suppress the motion of particles, and eectively localize the many-body system, without the presence of disorder.
While at this point we can not make conclusive statements about the nature of this phase in
higher dimensions, the lack of randomness and the low sensitivity to dimensionality may render
these systems more accessible to a theoretical investigation in dimensions larger than one.
Furthermore, we make steps towards employing well studiedmachine learning techniques to address the issue of nite size. Although we don't show explicitly if it is possible to use such techniques to numerically solve larger system sizes, we show that a mapping of the disorder realization to the level statistics is easily learned.
1. Y. Baum, Evert P. L. van Nieuwenburg and Gil Refael, "From Dynamical Localization to
Bunching in interacting Floquet Systems", SciPost Phys. 5, 017 (2018).
2. Y. Baum, Evert P. L. van Nieuwenburg and Gil Refael, "From Bloch Oscillations to Many
Body Localization in Clean Interacting Systems", arXiv:1808.00471 (2018).