Quantum Ising chain with boundary dephasing

Abstract

We study the quantum Ising chain with boundary dephasing. By doubling the Hilbert space, the model is mapped to the Su-Schrieffer-Heeger model with imaginary chemical potential at the edges. We show analytically and numerically that the Liouvillian gap, i.e., the inverse relaxation time of the model, scales with the system size $N$ as $N^{-3}$.

11 pages, 5 figures

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• Quantum critical systems with dissipative boundaries
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Zeno physics of the Ising chain with symmetry-breaking boundary dephasing
• Free fermions with dephasing and boundary driving: Bethe Ansatz results
• The failure of semiclassical approach in the dissipative fully-connected Ising model
• Dissipation meets conformal interface in open quantum systems: How the relaxation rate is suppressed
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Characterizing dynamical behaviors in topological open systems with boundary dissipations
• Closed dynamical recursion equations for correlation functions and the application on the construction of Liouvillian spectrum in Lindbladian systems
• Jordan Decomposition of Non-Hermitian Fermionic Quadratic Forms