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Register a new userStatistical localization: from strong fragmentation to strong edge modes
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Certain disorder-free Hamiltonians can be non-ergodic due to a emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of motion (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized emph{strong zero modes}, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.
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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.
We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of $mathbb{Z}_2$ gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.
We investigate the heat conductivity $kappa$ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of inter-chain coupling $J_perp$, by using several numerical methods and perturbation theory within the framework of linear response. We unveil that a perturbative prediction $kappa propto J_perp^{-2}$, based on simple golden-rule arguments and valid in the strict limit $J_perp to 0$, applies to a remarkably wide range of $J_perp$, qualitatively and quantitatively. In the large $J_perp$-limit, we show power-law scaling of opposite nature, namely, $kappa propto J_perp^2$. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at $J_perp = J_parallel$. As a function of temperature $T$, this minimum scales as $kappa propto T^{-2}$ down to $T$ on the order of the exchange coupling constant. These results provide for a comprehensive picture of $kappa(J_perp,T)$ of spin ladders.
We study quantum spin Hall insulators with local Coulomb interactions in the presence of boundaries using dynamical mean field theory. We investigate the different influence of the Coulomb interaction on the bulk and the edge states. Interestingly, we discover an edge reconstruction driven by electronic correlations. The reason is that the helical edge states experience Mott localization for an interaction strength smaller than the bulk one. We argue that the significance of this edge reconstruction can be understood by topological properties of the system characterized by a local Chern marker.
We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z2 lattice gauge theory (LGT) which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibits emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial non-interacting peer, and thus is of pure dynamical many-body effect. In this vein, our proposed setting provides possibly the minimal model dropping all the conventional assumptions regarding the existence of many-body localization. Through projective measurement of local constituting species, we also identify the coexistence of the disentangled nonergodic matter and thermalized gauge degrees of freedom which stands completely beyond the standard established phenomenology of quantum disentangled liquids. As a by product of self-localization of the proximate fermions, the spin subsystem hosts the long-lived topological edge zero modes, which are dynamically decoupled from the thermalized background Z2 charges of the bulk, and hence remains cold at arbitrary high-energy density. This provides a convenient platform for strong protection of the quantum bits of information which are embedded at the edges of completely ergodic sub-system; the phenomenon that in the absence of such proximity-induced self-localization could, at best, come about with a pre-thermal manner in translational invariant systems. Finally, by breaking local Z2 symmetry of the model, we argue that such admixture of particles no longer remains disentangled and the ergodic gauge degrees of freedom act as a small bath coupled to the localized components.
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