טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentEyal Bairey
SubjectInducing Many-Body Localization with a Periodic Drive
DepartmentDepartment of Physics
Supervisor Professor Lindner Netanel
Full Thesis textFull thesis text - English Version


Abstract

A promising direction in the search for novel phases of matter is the addition of a time-periodic driving field to an otherwise ordinary material. In addition to new ways for achieving known phases, this setting enables unique phases that could not exist in equilibrium. However, it faces a fundamental obstacle: the tendency of generic interacting systems to absorb energy indefinitely from the driving field. This limits the lifetime of these non-equilibrium phases - in the long-time limit, these systems are believed heat up to a featureless infinite-temperature state.

Surprisingly, this heating can be prevented by the addition of disorder. Sufficiently strong disorder can cause an interacting system to enter the many-body localized (MBL) phase, which extends the Anderson insulator to the setting of an interacting many-body system. This localized phase is characterized by a lack of transport and by long-term memory of local observables.

Generically, addition of a time-periodic drive to a static many-body localized system has a delocalizing effect. In particular, a low-frequency drive relaxes energy conservation, allowing the particles to hop more easily in the disordered potential; this often leads to delocalization and unbounded energy absorption. However, for a periodic drive with sufficiently high frequency, energy absorption by the localized particles is suppressed, and the localized phase survives if the driving amplitude is not too strong. Thus disorder allows meaningful correlations to survive for arbitrarily long times, such that a sharp notion of a phase can survive in the presence of a drive.

Can a specific periodic drive have an opposite effect, inducing localization? Here, we show such an effect for an AC electric field, which takes a static delocalized system into the many-body localized phase. Applying an AC-electric field to a 1D system of weakly disordered, interacting hardcore bosons leads to a suppression of the effective static hopping amplitude, through the phenomenon of coherent suppression of tunneling. The suppression of the hopping amplitude increases the relative strength of disorder, causing the system to enter the MBL phase. We investigate this transition numerically by examining quasi-energy level statistics obtained by exact diagonalization, as well as long term memory of local observables obtained by numerically exact methods for time evolution of an initial state. We find a transition into the MBL phase above a critical driving frequency and in a range of driving amplitudes, in agreement with theoretical arguments. Our results suggest the use of an AC electric field for stabilizing non-equilibrium phases, utilizing merely a weak static disorder.