טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBiadsy Tasneem
SubjectStuding Many-Body Localization in Disordered
Fermi-Hubbard Models using Spin-Echoes
DepartmentDepartment of Physics
Supervisor Professor Netanel Lindner


Abstract

The presence of imperfections and disorder in quantum systems is usually considered as a matter of concern. Strikingly, it turns out that disorder in quantum systems might be responsible for various fascinating and interesting phenomena including glassy behaviors and “localization”. In this work we study several aspects of localization in interacting many-body systems. In particular, we study its features in systems with a global non-Abelian symmetry, and present a new probe of this phenomenon in Fermi-Hubbard models.

The concept of “Localization” was first introduced by Philip Anderson in 1958. Back

then, Anderson showed that a propagating wave function of a quantum particle in a

disordered medium can be trapped in space. The taste of such a striking phenomenon coincided then with experimental discoveries showing a similar behavior in silicon-doped semiconductors. The presence of interactions in such a system extends this interesting phenomenon to a broader and richer phenomenon in which disorder and interactions both play role. The many-body localized (MBL) phase challenges thermalization, which is one of the core principles. In MBL systems, thermalization is impeded and the system fails to behave as a heat bath for its subsystems leading to a generic and exotic phase characterized by slow long-time dynamics. This unconventional slow dynamics enables the system to preserve its initial state for long times.

This thesis splits into two main projects. The first project deals with quantum

many body systems with global non-Abelian symmetries. Recently, it was conjectured that MBL is inconsistent with such symmetries. Our goal in the first project was to study the possibility of stabilizing MBL in a strongly disordered model by turning on an infinitesimally small field which breaks the non-abelian symmetry. In this project, I numerically show that in a random Heisenberg model, a finite strong disorder is needed to stabilize the system. Besides this, I further study the phase diagram of the MBL-to-ETH phase transition in the extended random XXZ model and I also find its dependence on energy, interaction strength and disorder strength in the system.

In the second work, which is the core of this thesis, I study the possibly to use a

global spin-echo protocol in the context of detecting MBL in disordered Fermi-Hubbard models. I show that the signal is characterized by a timescale that depends nonmonotonically on the disorder strength as it is increased through the many-body localization transition. The results of this work yield a strong tool for detecting the

transition acquiring only short time evolution, what makes it considerably efficient numerically and an attractive tool for experimental implementations.