Thursday, March 7, 2013

1303.1199 (János. K. Asbóth et al.)

Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks    [PDF]

János. K. Asbóth, Hideaki Obuse
A discrete-time quantum walk (DTQW) is defined by a periodic sequence of operations on a quantum particle. According to the choice of the starting time of the period, different effective Hamiltonians can be associated to the same quantum walk. We define a DTQW to have chiral symmetry (CS) if at least one of these Hamiltonians has CS. This can be ensured by using an "inversion symmetric" pulse sequence, which automatically gives two, inequivalent effective Hamiltonians with CS. We show that the sum and difference of the associated winding numbers, divided by two, gives the bulk topological invariants of a DTQW with CS, which control the number of 0 and $\pi$ energy edge states. We illustrate this bulk--boundary correspondence for the DTQW on the example of the "4-step quantum walk", where tuning CS and particle-hole symmetry realizes edge states in various symmetry classes.
View original: http://arxiv.org/abs/1303.1199

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