Related papers: Self-duality of One-dimensional Quasicrystals with…
The Aubry-Andr\'e model describes a system with quasiperiodic lattice modulation. In one dimension the AAH model is known to exhibit a sharp metal to insulator transition at a self-dual critical point at which all the states in the spectrum…
Mobility edges commonly arise in one-dimensional quasiperiodic systems once exact self-duality is broken, yet their origin is typically understood only at the level of individual Hamiltonians. Here we show that mobility edge positions are…
We review recent theoretical developments about the role of spins, electron-electron interactions, and spin-orbit coupling in metal nanoparticles and semiconductor quantum dots. For a closed system, in the absence of spin-orbit coupling or…
The interplay among interaction, non-Hermiticity, and disorder opens a new avenue for engineering novel phase transitions. We here study the spectral and localization features of two interacting bosons in one-dimensional nonreciprocal…
We show how quasi-one-dimensional correlated insulating states arise at two-thirds filling in organometallic multinuclear coordination complexes described by layered decorated honeycomb lattices. The interplay of spin-orbit coupling and…
We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC…
We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction $U$ and (ii) the…
We investigate a generalized Aubry-Andr\'{e}-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i) = V\left[ \cos(2\pi \beta i) \right]^p$. Our study reveals that the interplay between nonreciprocity,…
We re-express the Rashba and Dresselhaus interactions as non-Abelian spin-orbit gauges and provide a new perspective in understanding the persistent spin helix [Phys. Rev. Lett. 97, 236601 (2006)]. A spin-orbit interacting system can be…
In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking…
We propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker…
We investigate the superconducting Anderson impurity model for interacting quantum dot Josephson junctions with spin-orbit coupling and a term accounting for tunnelling through higher-energy orbitals. These elements establish the conditions…
We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-Andr\'e-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an…
We analyze the localization behavior in a non-Hermitian system subject to a quasiperiodic onsite potential. We characterize localization transitions using multiple quantitative indicators, including inverse participation ratio (IPR),…
We report on a direct connection between quasi-periodic topology and the Almost Mathieu (Andre-Aubry) metal insulator transition (MIT). By constructing quasi-periodic transfer matrix equations from the limit of rational approximate…
It is known that many-body correlations qualitatively modify the properties of a one-dimensional metal. However, for a quasi-one-dimensional metal these correlations are suppressed, at least partially. We study conditions under which the…
We present exact solutions for some eigenstates of hopping models on one and two dimensional quasiperiodic tilings and show that they are "critical" states, by explicitly computing their multifractal spectra. These eigenstates are shown to…
Flat-band systems have attracted significant attention as platforms for studying strongly correlated electron physics, where the dominance of electron-electron interactions over kinetic energy gives rise to a variety of emergent phenomena.…
We develop a theoretical scheme to perform a read-out of the properties of a quasi-periodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a 1D…
Interatomic hopping mediated by spin-orbit coupling (SOC) entangles spin, orbital and sublattice degrees of freedom of electrons, leading to the emergence of intriguing phenomena such as novel topological insulators and exotic…