arXiv subjects

Y. Hernández-Espinosa

Publications and source records attributed to Y. Hernández-Espinosa.

4 recordsLinked to original sources

arXiv2021

Tight-Binding realization of non-abelian gauge fields: singular spectra and wave confinement

We present a geometric construction of a lattice that emulates the action of a gauge field on a fermion. The construction consists of a square lattice made of polymeric sites, where all clustered atoms are identical and represented by potential wells or resonators supporting one bound state. The emulation covers both abelian and non-abelian gauge fields. In the former case, Hofstadter's butterfly is reproduced by means of a chain made of rotating dimers, subject to periodic boundary conditions parallel to the chain. A rigorous map between this model and Harper's Hamiltonian is derived. In the non-abelian case, band mixing and wave confinement are obtained by interband coupling using SU(2) as an internal group, \ie the effects are due to non-commutability of field components. A colored model with SU(3) made of trimers is also studied, finding thereby the appearance of flat bands in special configurations. This work constitutes the first all-geometric emulation of the Peierls substitution, and is valid for many types of waves.

quant-ph↗

arXiv2019

On the electronic structure of benzene and borazine: An algebraic description

The spectrum of a hexagonal ring is analysed using concepts of group theory and a tight-binding model with first, second and third neighbours. The two doublets in the spectrum are explained with the $C_3$ symmetry group together with time-reversal symmetry. Degeneracy lifts are induced by means of various mechanisms. Conjugation symmetry breaking is introduced via magnetic fields, while $C_3$ breaking is studied with the introduction of defects, similar to the inclusion of fluorine atoms. Concrete applications to benzene and borazine are shown to illustrate the generality of our description. Wave functions are described in connection with partial or full aromaticity. Electronic density currents are found for all cases. A detailed study of a supersymmetry in a $6$-ring is presented and its consequences on electronic spectra are discussed.

physics.chem-ph↗

arXiv2018

Dynamical symmetry in a minimal dimeric complex

The emergence of non-configurational symmetry is studied in a minimal example. The system under scrutiny consists of a dimeric hexagonal complex with configurational $C_3$ symmetry, formulated as a tight-binding model. An accidental three-fold degeneracy point in parameter space is found; it is shown that an internal $U(3)$ symmetry group operates on Hilbert space, but not on configuration space. The corresponding discrete Wigner functions for the irreducible representations of $C_6 \cong C_3 \times Z_2$ are utilized to show that a $6\times 6$ phase space is sufficient to exhibit an invariant subset. The dynamical symmetry is thus identified with a discrete semi-plane. Some implications on other known hidden symmetries of continuous systems are qualitatively discussed.

quant-ph↗

arXiv2016

The stabilizer group of honeycomb lattices and its application to deformed monolayers

Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing graphene or boron nitride. New crystalline arrays with conical (Dirac) points are obtained; in particular, a model for dichalcogenide monolayers is proposed and analyzed. In our studies we encounter unitary and non-unitary transformations. We show that the latter give rise to $\mbox{$\cal P\,$}\mbox{$\cal T\,$}$-symmetric Hamiltonians, in compliance with known results in the context of boosted Dirac equations. The results of the unitary part are applied to the description of invariant bandgaps and dispersion relations in materials such as MoS$_2$. A careful construction based on atomic orbitals is proposed and the resulting dispersion relation is compared with previous results obtained through DFT.

quant-ph↗