Related papers: Tenfold Way for Quadratic Lindbladians
We prove a no-go theorem: generic quadratic open fermionic systems governed by Lindblad master equations do not host dissipation-free topological edge states protected by the dissipation gap. By analogy with topological insulators and…
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 Schr\"{o}dinger…
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,…
We perform a systematic symmetry classification of many-body Lindblad superoperators describing general (interacting) open quantum systems coupled to a Markovian environment. Our classification is based on the behavior of the many-body…
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian.…
Decoherence and non-Hermiticity are two different effects of the open quantum systems. Both of them have triggered many interesting phenomena. In this paper, we theoretically study an open two-level non-Hermitian system coupling to a…
In open systems, topological edge states quickly lose coherence and cannot be used in topological quantum computation and quantum memory. Here we show that for dissipative quantum spin (or fermionic) systems, topologically non-Hermitian…
One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase…
Using the Lindblad master equation approach, we investigate the structure of steady-state solutions of open integrable quantum lattice models, driven far from equilibrium by incoherent particle reservoirs attached at the boundaries. We…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…
After briefly recalling the quantum entanglement-based view of topological phases of matter in order to outline the general context, we give an overview of different approaches to the classification problem of topological insulators and…
We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form…
The conditions for both the stability and the breakdown of the topological classification of gapped ground states of noninteracting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions are given for any…
The topological classifications of quadratic bosonic systems according to the symmetries of the dynamic matrices from the equations of motion of closed systems and the effective Hamiltonians from the Lindblad equations of open systems are…
This is the second part of a work in which we show how to solve a large class of Lindblad master equations for non-interacting particles on $L$ sites. Here we concentrate on fermionic particles. In parallel to part I for bosons, but with…
We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced…
Symmetry classification is crucial in understanding universal properties of quantum matter. Recently, the scope of symmetry classification has been extended to open quantum systems governed by the Lindblad master equation. However, the…
One of the most important practical hallmarks of topological matter is the presence of topologically protected, exponentially localised edge states at interfaces of regions characterised by unequal topological invariants. Here, we show that…
We classify the dissipative topological insulators (TIs) with edge dark states (EDS) by using the 38-fold way of non-Hermitian systems in this paper. The dissipative dynamics of these quadratic open fermionic systems is captured by a…
Robust edge states and non-Abelian excitations are the trademark of topological states of matter, with promising applications such as "topologically protected" quantum memory and computing. While so far topological phases have been…