Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
arXiv:2408.04987 · doi:10.1103/PhysRevB.111.094302
Abstract
Correlated quantum many-body states can be created and controlled by the dissipative protocols. Among these, particle number-conserving protocols are particularly appealing due to their ability to stabilize topologically nontrivial phases. Is there any fundamental limitation to their performance? We address this question by examining a general class of models involving a two-band fermion system subjected to dissipation designed to transfer fermions from the upper band to the lower band. By construction, these models have a guaranteed steady state - a dark state - with a completely filled lower band and an empty upper band. In the limit of weak dissipation, we derive equations governing the long-wavelength and long-time dynamics of the fermion densities and analyze them numerically. These equations belong to the Fisher-Kolmogorov-Petrovsky-Piskunov reaction-diffusion universality class. Our analysis reveals that the engineered dark state is generically unstable, giving way to a new steady state with a finite density of particles in the upper band. We also estimate the minimum system sizes required to observe this instability in finite systems. Our results suggest that number-conserving dissipative protocols may not be a reliable universal tool for stabilizing dark states.
v2, 18 pages, 14 figures
References in corpus (20)
- Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Dissipative preparation of Chern insulators
- Theory of free fermions under random projective measurements
- Nonlinear sigma models for monitored dynamics of free fermions
- Measurement-induced phase transition for free fermions above one dimension
- Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
- Field Theory of Many-Body Lindbladian Dynamics
- Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model
- Reaction-limited quantum reaction-diffusion dynamics
- Lieb-Schultz-Mattis Theorem in Open Quantum Systems
- Uniqueness of steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations: a simple proof
- Measurement induced criticality in quasiperiodic modulated random hybrid circuits
- Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation
- Hydrodynamic theory of scrambling in chaotic long-range interacting systems
- Quantum reaction-limited reaction-diffusion dynamics of noninteracting Bose gases
- Diffusive modes of two-band fermions under number-conserving dissipative dynamics