Dr. Natalia Chepiga

Abstract:

Abstract We report the emergence of exact zero modes in junctions of two, three and four short interacting Majorana wires, equivalent to a chain with an impurity bond, Y-and Xjunctions respectively. These exact zero modes arise from incommensurate short-range correlations and manifest as exact level crossings between in-gap states upon continuously tuning the interaction strength. In a junction of two chains the exact zero modes and parity switching appear as soon as the coupling across a junction is positive. This conclusion has a broad implication including the existence of exact zero mode in quenchdisordered systems. Remarkably, for junctions with multiple chains the in-gap states group up into sets of parity pairs -pairs of quasi-degenerate states with opposite parity attributed to the effective interaction of the outer edges of the junction. In the Y-junction with four in-gap states, we report exact zero modes not only within each parity pair but also between them. We demonstrate that this is attributed to an additional Majorana fermion localized at the center of the junction and protected by symmetry. Therefore, coupling between the Majorana fermions at the outer edges of the junction is mediated by the central one. We argue that this is a generic feature of junctions with an odd number of arms. Surprisingly, in the X-junction we identify eight in-gap states arising from two Majorana degrees of freedom localized at the junction center. In contrast to the Y-junction, however, we show that the emergence of Majorana modes at the center of the X-junction is not topologically protected. As a result, the system parameters can be tuned such that the Majorana modes are expelled from the junction center and remain localized exclusively at the outer edges of the system.

Abstract:

Abstract Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events with clear signatures in the extreme values of simple local observables, such as the on-site density or the local magnetization, which are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to study delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.