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arXiv:2302.02603 · Physical review. B./Physical review. B

Quantum spin helices more stable than the ground state: Onset of helical protection

Stefan Kühn, F. Gerken, Lena Funcke, Tobias Hartung, Paolo Stornati, Karl Jansen, Thore Posske

Published Jun 15, 2023• 8 citations
arXivHTMLPDF

Abstract

Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schr\"odinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. We find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered ``phantom helices.'' Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.

DOI
10.1103/physrevb.107.214422

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Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schr"odinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. We find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered ``phantom helices.'' Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.
A magnetic helix can be wound into a classical Heisenberg chain by fixing one end while rotating the other one. We show that in quantum Heisenberg chains of finite length, the magnetization slips back to the trivial state beyond a finite turning angle. Avoided level crossings thus undermine classical topological protection. Yet, for special values of the axial Heisenberg anisotropy, stable spin helices form again, which are nonlocally entangled. Away from these sweet spots, spin helices can be stabilized dynamically or by dissipation. For half-integer spin chains of odd length, a spin slippage state and its Kramers partner define a qubit with a nontrivial Berry connection.
Long-lived spin-helix states facilitate the study of non-equilibrium dynamics in quantum magnets. We consider the decay of transverse spin-helices in antiferromagnetic spin-SSS XXZ chains with single-ion anisostropy. The spin-helix decay is observable in the time evolution of the local magnetization that we calculate numerically for the system in the thermodynamic limit using infinite time-evolving block decimation simulations. Although the single-ion anisotropy prevents helix states from being eigenstates of the Hamiltonian, they still can be long-lived for appropriately chosen wave numbers. In case of an easy-axis exchange anisotropy the single-ion anisotropy may even stabilize the helices. Within a spin-wave approximation, we obtain a condition giving an estimate for the most stable wave number QQQ that agrees qualitatively with our numerical results.
Exact solutions for quantum many-body systems are rare and provide valuable insight to universal phenomena. Here we show experimentally in anisotropic Heisenberg chains that special helical spin patterns can have very long lifetimes. This finding confirms the recent prediction of phantom Bethe states, exact many-body eigenstates carrying finite momenta yet no energy. We theoretically find analogous stable spin helices in higher dimensions and in other non-integrable systems, where they imply non-thermalizing dynamics associated with quantum many-body scars. We use phantom spin helices to directly measure the interaction anisotropy which has a major contribution from short-range off-site interactions that have not been observed before. Phantom helix states open new opportunities for quantum simulations of spin physics and studies of many-body dynamics.
Motivated by cold-atom experiments and a desire to understand far-from-equilibrium quantum transport, we analytically study the dynamics of spin helices in the one-dimensional XX\mathit{XX}XX model. We use a Jordan-Wigner transformation to map the spin chain onto a noninteracting Fermi gas with simple equations of motion. The resulting dynamics are nontrivial, however, as the spin-helix initial condition corresponds to a highly nonequilibrium distribution of the fermions. We find a separation of timescales between the in-plane and out-of-plane spin dynamics. We gain insights from analyzing the case of a uniform spin chain and from a semiclassical model. One of our key findings is that the spin correlation functions decay as ${t}^{\ensuremath{-}1/2}$ at long time, in contrast to the experimentally observed exponential decay.
The recent experimental creation of knotted solitons in spin-1 Bose-Einstein condensates opens an interesting avenue for exploring the stability and dynamics of knot solitons. Knotted and helical vortices can be accommodated in spin-orbit-coupled antiferromagnetic spin-1 Bose-Einstein condensates. We demonstrate the stability of these topological structures via numerical simulations of the corresponding Gross-Pitaevskii equation. By changing the strength of the spin-orbit coupling, we find that the ground state undergoes a change from a knotted spin texture to a helical spin texture. Our results reveal that these types of topological object are experimentally realizable in spin-1 Bose-Einstein condensates.
In general, the summation of a set of sub-Hamiltonians cannot share a common eigenstate of each one, only if it is an unentangled product state, such as a phantom helix state in quantum spin system. Here we present a method, referred to as the building block method (BBM), for constructing possible spin-1/2 XXZ Heisenberg lattice systems possessing phantom helix states. We focus on two types of XXZ dimers as basic elements, with a non-Hermitian parity-time (PT ) field and Hermitian Dzyaloshinskii-Moriya interaction (DMI), which share the same degenerate eigenstates. Based on these two building blocks, one can construct a variety of Heisenberg quantum spin systems, which support helix states with zero energy. The underlying mechanism is the existence of a set of degenerate eigenstates. Furthermore, we show that such systems act as quantum spin graphs since they obey the analogs of Kirchhoff's laws for sets of spin helix states when the non-Hermitian PT fields cancel each other out. In addition, the dynamic response of the helix states for three types of perturbations is also investigated analytically and numerically. Our findings provide a way to study quantum spin systems with irregular geometries beyond the Bethe ansatz approach.