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Effective mass of the composite fermion in the fractional quantum Hall system, which is of purely interaction originated, is shown, from a numerical study, to exhibit a curious nonmonotonic behavior with a staircase correlated with the…
Local interactions among electrons underlie many complex properties of correlated materials. While the Jordan-Wigner transformation can preserve this locality along one spatial dimension, interactions along the remaining dimensions…
We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the…
There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of…
Statistics transmutations to composite fermions in fractional-quantum-Hall-effect systems are considered in the Hartree-Fock approximation and in the RPA. The Hartree-Fock ground-state energy shows that the transmutations are not…
We show that, for sudden quenches, the work distribution reduces to the statistics of traces of powers of Haar unitaries, which are random unitary matrices drawn uniformly from the unitary group. For translation-invariant quadratic…
Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for…
We study the scattering of a soliton-like propagating particle with a wall of bound particles, in several strongly interacting one-dimensional lattice models with discrete degrees of freedom. We consider spin-polarized fermions (anisotropic…
We consider momentum push-forwards of measures arising as quantum limits (semi-classical measures) of eigenfunctions of a point scatterer on the standard flat torus $\mathbb T^2 = \mathbb R^2/\mathbb Z^{2}$. Given any probability measure…
We show that two elementary worldline path integrals-the thermal partition function of the harmonic oscillator and the one-loop effective action of scalar QED in a constant field strength-exhibit a natural form of supersymmetric…
A two dimensional disordered system of non-interacting fermions in a homogeneous magnetic field is investigated numerically. By introducing a new magnetic gauge, we explore the renormalization group (RG) flow of the longitudinal and Hall…
Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H is a k-subgroup of G (not necessarily connected). Let S be a finite set of places of k. We compute the Brauer-Manin…
The theoretical formulation and numerical evaluation of the vertex corrections in multiorbital techniques of theories of electronic properties of random alloys are analyzed. It is shown that current approaches to static transport properties…
We examine the relation between supersymmetric localization on $\mathbb{S}^4$ and standard QFT results for non-conformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU($N$)…
We consider the k=1 Friedman-Lemaitre-Robertson-Walker (FLRW) model within loop quantum cosmology (LQC), from the perspective of the two available quantization prescriptions. We focus our attention on the existence of the so called `inverse…
Recent experiments have reported a lot of spectacular transport properties in topological materials, such as quantum oscillations and three-dimensional (3D) quantum Hall effect (QHE) in ZrTe$_5$. In this paper, by using a strong topological…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
Losev introduced the scheme $X$ of almost commuting elements (i.e., elements commuting upto a rank one element) of $\mathfrak{g}=\mathfrak{sp}(V)$ for a symplectic vector space $V$ and discussed its algebro-geometric properties. We…
The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this…