We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of eight-vertex model for roots of unity and superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations , by which we extra...

Recent advances in graphene-nanoribbon-based research have demonstrated the controlled synthesis of chiral graphene nanoribbons (chGNRs) with atomic precision using strategies of on-surface chemistry. However, their electronic characterization, including typical figures of merit like band gap or frontier band's effective mass, has not yet been reported. We provide a detailed characterization of...

The chiral Potts model continues to pose particular challenges in statistical mechanics: it is “exactly solvable” in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later. However, a derivation of that conjecture had to wait until 2005. ...

We find the rules which count the energy levels of the 3 state superintegrable chiral Potts model and demonstrate that these rules are complete. We then derive the complete spectrum of excitations in the thermodynamic limit in the massive phase and demonstrate the existence of excitations which do not have a quasi-particle form. The physics of these excitations is compared with the BCS supercon...

In this paper we study the large-N limits of the integrable N-state chiral Potts model. Three chiral solutions of the star-triangle equations are derived, with states taken from all integers, or from a finite or infinite real interval. These solutions are expected to be chiral-field lattice deformations of parafermionic conformal field theories. A new two-sided hypergeometric identity is derive...

Covalent organic frameworks (COFs) are a novel class of porous materials, and offer great potential for various applications. However, the applications of COFs in chiral separation and chiral catalysis are largely underexplored due to the very limited chiral COFs available and their challenging synthesis. Here we show a bottom-up strategy to construct chiral COFs and an in situ growth approach ...

Chiral surfaces are of growing importance as a result of their potential for use in enantioselective chemical processes. By far the most widely used and commonly studied chiral surfaces are those prepared by templating of achiral surface with chiral organic ligands. It is possible, however, to prepare naturally chiral surfaces by a number of means. This paper describes the various types of chir...

Chiral surfaces serve as media for enantioselective chemical processes. Their chirality is dictated by atomic- and molecular-level structure, and their enantioselectivity is determined by their enantiospecific interactions with chiral adsorbates. This Perspective describes three types of chiral metal surfaces: those modified by adsorption of chiral molecules, those templated by chiral lattices ...