arXiv subjects

Makio Kawasaki

Publications and source records attributed to Makio Kawasaki.

3 recordsLinked to original sources

arXiv2023

Topological Phases in a PT-Symmetric Dissipative Kitaev Chain

We study a topological phase in the dissipative Kitaev chain described by the Markovian quantum master equation. Based on the correspondence between Lindbladians, which generate the dissipative time-evolution, and non-Hermitian matrices, Lindbladians are classified in terms of non-Hermitian topological phases. We find out that the Lindbladian retains PT symmetry which is the prominent symmetry of open systems and then all the bulk modes can have a common lifetime. Moreover, when open boundary conditions are imposed on the system, the edge modes which break PT symmetry emerge, and one of the edge modes has a zero eigenvalue.

cond-mat.mes-hall↗

arXiv2022

Topological phases protected by shifted sublattice symmetry in dissipative quantum systems

Dissipative dynamics of quantum systems can be classified topologically based on the correspondence between the Lindbladian in the Gorini-Kossakowski-Sudarshan-Lindblad equation and the non-Hermitian Hamiltonian in the Schrödinger equation. While general non-Hermitian Hamiltonians are classified into 38 symmetry classes, previous studies have shown that the Lindbladians are classified into 10 symmetry classes due to a physical constraint. In this work, however, we unveil a topological classification of Lindbladians based on shifted sublattice symmetry (SLS), which can increase the number of symmetry classes for the Lindbladians. We introduce shifted SLS so that the Lindbladian can retain this symmetry and take on the same role as SLS for the topological classification. For verification, we construct a model of a dissipative quantum system retaining shifted SLS and confirm the presence of edge states protected by shifted SLS. Moreover, the relationship between the presence of shifted SLS protected edge states and the dynamics of an observable quantity is also discussed.

cond-mat.mes-hall↗

arXiv2020

Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{PT}$ symmetric non-Hermitian system by using non-unitary quantum walks

Topological phases and the associated multiple edge states are studied for parity and time-reversal $(\mathcal{PT})$ symmetric non-Hermitian open quantum systems by constructing a non-unitary three-step quantum walk retaining $\mathcal{PT}$ symmetry in one dimension. We show that the non-unitary quantum walk has large topological numbers of the $\mathbb{Z}$ topological phase and numerically confirm that multiple edge states appear as expected from the bulk-edge correspondence. Therefore, the bulk-edge correspondence is valid in this case. Moreover, we study the stability of the multiple edge states against a symmetry-breaking perturbation so that the topological phase is reduced to $\mathbb{Z}_2$ from $\mathbb{Z}$. In this case, we find that the number of edge states does not become one unless a pair of edge states coalesce at an exceptional point. Thereby, this is a new kind of breakdown of the bulk-edge correspondence in non-Hermitian systems. The mechanism of the prolongation of edge states against the symmetry-breaking perturbation is unique to non-Hermitian systems with multiple edge states and anti-linear symmetry. Toward experimental verifications, we propose a procedure to determine the number of multiple edge states from the time evolution of the probability distribution.

quant-ph↗