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arXiv:1902.00273 · Physical Review A

Bloch oscillations of multimagnon excitations in a Heisenberg XXZ chain

Wenjie Liu, Yongguan Ke, Li Zhang, Chaohong Lee

Published Jun 18, 2019• 13 citations
arXivHTMLPDF

Abstract

The studies of multimagnon excitations will extend our understandings of quantum magnetism and strongly correlated matters. Here, by using the time-evolving block decimation algorithm, we investigate the Bloch oscillations of two-magnon excitations under a gradient magnetic field. Through analyzing the symmetry of our Hamiltonian, we derive a rigorous and general relation between ferromagnetic and antiferromagnetic systems. Under strong interactions, in addition to free-magnon Bloch oscillations, fractional bounded-magnon Bloch oscillations appear which can be understood by an effective single-particle model. To extract the frequencies of Bloch oscillations and determine the gradient of the magnetic field, we analyze the fidelity and the substandard deviation in both time and frequency domains. Our study not only explores the interaction-induced Bloch oscillations of multimagnon excitations, but also provides an alternative approach to determine the gradient of the magnetic field via ultracold atoms in optical lattices.

DOI
10.1103/physreva.99.063614

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The studies of multimagnon excitations will extend our understandings of quantum magnetism and strongly correlated matters. Here, by using the time-evolving block decimation algorithm, we investigate the Bloch oscillations of two-magnon excitations under a gradient magnetic field. Through analyzing the symmetry of our Hamiltonian, we derive a rigorous and general relation between ferromagnetic and antiferromagnetic systems. Under strong interactions, in addition to free-magnon Bloch oscillations, fractional bounded-magnon Bloch oscillations appear which can be understood by an effective single-particle model. To extract the frequencies of Bloch oscillations and determine the gradient of the magnetic field, we analyze the fidelity and the substandard deviation in both time and frequency domains. Our study not only explores the interaction-induced Bloch oscillations of multimagnon excitations, but also provides an alternative approach to determine the gradient of the magnetic field via ultracold atoms in optical lattices.
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Few-magnon physics in the spin-SSS periodic XXZXXZXXZ chain
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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.
Abstract Magnon excitations play an important role in understanding quantum magnetism and magnon bound states observed with ultracold atoms in optical lattices. Here, we investigate how gradient magnetic field and periodically modulated spin-exchange strength affect the two-magnon excitations. In the Stark resonance where the driving frequency matches and smooths the potential bias, the system gains translational invariance in both space and time in the rotating frame, and thus we can develop a Floquet–Bloch band theory for two magnons. We find a new kind of bound states with relative distance no less than two sites, apart from the conventional bound states with relative distance at one site, which indicates the modulation-induced long-range interaction. We analytically derive an effective Hamiltonian via the many-body perturbation theory for a deeper understanding of such novel bound states and explore the interplay between these two types of bound states. Moreover, we propose to probe modulation-induced bound states via quantum walks. Our study not only provides a scheme to form long-range magnon bound states, but also lays a cornerstone for engineering exotic quantum states in multi-particle Floquet systems.
Linear-chain ferromagnets such as \\ce{CoCl_2\\cdot 2H_2 O} have been shown to be capable of magnetic Bloch oscillations. This means that domain walls in he material undergo Bloch oscillations, resulting in an oscilling magnetization. It was recently suggested to use lasers in resonance with energies from the Wannier-Zeeman ladder to provoke such oscillations. Simulating this process in the fully interacting system requires quantum many-body simulations. Since the system is one-dimensional, the method of time-evolving block decimation (TEBD) seems appropriate. We describe and implement this method and use it to simulate lasers acting on the linear chain. This results in robust oscillations in the magnetization with the expected Bloch frequency, with little sign of decoherence.
We solve few-magnon problems for a finite-size spin-SSS periodic Heisenberg XXZ chain with single-ion anisotropy through constructing sets of exact Bloch states achieving block diagonalization of the system. Concretely, the two-magnon (three-magnon) problem is converted to a single-particle one on a one-dimensional (two-dimensional) effective lattice whose size depends linearly (quadratically) on the total number of sites. For parameters lying within certain ranges, various types of multimagnon bound states are manifested and shown to correspond to edge states on the effective lattices. In the absence of the single-ion anisotropy, we reveal the condition under which exact zero-energy states emerge. As applications of the formalism, we calculate the transverse dynamic structure factor for a higher-spin chain near saturation magnetization and find signatures of the multimagnon bound states. We also calculate the real-time three-magnon dynamics from certain localized states, which are relevant to cold-atom quantum simulations, by simulating single-particle quantum walks on the effective lattices. This provides a physically transparent interpretation of the observed dynamics in terms of propagation of bound state excitations. Our method can be directly applied to more general spin or itinerant particle systems possessing translational symmetry.