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arXiv:2303.14056 · Physical Review Letters

Chiral Basis for Qubits and Spin-Helix Decay

Vladislav Popkov, Xin Zhang, Frank Göhmann, Andreas Klümper

Published May 31, 2024• 6 citations
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Abstract

We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well-suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, σ_{n}^{x} and σ_{n}^{y}, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the XX model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.

DOI
10.1103/physrevlett.132.220404

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We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well-suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, σ_{n}^{x} and σ_{n}^{y}, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the XX model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.
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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.
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We calculate the values of observables in chiral eigenstates of the XX quantum spin chain that were introduced in previous work and compare the form of the result with the respective expressions obtained in the more familiar eigenbasis of states with fixed magnetization in the zzz direction. We carry out the diagonalization of the XY spin chain in the chiral basis. We calculate the norm of the chiral XY eigenstates, and the values of the one-point functions and some neighbor two-point correlation functions. We interpret the spectrum and the particle content of the XY chain in terms of scattering states of an even number of kink and antikink excitations that are created over a reduced Brillouin zone.
Motivated by discrepancies between recent cold-atom experiments and the associated theory, we explore the effect of immobile holes on the quantum dynamics of $x\text{\ensuremath{-}}z$ spin helices in the one-dimensional XXXXXX model. We calculate the exact spin dynamics by mapping onto a system of noninteracting fermions, averaging over the distribution of holes. At small hole densities we find that the helical spin pattern decays exponentially, with a pitch dependence that agrees with the experiments. At large hole densities we instead find persistent oscillations. While our analytic approach does not generalize to the XXZXXZXXZ model with arbitrary anisotropies, we validate a matrix-product-state technique which might be used to model the experiments in those settings.