Partitioning technique for a discrete quantum system

Abstract

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.

7 pages, 2 figures

References in corpus (6)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• The cold atom Hubbard toolbox
• Controllable scattering of photons inside a one-dimensional resonator waveguide
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Impurity Scattering of Wave Packets on a Lattice
• Rigorous results for tight-binding networks: particle trapping and scattering

Cited by in corpus (16)

• Flat bands by latent symmetry
• Spin-valley system in a gated MoS${}_2$-monolayer quantum dot
• Probability-preserving evolution in a non-Hermitian two-band model
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Simple harmonic oscillation in non-Hermitian SSH chain at exceptional point
• Giant spin Nernst effect in a two-dimensional antiferromagnet due to magnetoelastic coupling-induced gaps and interband transitions between magnon-like bands
• High-order spectral singularity
• Coalescing Majorana edge modes in non-Hermitian PT-symmetric Kitaev chain
• Robust incoherent perfect absorption
• Hidden exceptional point, localization-delocalization phase transition in Hermitian bosonic Kitaev model
• Cooper pairs localization in tree-like networks of superconducting islands
• High-Order Perfect Absorption in the Absence of Exceptional Point
• Coalescing hardcore-boson condensate states with nonzero momentum
• Parallel dynamics between non-Hermitian and Hermitian systems
• Higher order coherence as witness of exceptional point in Hermitian bosonic Kitaev dimer
• Generation of Helical states -- breaking of symmetries, Curie's principle, and excited states