Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions

Abstract

Realizing and characterizing interacting topological phases in synthetic quantum systems is a formidable challenge. Here, we propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. Based on analytical and numerical arguments, we show that this model features a quantum phase transition from a liquid to a valence bond solid that spontaneously breaks lattice translational symmetry and is reminiscent of the Majumdar-Ghosh state. The different phases can be probed dynamically by measuring the evolution of a fully dimerized state. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of the interacting many-body system.

13 pages, 12 figures, revised version contains significantly extended discussion of the implementation of the Zak protocol

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Cited by in corpus (16)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Experimental observation of thermalization with noncommuting charges
• Engineering dynamically decoupled quantum simulations with trapped ions
• Observation of magnon bound states in the long-range, anisotropic Heisenberg model
• Generalized Higgs mechanism in long-range interacting quantum systems
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics
• Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
• Dynamical properties of quantum many-body systems with long range interactions
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Deconfined Quantum Criticality in the long-range, anisotropic Heisenberg Chain
• Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system
• Generation of complete graph states in a spin-$1/2$ Heisenberg chain with a globally optimized magnetic field
• Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point
• Floquet control of interactions and edge states in a programmable quantum simulator
• Quasiballistic transport in long-range anisotropic Heisenberg model
• A theory of quasiballistic spin transport