Related papers: Phase space analysis of interacting fermions
We present a comprehensive pedagogical introduction to the dimensional reduction protocol (DRP), a versatile framework for analyzing instabilities and critical points in interacting fermionic systems. The DRP simplifies the study of…
The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its…
We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-$1/2$ fermionic system on the kagom\'{e} lattice with a quadratic band crossing point. With the help of the renormalization group…
We derive a widely-applicable first principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous…
Phase-space representations are a family of methods for dynamics of both bosonic and fermionic systems, that work by mapping the system's density matrix to a quasi-probability density and the Liouville-von Neumann equation of the…
Orbital degrees of freedom play an important role for understanding the emergence of unconventional quantum phases. Ultracold atomic gases in optical lattices provide a wonderful platform to simulate orbital physics. In this work, we…
We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in circularly shaken square lattice…
We study a two species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive interaction. Such a model can be realized in a cold atom system with fermionic atoms…
In correlated electron materials, the application of many-body techniques for the study of interaction effects or unconventional superconductivity often requires the formulation of an effective low-energy model that contains only the…
A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…
In this thesis, we study the breakdown of the Fermi liquid state in cuprate superconductors using the renormalization group (RG). We seek to extend earlier work on the crossover from the Fermi liquid state to the pseudo gap phase based on…
Recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides opportunity to engineer Hubbard-like models with long range interactions. Motivated by these experiments, we chart out the theoretical phase…
The many-body theory of interacting electrons poses an intrinsically difficult problem that requires simplifying assumptions. For the determination of electronic screening properties of the Coulomb interaction, the Random Phase…
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 introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive…
A system of N interacting bosons or fermions in a two-dimensional harmonic potential (or, equivalently, magnetic field) whose states are projected onto the lowest Landau level is considered. Generic expressions are derived for matrix…
We study low-dimensional quantum systems with analytical and computational methods. Firstly, the one-dimensional extended $t$-$V$ model of fermions with interactions of a finite range is investigated. The model exhibits a phase transition…
We show that the Hubbard Hamiltonian with particle-assisted tunneling rates --recently proposed to model a fermionic mixture near a broad Feshbach resonance-- displays a ground state phase diagram with superfluid, insulating, and phase…
We examine a one-dimensional two-component fermionic system in a trap, assuming that all particles have the same mass and interact through a strong repulsive zero-range force. First we show how a simple system of three strongly interacting…
We formulate the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a space-time lattice in the worldline approach. We show that worm algorithms can efficiently sample the…