Related papers: Long-range hopping and indexing assumption in one-…
Many-body localization in an $XY$ model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping)…
A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of 1D system with a non-trivial band topology. An interplay of disorder and topological ordering in the SSH model is of a great interest owing…
In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A…
We construct new many-body invariants for 2d Chern and 3d chiral hinge insulators, which are characterized by quantized pumping of dipole and quadrupole moments. The invariants that we devise are written entirely in terms of many-body…
The Su-Schrieffer-Heeger (SSH) model is fundamental in topological insulators and relevant to understanding higher-order topological phases. This study explores the relationship between the $n$-dimensional SSH model and its…
We propose a scheme to implement the phase-robust topological router based on a one-dimensional dimerized superconducting circuit lattice with long-range hopping. We show that the proposed dimerized superconducting circuit lattice can be…
Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists…
We present a study of complex energy braiding in a 1D non-Hermitian system with $n$th order long range asymmetrical coupling. Our work highlights the emergence of novel topological phenomena in such systems beyond the conventional…
The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long…
Working in the context of the Su-Schreiffer-Heeger (SSH) model, the effect of topological transitions on the structure and properties of bulk position-space wavefunctions is studied for a particle undergoing a quantum walk in a…
Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials. Through the bulk-boundary correspondence, these topological phases have a one-to-one…
$\mathbb{Z}$-classified topological phases lead to larger-than-unity topological states. However, these multiple topological states are only localized at the corners in nonlocal systems. Here, first, we rigorously prove that the multiple…
We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon the…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
Transport studies of a bent quantum Hall junction at integer filling factors show strongly insulating states at higher fields. In this paper we analyze the strongly insulating behavior as a function of temperature T and dc bias V, in order…
Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory…
We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial $\mathbb{Z}_2$ topological invariant defined in terms of the "partial"…
Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…
We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel…
Topological insulators are a new class of insulators in which a bulk gap for electronic excitations is generated by strong spin orbit coupling. These novel materials are distinguished from ordinary insulators by the presence of gapless…