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According to the composite fermion theory, the interacting electron system at filling factor $\nu$ is equivalent to the non-interacting composite fermion system at $\nu^*=\nu/(1-2m\nu)$, which in turn is related to the non-interacting…
The extended dynamical mean field theory has played an important role in the study of quantum phase transitions in heavy fermion systems. In order to incorporate the physics of unconventional superconductivity, we develop a cluster version…
The two dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a…
We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is…
By developing an algorithm for evaluating the basis states for the composite fermions with negative effective magnetic field, we perform the composite-fermion-diagonalization study for the fully spin-polarized fractional quantum Hall states…
The Lowest Landau Level (LLL), long distance theory of Composite Fermions (CF) developed by Murthy and myself is minimally extended to all distances, guided by very general principles. The resulting theory is mathematically consistent, and…
Strong interactions and topology drive a wide variety of correlated ground states. Some of the most interesting of these ground states, such as fractional quantum Hall states and fractional Chern insulators, have fractionally charged…
We compute the Hall angle and the magnetoresistance of the spin-fermion model, which is a successful phenomenological theory to describe the physics of the cuprates and iron-based superconductors within a wide range of doping regimes. We…
We investigate a lateral semiconductor quantum dot with a large number of electrons in the limit of strong coupling to the leads. A Kondo effect is observed and can be tuned in a perpendicular magnetic field. This Kondo effect does not…
This report is devoted to the building of the theory and analyzing the phenomenon which take place in such strong correlated Fermi systems as High temperature superconductors, metals with heavy fermions and quasi two dimensional…
The electronic properties of graphene are described by a Dirac Hamiltonian with a fourfold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative…
A rather general enhancement of superconductivity is demonstrated in a hybrid structure consisting of submicron superconducting (SC) sample combined with an in-plane ferromagnet (FM). The superconducting state resists much higher applied…
We derive a dynamical mean-field theory for mixtures of interacting bosons and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose-Fermi mixtures…
We derive a microscopic theory of the composite fermions describing the low-lying edge excitations in the fractional quantum Hall liquid. Using the composite fermion transformation, one finds that the edge states of the $\nu=1/m$ system in…
We investigate the spectrum of interacting electrons at arbitrary filling factors in the limit of vanishing Zeeman splitting. The composite fermion theory successfully explains the low-energy spectrum {\em provided the composite fermions…
We propose to describe bulk wave functions of fractional quantum Hall states in terms of correlators of non-unitary b/c-spin systems. These yield a promising conformal field theory analogon of the composite fermion picture of Jain.…
We calculate the self-energy of fermions in Landau level n, in a finite field. Two cases are considered, in which fermions couple either to gauge fluctuations (as in the composite fermion gauge theory) or to phonons, as an example of a…
We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the $\nu=\frac12$…
We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and im-balanced Bi-Layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is…
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of…