Dynamics of Open Tight-binding Model

Abstract

In this paper, we investigate the open tight-binding model with $N$ sites coupled to two reservoirs on its edges with the nonequilibrium Green function method to understand effects of open boundaries. As a result, we obtain an analytical expression of the electron density in the steady state and in the transient regime for $N\to \infty$ and at absolute zero temperature. From the expression of the electron density in the steady state, we show that the open boundaries do not affect the qualitative behavior of the electron density and the phase transition which has been observed for the isolated tight-binding model also exists in our open case. Using the expression of the time-dependent electron density, we show that a two-step decay appears in the relaxation process purely caused by open boundaries. In addition, we show that the dependence of speed of convergence on boundary coupling strength qualitatively changes at a certain value of the boundary parameters. This is a result of special eigenvalues of a non-hermitian matrix whose imaginary parts do not vanish even in the limit $N\to \infty$.

34 pages, 17 figures

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Conduction of Ultracold Fermions Through a Mesoscopic Channel
• Time-Dependent Partition-Free Approach in Resonant Tunneling Systems
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime
• Relaxation times of dissipative many-body quantum systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED
• Matrix product solutions of boundary driven quantum chains
• Dissipative spin chain as a non-Hermitian Kitaev ladder
• Charge dynamics in molecular junctions: Nonequilibrium Green's Function approach made fast
• Dynamics of Ultracold Quantum Gases in the Dissipative Fermi-Hubbard Model
• Dynamic scaling of fronts in the quantum XX chain
• Experimental signatures of an absorbing-state phase transition in an open driven many-body quantum system
• The Diffusion of the Magnetization Profile in the XX-model
• Partition-free theory of time-dependent current correlations in nanojunctions in response to an arbitrary time-dependent bias
• Power-law approach to steady state in open lattices of non-interacting electrons

Cited by in corpus (1)

• Quantum interference and the time-dependent radiation of nanojunctions