Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

Abstract

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound-states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms [Phys. Rev. Lett. \textbf{111}, 185301 (2013); Phys. Rev. Lett. \textbf{111}, 185302 (2013)]. Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound-states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound-states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

26 papges, 6 figures

References in corpus (13)

• Classification of topological insulators and superconductors in three spatial dimensions
• Nonlinear atom interferometer surpasses classical precision limit
• Observation of the Magnon Hall Effect
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Topological Magnon Insulator in Insulating Ferromagnet
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Simplified topological invariants for interacting insulators
• Two-body physics in the Su-Schrieffer-Heeger model
• Topological edge states of bound photon pairs
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Multi-particle Wannier states and Thouless pumping of interacting bosons
• Multihole edge states in Su-Schrieffer-Heeger chains with interactions

Cited by in corpus (16)

• Topological Magnons: A Review
• Interaction-induced topological bound states and Thouless pumping in a one-dimensional optical lattice
• Topological two-body bound states in the interacting Haldane model
• Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons
• Radiative topological biphoton states in modulated qubit arrays
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices
• Doublons, topology and interactions in a one-dimensional lattice
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Topological pumping induced by spatiotemporal modulation of interaction
• Decay rates and energies of free magnons and bound states in dissipative XXZ chains
• Confinement and oscillating deconfinement crossover of two-magnon excitations in quantum spin chains quantified by spin entanglement entropy
• Scattering Theory of Chiral Edge Modes in Topological Magnon Insulators
• Finite size effects and Hofstadter butterfly in a bosonic Mott insulator with relativistic dispersion background
• Topological two-particle dynamics in a periodically driven lattice model with on-site interactions