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arXiv:2011.06164 · Physical Review A

Edge states in quantum spin chains: The interplay among interaction, gradient magnetic field, and Floquet engineering

Wenjie Liu, Bo Zhu, Li Zhang, Yongguan Ke, Chaohong Lee

Published Aug 4, 2021• 3 citations
arXivHTMLPDF

Abstract

We explore the edge defects induced by spin-spin interaction in a finite paradigmatic Heisenberg spin chain. By introducing a gradient magnetic field and a periodically modulated spin-exchange strength, the resonance between modulation frequency and magnetic-field gradient can also induce asymmetric defects at the edges, dubbed as Floquet-Wannier-Zeeman edge defects. The interplay between these two types of edge defects allows us to manipulate the magnon edge states from an isolated band into a continuum one. In the high-frequency regime, we analytically derive effective models to interpret the formation mechanisms for edge states by employing the multiscale perturbation analysis. Our study offers insights to understand and control the magnon edge states governed by the interplay between edge defects induced by the spin-spin interaction and the Floquet-Wannier-Zeeman manipulation.

DOI
10.1103/physreva.104.023305

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We explore the edge defects induced by spin-spin interaction in a finite paradigmatic Heisenberg spin chain. By introducing a gradient magnetic field and a periodically modulated spin-exchange strength, the resonance between modulation frequency and magnetic-field gradient can also induce asymmetric defects at the edges, dubbed as Floquet-Wannier-Zeeman edge defects. The interplay between these two types of edge defects allows us to manipulate the magnon edge states from an isolated band into a continuum one. In the high-frequency regime, we analytically derive effective models to interpret the formation mechanisms for edge states by employing the multiscale perturbation analysis. Our study offers insights to understand and control the magnon edge states governed by the interplay between edge defects induced by the spin-spin interaction and the Floquet-Wannier-Zeeman manipulation.
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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.
In this paper, we study periodically modulated s=1/2s=1/2s=1/2 spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization plateau for a uniform external magnetic field. These topological states have a finite integer Chern number and their stability is clarified by an equivalent spinless fermion system derived by a Jordan-Wigner transformation. We show that the LP, which is nothing but a constant electric field in the spinless fermion system, destabilizes the topological states, because it induces localization called Wannier-Stark (WS) localization. We clarify the phase diagram in the presence of the LP and on-site diagonal disorder. To this end, we carefully study edge excitations under the open boundary condition, which are a hallmark of the topological order. We find a very interesting phenomenon indicating existence of a quasiedge modes that take the place of the genuine edge modes in certain parameter regions. This is a precursor of the WS localization realized in topological states. Finally, we investigate many-body localization induced by a sufficiently strong LP or disorder. To this end, we study the energy-level statistics for whole energy levels, and we find unexpected extended-state regimes located in intermediate potential-gradient and weak on-site disorder regimes. We verify this phenomenon by calculating variance of the entanglement entropy. The present system is closely related to quantum Hall state in two dimensions, and therefore our findings can be observed not only in experiments on ultracold atomic gases but also quantum Hall physics.
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.
We study the realizations of topological defects in a one-dimensional quantum Ising model with an open boundary condition at criticality. Applying the construction discussed in M. Hauru, G. Evenbly, W. W. Ho, D. Gaiotto, and G. Vidal, Phys. Rev. B 94, 115125 (2016), we prove that the Ising model on an open chain with multiple topological defects can be transformed to the same model with boundary magnetic fields and noninteracting boundary degrees of freedom. This results in the appearance of a linear combination of Cardy states, which can be interpreted as an edge state of the spin or fermion chain. We show that this edge state with the large boundary entropy can be protected under bulk perturbation, whereas it is fragile to a boundary perturbation. Our formulation suggests the existence of nontrivial edge physics under the existence of topological defects and opens many interesting questions for future analysis related to boundary and bulk physics.
We consider the remote manipulation of the quantum state of the edge emergent spins of Haldane spin chains using a weak local perturbation on the opposite edge. We derive an effective four-level model that correctly captures the response of the local magnetization to local perturbations and we use it to show that applying a small local field on one edge of the chain induces a strong variation of the magnetization on the opposite edge. Using a Landau-Zener protocol, we show how local control of the field on one edge of the chain, implemented, for instance, with a spin-polarized scanning tunneling microscope tip, can adiabatically switch the magnetization direction on the other side of the chain.