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Register a new userLong-lived $pi$ edge modes of interacting and disorder-free Floquet spin chains
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Floquet spin chains have been a venue for understanding topological states of matter that are qualitatively different from their static counterparts by, for example, hosting $pi$ edge modes that show stable period-doubled dynamics. However the stability of these edge modes to interactions has traditionally required the system to be many-body localized in order to suppress heating. In contrast, here we show that even in the absence of disorder, and in the presence of bulk heating, $pi$ edge modes are long lived. Their lifetime is extracted from exact diagonalization and is found to be non-perturbative in the interaction strength. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace. In this subspace, the $pi$ edge mode manifests as the quasi-stable edge mode of an inhomogeneous Su-Schrieffer-Heeger model whose dimerization vanishes in the bulk of the Krylov chain.
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Integrable Floquet spin chains are known to host strong zero and $pi$ modes which are boundary operators that respectively commute and anticommute with the Floquet unitary generating stroboscopic time-evolution, in addition to anticommuting with a discrete symmetry of the Floquet unitary. Thus the existence of strong modes imply a characteristic pairing structure of the full spectrum. Weak interactions modify the strong modes to almost strong modes that almost commute or anticommute with the Floquet unitary. Manifestations of strong and almost strong modes are presented in two different Krylov subspaces. One is a Krylov subspace obtained from a Lanczos iteration that maps the Heisenberg time-evolution generated by the Floquet Hamiltonian onto dynamics of a single particle on a fictitious chain with nearest neighbor hopping. The second is a Krylov subspace obtained from the Arnoldi iteration that maps the Heisenberg time-evolution generated directly by the Floquet unitary onto dynamics of a single particle on a fictitious chain with longer range hopping. While the former Krylov subspace is sensitive to the branch of the logarithm of the Floquet unitary, the latter obtained from the Arnoldi scheme is not. The effective single particle models obtained in the two Krylov subspaces are discussed, and the topological properties of the Krylov chain that ensure stable $0$ and $pi$ modes at the boundaries are highlighted. The role of interactions is discussed. Expressions for the lifetime of the almost strong modes are derived in terms of the parameters of the Krylov subspace, and are compared with exact diagonalization.
Certain periodically driven quantum many-particle systems in one dimension are known to exhibit edge modes that are related to topological properties and lead to approximate degeneracies of the Floquet spectrum. A similar situation occurs in spin chains, where stable edge modes were shown to exist at all energies in certain integrable spin chains. Moreover, these edge modes were found to be remarkably stable to perturbations. Here we investigate the stability of edge modes in interacting, periodically driven, clean systems. We introduce a model that features edge modes that persist over times scales well in excess of the time needed for the bulk of the system to heat to infinite temperatures.
Harnessing power-law interactions ($1/r^alpha$) in a large variety of physical systems are increasing. We study the dynamics of chiral spin chains as a possible multi-directional quantum channel. This arises from the nonlinear character of the dispersion with complex quantum interference effects. Using complementary numerically and analytical techniques, we engineer models to transfer quantum states. We illustrate our approach using the long-range XXZ model modulated by Dzyaloshinskii-Moriya (DM) interaction. With exploring non-equilibrium dynamics after a local quantum quench, we identify at fully nonlocal regime (which breaks generalized Lieb-Robinson bounds ) the interplay of interaction range $alpha$ and Dzyaloshinskii-Moriya coupling gives rise to spatially asymmetric spin excitations transport. This could be interesting for quantum information protocols to transfer quantum states and maybe testable with current trapped-ion experiments. We further explore the growth of block entanglement entropy in these systems and the order of magnitude reduction distinguished. A possible effective interaction induces by DM coupling and integrability breaking in these systems is discussed.
We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization.
We propose and analyse a scheme for performing a long-range entangling gate for qubits encoded in electron spins trapped in semiconductor quantum dots. Our coupling makes use of an electrostatic interaction between the state-dependent charge configurations of a singlet-triplet qubit and the edge modes of a quantum Hall droplet. We show that distant singlet-triplet qubits can be selectively coupled, with gate times that can be much shorter than qubit dephasing times and faster than decoherence due to coupling to the edge modes. Based on parameters from recent experiments, we argue that fidelities above 99% could in principle be achieved for a two-qubit entangling gate taking as little as 20 ns.
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