Nonlinear breathers with crystalline symmetries

Abstract

Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and exponentially localized Wannier states are a central tool in the classification of band structures with crystalline symmetries. Moreover, the quantized transport observed in nonlinear Thouless pumps relies on the fact that -- at least in a specific model -- discrete breathers recover Wannier states in the limit of vanishing nonlinearity. Motivated by these observations, we investigate the correspondence between nonlinear breathers and exponentially localised Wannier states for a family of discrete nonlinear Schrödinger equations with crystalline symmetries. We develop a formalism to analytically predict the breathers' spectrum, center of mass and symmetry data, and apply this to nonlinear generalizations of the Su-Schrieffer-Heeger chain and the breathing kagome lattice.

v2: minor revisions, accepted manuscript. 14+8 pages, 9+2 figures

References in corpus (16)

• Maximally localized Wannier functions: Theory and applications
• Topological quantum chemistry
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• Quantized Nonlinear Thouless Pumping
• Quantized Fractional Thouless Pumping of Solitons
• Compactly-supported Wannier functions and algebraic $K$-theory
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Fragile topological phases in interacting systems
• Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation
• Stability of the spin-$1/2$ kagome ground state with breathing anisotropy
• Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators
• Krein signature for instability of $\mathcal{P}\mathcal{T}$-symmetric states

Cited by in corpus (4)

• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Nonlinearity-induced corner states in a kagome lattice
• Orbital Frontiers: Harnessing Higher Modes in Photonic Simulators