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It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in d dimensions is the number operator of fictitious bosons and fermions over d quantum states. This result allows one to obtain the complete…
Slowly varying nonuniform strains of non-magnetic wave propagating media with honeycomb symmetry induce an effective- or pseudo-magnetic field, a phenomenon observed first in graphene, and later in photonic crystals and other physical…
Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian…
Massless Dirac fermions in an electric field propagate along the field lines without backscattering, due to the combination of spin-momentum locking and spin conservation. This phenomenon, known as "Klein tunneling", may be lost if the…
With topologcial semimetal developing, semimetal with nodal-line ring comes into people's vision as a powerful candidate for practical application of topological devices. We propose a method using ultracold atoms in two-dimensional…
We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…
Different from the Fermi surface of the type-I Dirac semimetal being a point, that of the type-II Dirac semimetal is a pair of crossing lines because the Dirac cone is tilted with open and hyperbolic isofrequency contours. As an optical…
We combine a pair of independent Weyl fermions to compose a Dirac fermion on the four-dimensional Euclidean lattice. The obtained Dirac operator is antihermitian and does not reproduce anomaly under the usual chiral transformation. To…
I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark…
We consider the behavior of Fermi atoms on optical superlattices with two-well structure of each node. Fermions on such lattices serve as an analog simulator of Fermi type Hamiltonian. We derive a mapping between fermion quantum ordering in…
The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used…
We study the topology and geometry of a fermionic model on the honeycomb lattice with spin-dependent hopping which breaks the time-reversal and charge-conjugation symmetries but preserves their composition. We show that in such a case the…
We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight binding or…
In this article we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight binding Fermi-Hubbard model with non unitary tunnelings. We find the form of the nonunitary tunneling…
We describe a random matrix model suitable for the simulation of the eigenvalues of the Dirac operator on the lattice for Wilson fermions. We compare the obtained global eigenvalue spectrum for various values of the hopping parameter \kappa…
A novel gapped metallic state coined orthogonal Dirac semimetal is proposed in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of Hubbard model. This state corresponds to the disordered phase of slave-spin and has the…
We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime, focusing on a (1+1)-dimensional case in which the evolution of the scale factor is set by the equations of…
The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $\psi$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $\omega$, respectively. This theory is connected to…
The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical…
We prove that the two-dimensional Schroedinger operator with a potential having the symmetry of a honeycomb structure has dispersion surfaces with conical singularities (Dirac points) at the vertices of its Brillouin zone. No assumptions…