Hideaki Obuse

Topological phases and delocalization of quantum walks in random environments

We investigate one-dimensional (1D) discrete time quantum walks (QWs) with spatially or temporally random defects as a consequence of interactions with random environments. We focus on the QWs with chiral symmetry in a topological phase, and reveal that chiral symmetry together with bipartite nature of the QWs brings about intriguing behaviors such as coexistence of topologically protected edge states at zero energy and Anderson transitions in the 1D chiral class at non-zero energy in their dynamics. Contrary to the previous studies, therefore, the spatially disordered QWs can avoid complete localization due to the Anderson transition. It is further confirmed that the edge states are robust for spatial disorder but not for temporal disorder.

Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of anderson localization

We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a Z2 topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The Z2 topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This Z2 topological effect can be relevant to graphene when the impurity potential is long ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of Z2 topological insulators in the symplectic symmetry class.

Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk

Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a time-periodic field. While there is ample theoretical work on topological phases of quantum walks where the coin operators are spin rotations, in experiments a different coin, the Hadamard operator is often used instead. This was the case in a recent photonic quantum walk experiment, where protected edge states were observed between two bulks whose topological invariants, as calculated by the standard theory, were the same. This hints at a hidden topological invariant in the Hadamard quantum walk. We establish a relation between the Hadamard and the spin rotation operator, which allows us to apply the recently developed theory of topological phases of quantum walks to the one-dimensional Hadamard quantum walk. The topological invariants we derive account for the edge state observed in the experiment, we thus reveal the hidden topological invariant of the one-dimensional Hadamard quantum walk.

Finite-size effects and irrelevant corrections to scaling near the integer quantum Hall transition.

We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present.

Spin-directed network model for the surface states of weak three-dimensional Z(2) topological insulators

A two-dimensional spin-directed

Two-dimensional spin-filtered chiral network model for the Z2 quantum spin-Hall effect

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Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class.

network model is constructed that describes the combined effects of dimerization and disorder for the surface states of a weak three-dimensional

Explicit definition of PT symmetry for nonunitary quantum walks with gain and loss

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Exact exponents for the spin quantum hall transition in the presence of multiple edge channels

topological insulator. The network model consists of helical edge states of two-dimensional layers of

Critical level statistics and anomalously localized states at the Anderson transition

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