Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect

• URL: http://arxiv.org/abs/2210.14212v2
• Date: Mon, 28 Aug 2023 16:44:33 GMT
• Title: Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Authors: Gideon Lee and Alexander McDonald and Aashish Clerk
• Abstract summary: We show for generic quantum non-Hermitian tight-binding models that relaxation of local observables are not controlled by the localization length. interference between eigenvectors effectively makes the extreme localization of modes largely irrelevant to relaxation. Our work highlights an important aspect of the non-Hermitian skin effect: the exceptional sensitivity to boundary conditions here necessarily takes a finite amount of time to manifest itself.
• Score: 49.1574468325115
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show for generic quantum non-Hermitian tight-binding models that relaxation timescales of local observables are not controlled by the localization length $\xi_{\rm loc}$ associated with the non-Hermitian skin effect, contrary to popular belief. Instead, interference between eigenvectors effectively makes the extreme localization of modes largely irrelevant to relaxation; this is ultimately a consequence of causality and locality. Focusing on the paradigmatic Hatano-Nelson model, we demonstrate that there exists instead a much larger length scale $\xi_{\rm prop}$ which controls the rate of decay towards the steady state. Further, varying $\xi_{\rm prop}$ can lead to anomalously large relaxation times that scale with system size, or to the expected behavior where the dissipative gap correctly predicts the rate of decay. Our work highlights an important aspect of the non-Hermitian skin effect: the exceptional sensitivity to boundary conditions here necessarily takes a finite amount of time to manifest itself.

Related papers

• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Many-Body Non-Hermitian Skin Effect for Multipoles [0.0]
  We investigate the fate of the non-Hermitian skin effect in one-dimensional $textU(1)$ systems. Key feature of the non-Hermitian skin effect for $m$-pole conserving systems is the generation of an $(m+1)$th multipole moment. In addition, we explore the dynamical consequences of the $m$-pole skin effect, focusing on charge and entanglement propagation.
  arXiv  Detail & Related papers  (2024-01-08T19:00:01Z)
• Stochastic Error Cancellation in Analog Quantum Simulation [0.6410191755165466]
  We consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian. We show that, due to error cancellation, the error scales as the square root of the number of qubits instead of linearly. We also show that error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise.
  arXiv  Detail & Related papers  (2023-11-24T19:25:08Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model [12.632098351321218]
  We investigate the role of non-Hermiticity in the Chern insulating Haldane model on a dice lattice. We introduce non-Hermiticity into this model in two ways -- through balanced non-Hermitian gain and loss, and by non-reciprocal hopping in one direction. Our results place the dice-Haldane model as an exciting platform to explore non-Hermitian physics.
  arXiv  Detail & Related papers  (2022-07-29T11:13:09Z)
• Quantum chaos and thermalization in the two-mode Dicke model [77.34726150561087]
  We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model. The two-mode Dicke model exhibits normal to superradiant quantum phase transition. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size.
  arXiv  Detail & Related papers  (2022-07-08T11:16:29Z)
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains [68.8204255655161]
  We show that even in the absence of disorder, and in the presence of bulk heating, $pi$ edge modes are long lived. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace.
  arXiv  Detail & Related papers  (2021-05-28T12:13:14Z)
• Quasi-stationary solutions in non-Hermitian systems [0.0]
  Eigenstates exhibit localization at an open edge in a non-Hermitian lattice due to non-Hermitian skin effect. We predict quasi-stationary solutions, which are approximately time-independent.
  arXiv  Detail & Related papers  (2021-03-23T17:25:04Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Critical non-Hermitian Skin Effect [2.6109033135086777]
  This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit. We present stimulating examples with anomalous scaling behavior regarding spectrum, correlation functions, entanglement entropy, and scale-free wavefunctions that decay exponentially rather than power-law.
  arXiv  Detail & Related papers  (2020-03-06T05:48:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.