Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems

Abstract

One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary condition but exponential under open boundary condition. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wavefront. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.Model.-The system is illustrated in Fig.1(a). Our Hamiltonian H = ij h ij c † i c j , where c † i , c i are fermion creation and annihilation operators at site i (including

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

“…Finally, we mention that in the previous works [21,22,[120][121][122][123][124][125][126][127][128][129], the Bloch wave number becomes complex. In these previous works, the eigenstates localized at either end of an open chain were mainly focused on because these localized states can lead to the novel nonreciprocal phenomena.…”

Probing non-Hermitian skin effect and non-Bloch phase transitions

“…Topological characterization of non-Hermitian models is currently a hot area of research (see [4][5][6][7][8][9][10][11][12][13][14] and references therein). Among the most relevant features observed in non-Hermitian systems, one should mention the strong sensitivity of the energy spectra on boundary conditions [7,[15][16][17][18][19][20][21], the non-Hermitian skin effect (NHSE) [7,9,17,18,[20][21][22][23][24], i.e. the exponential localization of continuum-spectrum eigenstates to the edges, and the failure of the bulkboundary correspondence based on Bloch band topological invariants [4,17,18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Untying links through anti-parity-time-symmetric coupling

“…If the non-Hermiticity is = (0, 0, γ ), the topological phase transition and the existence of the edge state are unaltered because of the pseudo-anti-Hermiticity protection [34]; the topological properties of the non-Hermitian system are inherited by the EPs (exceptional rings or exceptional surfaces in 2D or 3D) [60][61][62][63][64][65][66][67]. If the non-Hermiticity is = (0, γ , 0), the non-Hermitian skin effect occurs under open boundary condition [54][55][56][57][58][59][68][69][70][71][72][73][74][75][76][77][78], the non-Hermitian Aharonov-Bohm effect under periodical boundary condition invalidates the conventional bulk-boundary correspondence [54], and the non-Bloch band theory is developed for topological characterization [77][78][79][80][81][82]. Here, the dissipation induced anti-PT -symmetric coupling corresponds to the imaginary part = (γ , 0, 0).…”