Spectroscopic shifts as a signature of manybody localization phase transition in a onedimensional transmon array 

Author:  Tuohino, Sasu^{1} 
Organizations: 
^{1}University of Oulu, Faculty of Science, Physics 
Format:  ebook 
Version:  published version 
Access:  open 
Online Access:  PDF Full Text (PDF, 2.2 MB) 
Pages:  76 
Persistent link:  http://urn.fi/URN:NBN:fi:oulu201909212918 
Language:  English 
Published: 
Oulu : S. Tuohino,
2019

Publish Date:  20190924 
Thesis type:  Master's thesis 
Tutor: 
Silveri, Matti 
Reviewer: 
Tuorila, Jani Silveri, Matti 
Description: 
Abstract Manybody localization is a phase of matter, which can occur in systems with strong disorder and interactions. One of the main characteristics of the manybody localized phase is that it cannot thermalize because localization slows or stops the propagation of information inside the system. Here, we study manybody localization in a onedimensional transmon qubit array theoretically and numerically. Differing from frequently used approaches to manybody localization, we study the dynamical phase transition between a thermalized phase and the manybody localized phase by using a numerical method that is based on Fermi’s golden rule. This method makes it possible to distinguish the thermalized phase from the manybody localized phase and allows one to estimate how much disorder is required for the manybody localization phase transition. The distinction between the phases is made by a “soft” gap which appears at the zerofrequency and is known as a universal sign of localization. Unlike many other methods, which are used to recognize the manybody localized phase, the method in question can be easily applied to experiments. In the system that we have chosen the transmon qubits are capacitively coupled to each other, and the system is driven by a harmonic external magnetic flux that induces transitions between the energy eigenstates of the system. We calculated the numerical results for a system with eight transmon qubits, and to make calculations simpler, we assumed that the temperature of the system is infinite. The size of the system is limited by the computational expensiveness of our method. Somewhat surprisingly, the most laborious part of the calculations proved to be the Fermi’s golden rule, which is used to calculate the transition rate spectrum. The results show that the method in question can distinguish the manybody localized phase if the strength of disorder in the system is large, but near the manybody localized phase transition, it is challenging to observe the difference between the thermalized phase and the manybody localized phase. We calculated the transition rate spectra using different values of onsite interaction strength. The results show us that the disorder strength needed for the phase transition is smaller if the onsite interaction strength is weak or very strong. Lastly, we demonstrated the manybody localization phase transition by calculating the energy eigenstates as a function of disorder strength and observing how strongly the eigenenergies repel each other. This method proved to be relatively imprecise to specify the critical disorder strength needed for the manybody localized phase. However, one can clearly notice that the repulsion between energy levels grows weaker as the disorder strength grows stronger. see all

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Copyright information: 
© Sasu Tuohino, 2019. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited. 