Rigorous decoupling between edge states in frustrated spin chains and ladders

Abstract

We investigate the occurrence of exact zero modes in one-dimensional quantum magnets of finite length that possess edge states. Building on conclusions first reached in the context of the spin-1/2 XY chain in a field, then for the spin-1 $J_1-J_2$ Heisenberg model, we show that the development of incommensurate correlations in the bulk invariably leads to oscillations in the sign of the coupling between edge states, hence to exact zero energy modes at the crossing points where the coupling between the edge states rigorously vanishes. This is true regardless of the origin of the frustration (e.g. next-nearest neighbor coupling or biquadratic coupling for the spin-1 chain), of the value of the bulk spin (we report on spin-1/2, spin-1 and spin-2 examples), and of the value of the edge-state emergent spin (spin-1/2 or spin-1).

8 pages, 14 figures

References in corpus (13)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• The density-matrix renormalization group in the age of matrix product states
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Atomic spin chain realization of a model for quantum criticality
• Excitation spectrum and Density Matrix Renormalization Group iterations
• Realization of higher Wess-Zumino-Witten models in spin chains
• Spontaneous dimerization, critical lines, and short-range correlations in a frustrated spin-1 chain
• Topological Identification of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
• Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
• Level crossings induced by a longitudinal coupling in the transverse field Ising chain
• Exact zero modes in frustrated Haldane chains
• Emergent incommensurate correlations in the frustrated ferromagnetic spin-1 chains

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• Dimerization and effective decoupling in two spin-1 generalizations of the spin-1/2 Majumdar-Ghosh chain
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Promising regimes for the observation of topological degeneracy in spin chains
• Perturbative approach to quantum tunneling and quantum interferences in spin clusters