טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDiringer Asaf
SubjectMany Body Localized Systems Subjected to Two-tone Drives
DepartmentDepartment of Physics
Supervisor Professor Netanel Lindner


Abstract

Systems subjected to a time-periodic drive, also known as Floquet systems, offer an exciting way to manipulate ordinary materials into producing exotic behavior. In particular, these systems provide a promising direction in the search for novel phases, which are absent in equilibrium systems. However, a significant challenge is met when this approach is applied to isolated interacting quantum systems. Generically, such systems tend to heat up in the presence of a time-periodic drive, approaching an infinite-temperature like state. This tendency poses a fundamental obstacle to Floquet-engineering of novel non-equilibrium phases in closed quantum systems.

Fortunately, by adding disorder, the absorption of energy from the drive can be avoided. In the presence of strong disorder, many-body systems enter a localized phase. This quantum many-body localized phase (MBL) is characterized by a lack of transport and by long-term memory of local observables. For an MBL phase, energy absorption from a weak time-periodic drive may be suppressed, such that many-body localization persists in the presence of the drive. However, a sufficiently strong drive leads to delocalization. By relaxing the energy conservation, a time-periodic drive provides additional means for excitations to delocalize; when these processes proliferate, the system thermalizes. Importantly, the critical driving amplitude for delocalization generically decreases with decreasing driving frequency.

In this thesis, we studied the relation between the critical driving amplitude for delocalization and the driving frequency. First, we studied the frequency dependence of the critical driving amplitudes for a system characterized by a single fundamental frequency. We studied numerically a periodically driven spin-1/2 chain and obtained the phase diagram in the case of a cosine and a square-wave drive. Comparing the two drives, we find that for both of them the critical amplitude is monotonic as a function of frequency. However, for the smooth cosine drive we find that the critical amplitude as a function of frequency exhibits a plateau at intermediate frequencies, which is absent in the case of the square-wave drive. We suggest a scheme based on the density of drive-induced resonances, capable of providing a qualitative estimation for the frequency dependence of the critical driving amplitudes of our two different drives . This scheme can be easily generalized to drives of any operator or temporal form.

Next, we studied the fate of many-body localization in the presence of a two-frequency drive. Two fast drives that synchronize only after many cycles effectively generate a long period. We investigated the critical driving amplitudes as a function of the commensurability of the two frequencies. For the case of a smooth drive, we found that the critical driving amplitude saturates at small effective frequencies. Our numerical simulations suggest that the drive induced transition is governed by the lowest order in perturbation theory which generates a frequency smaller than the local bandwidth. Our results raise the possibility that MBL may persist in isolated quantum systems subjected to a quasi-periodic drive, extending the notion of stable non-equilibrium phases even further.