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arXiv:1602.03217 · Physical review. B./Physical review. B

Topological magnon bound states in periodically modulated Heisenberg XXZ chains

Xizhou Qin, Feng Mei, Yongguan Ke, Li Zhang, Chaohong Lee

Published Nov 15, 2017• 35 citations
arXivHTMLPDF

Abstract

Strongly interacting topological states in multiparticle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multiparticle quantum states, which enables us to characterize the topological features of multimagnon excitations. We calculate energy spectra, density distributions, correlations, and Chern numbers of the two-magnon bound states and show the existence of topological protected edge bound states. Our study not only opens a prospect to pursue topological magnon bound states, but also gives insights into the characterization and understanding of strongly interacting topological states.

DOI
10.1103/physrevb.96.195134

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Strongly interacting topological states in multiparticle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multiparticle quantum states, which enables us to characterize the topological features of multimagnon excitations. We calculate energy spectra, density distributions, correlations, and Chern numbers of the two-magnon bound states and show the existence of topological protected edge bound states. Our study not only opens a prospect to pursue topological magnon bound states, but also gives insights into the characterization and understanding of strongly interacting topological states.
It is still an outstanding challenge to characterize and understand the topological features of strongly correlated states such as bound-states in interacting multi-particle quantum systems. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore an unprecedented topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry allows us to formulate a direct topological invariant for the multi-particle quantum states, which can be used to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and topological invariants of the two-magnon bound-states and show the existence of topological magnon bound-states. Our study not only opens a new prospect to pursue topological bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.
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 (Aidelsburger et al 2013 Phys. Rev. Lett. 111 , 185301; Miyake et al 2013 Phys. Rev. Lett. 111 , 185302). 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.
Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems has not been extensively explored due to the failure of direct explanation from the topological band insulator theory on such systems and the origin of the topological property is unclear. Here we report the theoretical discovery of strongly correlated topological states in quasi-periodic Heisenberg spin chain systems corresponding to a series of incommensurate magnetization plateaus under the presence of the magnetic field, which are uniquely determined by the quasi-periodic structure of exchange couplings. The topological features of plateau states are demonstrated by the existence of non-trivial spin-flip edge excitations, which can be well characterized by nonzero topological invariants defined in a two-dimensional parameter space. Furthermore, we demonstrate that the topological invariant of the plateau state can be read out from a generalized Streda formula and the spin-flip excitation spectrum exhibits a similar structure of the Hofstadter's butterfly spectrum for the two-dimensional quantum Hall system on a lattice.
Searching topological states in artificial systems has recently become a rapidly growing field of research. Meanwhile, significant experimental progress on observing topological phenomena has been made in superconducting circuits. However, topological insulator states have not yet been reported in this system. Here, for the first time, we experimentally realize a tunable dimerized spin chain model and observe the topological magnon insulator states in a superconducting qubit chain. Via parametric modulations of the qubit frequencies, we show that the qubit chain can be flexibly tuned into topologically trivial or nontrivial magnon insulator states. Based on monitoring the quantum dynamics of a single-qubit excitation in the chain, we not only measure the topological winding numbers, but also observe the topological magnon edge and defect states. Our experiment exhibits the great potential of tunable superconducting qubit chain as a versatile platform for exploring noninteracting and interacting symmetry-protected topological states.
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We study topological features of interacting spin-12\frac{1}{2}21​ particles in one-dimensional state-dependent optical lattices. Due to the cotranslational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound states appear as a result of the nontrivial center-of-mass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center of mass can be described by a nontrivial center-of-mass Chern number.