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We study ``frustrated'' hopping models, in which at least one energy band, at the maximum or minimum of the spectrum, is dispersionless. The states of the flat band(s) can be represented in a basis which is fully localized, having support…

The unambiguous detection of the band topology for topological nodal systems remains an urgent problem in this field. Usually in experiments this relies on the detection for the topological edge modes, which may requires the high demands…

Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation…

Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…

We present a perturbative approach to the study of the Hofstadter model for when the amount of flux per plaquette is close to a rational fraction. Within this approximation certain eigenstates of the system are shown to be multi-component…

The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…

We present a method which allows to extract theoretical informations out of a limited set of experimental data and observables, forming up in general an under- constrained system. It has been applied to the field of nucleon structure, in…

We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and…

We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at finite density non-perturbatively, i.e., by including vertex corrections to high orders. Using Holstein model on a square lattice as a…

The canonical one-band Hubbard model is studied using a computational method that mixes the Monte Carlo procedure with the mean field approximation. This technique allows us to incorporate thermal fluctuations and the development of…

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…

Given a Taylor series with a finite radius of convergence, its Borel transform defines an entire function. A theorem of P\'olya relates the large d istance behavior of the Borel transform in different directions to singularities of the…

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications…

We propose a procedure that characterizes free-fermion or interacting multipolar higher-order topological phases via their bulk entanglement structure. To this end, we construct nested entanglement Hamiltonians by first applying an…

We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…

Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved,…

We present $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians parametrised by {\it ab initio} density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the $K$, $Q$, $\Gamma$, and $M$…

The interplay of high-order Van Hove singularities and topology plays a central role in determining the nature of the electronic correlations governing the phase of a system with unique signatures characterising their presence. Layered van…

We prove a HVZ theorem for a general class of no-pair Hamiltonians describing an atom or positively charged ion with several electrons in the presence of a classical external magnetic field. Moreover, we show that there exist infinitely…

In this work, we leverage the Hamiltonian kind structure for accurate uncertainty propagation through a nonlinear dynamical system. The developed approach utilizes the fact that the stationary probability density function is purely a…