2021/10/13 by Motohiko Ezawa · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Condensed matter physics #Lambda #Lattice (music) #Mathematics #Nonlinear Photonic Systems #Nonlinear system #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum mechanics #Statistical physics #Theoretical and Computational Physics #Topological order #Topology (electrical circuits) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.104.235420
published as Phys. Rev. B 104, 235420 (2021) · 11 pages, 8 figures
arxiv created 2021/10/13 · openalex publication_date 2021/12/16 · arxiv updated 2021/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the topological physics in nonlinear Schr"odinger systems on lattices. We employ the quench dynamics to explore the phase diagram, where a pulse is given to a lattice point and we analyze its time evolution. There are two system parameters \ensuremathλ and \ensuremathξ, where \ensuremathλ controls the hoppings between the neighboring links and \ensuremathξ controls the nonlinearity. The dynamics crucially depends on these system parameters. Based on analytical and numerical studies, we derive the phase diagram of the nonlinear Su-Schrieffer-Heeger (SSH) model in the (\ensuremathλ,\ensuremathξ) plane. It consists of four phases. The topological and trivial phases emerge when the nonlinearity \ensuremathξ is small. The nonlinearity-induced localization phase emerges when \ensuremathξ is large. We also find a dimer phase as a result of a cooperation between the hopping and nonlinear terms. A similar analysis is made of the nonlinear second-order topological system on the breathing Kagome lattice, where a trimer phase appears instead of the dimer phase.