Proposal of a quantum version of active particles via a nonunitary quantum walk.

The main aim of the present paper is to define an active particle in a quantum framework as a minimal model of quantum active matter and investigate the differences and similarities of quantum and classical active matter. Although the field of active matter has been expanding, most research has been conducted on classical systems. Here, we propose a truly deterministic quantum active-particle model with a nonunitary quantum walk as the minimal model of quantum active matter.

Bose glass and Fermi glass.

It is known that two-dimensional superconducting materials undergo a quantum phase transition from a localized state to superconductivity. When the disordered samples are cooled, bosons (Cooper pairs) are generated from Fermi glass and reach superconductivity through Bose glass. However, there has been no universal expression representing the transition from Fermi glass to Bose glass.

Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms.

We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble.

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.

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

Critical properties of quantum Hall systems are affected by the presence of extra edge channels-those that are present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using supersymmetry, we map the corresponding network model to a classical loop model, whose boundary critical behavior was recently determined exactly.