The Study On Optimization Of Many-body Localization In One-dimensional Disordered Systems

There are many fascinating themes in the field of quantum many-body physics.Among them,the many-body localization phenomenon and the quantum thermalization phenomenon have been more and more appealing.An isolated quantum system which thermalizes satisfies the so-called eigenstate thermalization hypothesis:The eigenstates of the Hamiltonian of the system themselves appear to have the properties of thermalization.This hypothesis in quantum systems is like the ergodic hypothesis in classic systems.Due to the validation of the ergodic hypothesis,the long-time average of an observable of an isolated classic system is in accordance with its ensemble average in theory.Quantum systems that satisfy the eigenstate thermalization hypothesis have similar properties.Some quantum systems,however,don’t satisfy the eigenstate thermalization hypothesis.The eigenstates of such systems don’t possess the property of thermalization and therefore the system won’t thermalize and no classic correspondences can be found.Among them,there are many-body localized systems.These systems have many novel properties.For instance,the system has a set of quasi-local integrals of motion.This emergent integrability resists the loss of local characters as the systems evolve which can be understood as a kind of protection of information.Numerous approaches can be applied to reach many-body localization phase,e.g.,by on-site chemical potentials with disorders or by applying linear chemical potentials,etc.Since in practice,the strengths of the controls applied in a system are always finite,how to realize many-body localization systems in a more effective fashion becomes a meaningful topic.In this thesis,we introduce the problem of the most effective disorder for realizing many-body localization.The meaning of "effective" is defined by using the following two aspects:1)The strength of the random field is the lowest;2)The system suffers the slowest thermalization after the system was prepared in a state far from thermal equilibrium.We chose a series of 1-dimensional spinless fermion chains with different parameters as our objects of study.For short chains,we used exact diagonalization to investigate their entanglement entropies and gap ratios as well as their time evolution dynamics.For long chains,we used real-space renormalization which dropped off many physical details but lowered time and space complexities.We improved a kind of real-space renormalization groups so that it contains more physical details.This is the main innovation in this thesis.Besides,as the existence of the many-body phase transition is still under debate in the classic thermodynamics limit,we studied the dynamics of the many-body system under the influence of different random distributions.We initialized the systems with a set of product states and observe the growth of the halfchain entanglement entropy.By comparing the rates of growth of the entanglement entropies of the systems,we found an optimized random distribution as well,which can be seen as a generalization of our optimization.All these numerical methods and analyses inferred that the most effective disorder is not the uniform distribution as commonly considered.Some of our studies predicted that the most optimized distribution lies between the uniform distribution and the binary distribution.Our study can be used to build many-body localized systems more effectively in mesoscopic systems and can be tested in the near-term experiments.