CMT seminar on Monday, January 11th

[Ilya Gruzberg]

Dear Colleagues,

I will be hosting a visitor, Prof. Hideaki Obuse (Department of Applied 
Physics, Hokkaido University, Japan), all of the coming week (January 
11-15).

Prof Obuse will give a CMT seminar on Monday, January 11th, at 11:30am 
in the Smith Seminar Room (PRB 1080). The title and abstract are below. 
Please let me know if you are interested to meet with the visitor during 
his stay in Columbus.

Ilya Gruzberg


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Title: *Floquet Topological Phases of Quantum Walks *

Author & Affiliation: Prof. Hideaki Obuse (Department of Applied 
Physics, Hokkaido University,
Japan)

Abstract:

A quantum walk(QW) describing quantum mechanical time evolution of a 
particle is identified as a random walk when the system is brought to 
the classical limit. The QW would provide potential applications on 
quantum computing and information. Furthermore, since QWs are defined by 
time-evolution operators, they can possess topological phases akin to 
those of Floquet topological insulators, which are topological 
insulators driven by a time-periodic field. Compared with 
time-independent topological insulators, Floquet topological insulators 
have unique nature, such as versatile controls of symmetries, edge 
states at pi energy states, and so on.

In this talk, I explain how to identify time-reversal, particle-hole, 
and chiral symmetries for the time-evolution operator of QWs, which are 
relevant to establish topological phases. To this end, a concept of the 
symmetry time frame is introduced. This is important for nonlocal 
symmetry in the time
direction, that is, time-reversal and chiral symmetries[1]. Then, I 
present a procedure to calculate topological numbers not only at zero 
energy but also at pi energy for the QW in one dimension with chiral 
symmetry[1]. By applying this method, we succeeded to unveil hidden 
topological phases found in the photonic QW experiment[2]. I will also 
mention a relation between QWs and network models which are ideal 
theoretical models to study the Anderson transition.

[1] J.K. Asboth and H. Obuse, PRB 88, 121406(R) (2013).
[2] H. Obuse, J.K. Asboth, Y. Nishimura, and N. Kawakami, PRB 92, 045424 
(2015).
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Ilya A. Gruzberg
Professor
The Ohio State University
Department of Physics
2032 Physics Research Building
191 W. Woodruff Ave., Columbus, OH 43210
614-292-7995
gruzberg.1 at osu.edu

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