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Abstract We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems. 

Abstract We investigate the boundary phenomena that arise in a finite-sizeXXspin chain interacting through anXXinteraction with a spin $-\frac{1}{2}$impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using bothBethe Ansatzandexact diagonalizationtechniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling $\frac{J_{\mathrm{imp}}}{J}$. When the ratio falls below the critical value $\sqrt{2}$, the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value $\sqrt{2}$an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling $J_{\mathrm{imp}}$exceeds the critical value $\sqrt{2}J$, the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site. 

Abstract Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications. 

In magnetic pyrochlore materials, the interplay of spin-orbit coupling, electronic correlations, and geometrical frustration gives rise to exotic quantum phases, including topological semimetals and spin ice. While these phases have been observed in isolation, the interface-driven phenomena emerging from their interaction have never been realized previously. Here, we report on the discovery of interfacial electronic anisotropy and rotational symmetry breaking at a heterostructure consisting of the Weyl semimetal Eu₂Ir₂O₇and spin ice Dy₂Ti₂O₇. Subjected to magnetic fields, we unveil a sixfold anisotropic transport response that is theoretically accounted by a Kondo-coupled heterointerface, where the spin ice’s field-tuned magnetism induces electron scattering in the Weyl semimetal’s topological Fermi-arc states. Furthermore, at elevated magnetic fields, we reveal a twofold anisotropic response indicative of the emergence of a symmetry-broken many-body state. This discovery showcases the potential of pyrochlore frustrated magnet/topological semimetal heterostructures in search of emergent interfacial phenomena.