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We review application of the SU(4) model of strongly-correlated electrons to cuprate and iron-based superconductors. A minimal self-consistent generalization of BCS theory to incorporate antiferromagnetism on an equal footing with pairing…

We develop a field theory for a partially filled Landau level based on composite fermions with a finite vortex core, whose mean-field states are exactly those described by well-tested trial wave functions. Despite non-orthogonality of free…

We present an implementation of the rotationally invariant slave boson technique as an impurity solver for density functional theory plus dynamical mean field theory (DFT+DMFT). Our approach provides explicit relations between quantities in…

Using the U(1) holon pair slave boson theory [Phys. Rev. B 64, 052501 2001)], we derive a low energy field theory of dealing with both d-wave superconductivity and antiferromagnetism for underdoped cuprates by constructing both the Cooper…

An ancient Hamiltonian of electrons with entangled spin and orbital degrees of freedom is re-examined as a model of magneto-electric multipoles. In the model, a magnetic charge and simple quantum rotator are tightly locked in action, some…

In conventional superconductors, phonons glue two electrons with opposite spins to form Cooper pairs and condensation of these pairs leads to the superconductivity. Identifying the underlying mechanism of the high temperature…

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a homogenous…

We consider an electrostatically induced square lattice of quantum dots and study the role of electron-electron correlations in the resulting electronic features of the system. We utilize the Wannier functions methodology in order to…

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large N theory provide…

The evolution of the so-called `41meV resonance' in the magnetic response of YBCO cuprates is studied with slave-boson theory for the t-t'-J-model. The resonance appears as a collective spin fluctuation in the d-wave superconducting (SC)…

A new approach is proposed which encompasses the dynamical mean field theory (DMFT) for strongly correlated electron systems and the self-consistent renormalization (SCR) theory of spin fluctuations. The latter is incorporated into DMFT as…

We develop a mean-field theory of the stability of fractional Chern insulators based on the dipole picture of composite fermions (CFs). We construct CFs by binding vortices to Bloch electrons and derive a CF single-particle Hamiltonian that…

This thesis deals with the Hubbard model as prototypical model to describe the physics of electrons in the two-dimensional copper-oxide planes of high-$T_c$ cuprates. To get approximate solutions, we employ functional renormalization group…

We develop, clarify and test various aspects of cluster methods dynamical mean field methods using a soluble toy model as a benchmark. We find that the Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and compare its…

In this work, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moir\'e systems, that captures both the formation of Wigner crystals as well as exotic spin states on top of…

We investigate a Kondo lattice model with correlated conduction electrons. Within dynamical mean-field theory the model maps onto an impurity model where the host has to be determined self-consistently. This impurity model can be derived…

Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron-pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as…

An effective field theory for clean electron systems is developed in analogy to the generalized nonlinear sigma-model for disordered interacting electrons. The physical goal is to separate the soft or massless electronic degrees of freedom…

The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied to 2-D t-J model in the limit t >> J, to study the normal state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition…