Related papers: Gap-labelling conjecture with nonzero magnetic fie…
Let $\fre\subset\bbR$ be a finite union of $\ell+1$ disjoint closed intervals and denote by $\omega_j$ the harmonic measure of the $j$ leftmost bands. The frequency module for $\fre$ is the set of all integral combinations of $\omega_1,...,…
Free standing InP quantum dots have previously been theoretically and experimentally shown to have a direct band gap across a large range of experimentally accessible sizes. We demonstrate that when these dots are embedded coherently within…
We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a…
We show that the class $\mathscr{B}$, of discrete groups which satisfy the conclusion of Popa's Cocycle Superrigidity Theorem for Bernoulli actions, is invariant under measure equivalence. We generalize this to the setting of discrete…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
We investigate dynamical mean-field calculations of the three-band Emery model at the one- and two-particle level for material-realistic parameters of high-$T_c$ superconductors. Our study shows that even within dynamical mean-field theory,…
We propose the multiband extension of the spin-fermion model to address the superconducting d-wave pairing due to magnetic interaction near critical point. We solve the unrestricted gap equation with a general d-wave symmetry gap and find…
A connection of a variety of tight-binding models of noninteracting electrons on a rectangular lattice in a magnetic field with theta functions is established. A new spectrum generating symmetry is discovered which essentialy reduces the…
Two-dimensional systems with $C_{2}\mathcal{T}$ ($P\mathcal{T}$) symmetry exhibit the Euler class topology $E\in\mathbb{Z}$ in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying…
Many extensions of the Standard Model require the existence of a "hidden" sector. We consider settings where the hidden sector in the infrared contains a U(1) gauge factor with magnetic monopoles, for instance 't Hooft-Polyakov monopoles of…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
We consider Dirac monopoles embedded into SU(N) gauge theory with theta-term for $\theta = 4\pi M $ (where $M$ is half-integer for $N = 2$ and is integer for $N>2$). Due to the theta - term those monopoles obtain the SU(N) charge and become…
Aspects of electron critical differentiation are clarified in the proximity of the Mott insulator. The flattening of the quasiparticle dispersion appears around momenta $(\pi,0)$ and $(0,\pi)$ on square lattices and determines the…
A momentum space, mean field d-density wave (DDW) Hamiltonian is investigated self-consistently. The pseudo-gapped(PG)state of YBCO is assumed to correspond to the pure DDW state. A relation between thermodynamic potential of the system and…
We consider the magnetic Schr\"odinger operator in the unit disk with constant magnetic field of strength $b>0$ and magnetic Neumann boundary condition. If $\lambda_1(b)$ denotes its lowest eigenvalue, then we prove that $\lambda_1(b) <…
In this paper we study the spectrum $\Sigma$ of the infinite Feinberg-Zee random hopping matrix, a tridiagonal matrix with zeros on the main diagonal and random $\pm 1$'s on the first sub- and super-diagonals; the study of this…
We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $\mathrm{SU}(2)$ symmetry, constrained to fixed total spin $J$ and magnetization $J_z = 0$. Focusing on spin-$\tfrac12$…
We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant Umklapp scattering, the system is gapped in the bulk and supports chiral edge states in…
We discuss the form of the damping of magnetic excitations in a metal near a ferromagnetic instability. The paramagnon theory predicts that the damping term should have the form $\Omega/\Gamma (q)$ with $\Gamma (q) \propto q$ (the Landau…
The tower Weak Gravity Conjecture predicts infinitely many super-extremal states along every ray in the charge lattice of a consistent quantum gravity theory. We show this far-reaching claim in five-dimensional compactifications of M-theory…