Related papers: On Relative Bounds for Interacting Fermion Operato…
We derive rigorous bounds on the average momentum occupation numbers $\langle n_{\mathbf{k}\sigma}\rangle$ in the Hubbard and Kondo models in the ground state and at non-zero temperature ($T>0$) in the grand canonical ensemble. For the…
We demonstrate that the skeleton of the Fermi surface S_{F;s} pertaining to a uniform metallic ground state (corresponding to fermions with spin index s) is determined by the Hartree-Fock contribution to the dynamic self-energy. The Fermi…
Fermions and hardcore bosons share the same restriction: no more than one particle can occupy a single site in a lattice system. Specifically, in one dimension, two systems can share the same matrix representation. In this work, we…
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight binding Hamiltonian with nearest neighbour (-t) and next nearest neighbour (t') hopping matrix elements. In…
We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schr{\"o}dinger's equation with the…
We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field limiting regime, the dynamics is described by the Hartree-Fock equation. This extends previous work of Bardos et al. to the case of…
We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge…
We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate…
The finite-temperature transport properties of the spinless interacting fermion model coupled to non-interacting leads are investigated. Employing the unrestricted time-dependent Hartree-Fock (HF) approximation, the transmission probability…
The temporal finite volume induces significant effects in Monte Carlo simulations of systems in low dimensions, such as graphene, a 2-D hexagonal system known for its unique electronic properties and numerous potential applications. In this…
We study a two-dimensional electron system in a magnetic field with a fermion hardcore interaction and without disorder. Projecting the Hamiltonian onto the n-th Landau level, we show that the Hartree-Fock theory is exact in the limit n…
We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anti-commuting operators and generalize a long-range Lieb-Robinson type bound. Our…
We study the dynamics of the thermal momentum distribution function for an interacting, homogenous Fermi gas on $\Z^3$ in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled…
We use different types of determinantal Hartree-Fock (HF) wave functions to calculate variational bounds for the ground state energy of spin-half fermions in volume V_0, with mass m, electric charge zero, and magnetic moment mu, which are…
We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a…
We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest…
To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double well potential. From the spectrum, we…
We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For…
Top interactions beyond the Standard Model can be conveniently described in the framework of gauge-invariant effective operators. We briefly review the general form of the fermion-fermion-gauge boson and fermion-fermion-Higgs interactions…
We show how to derive an effective nonlinear dynamics, described by the Hartree-Fock equations, for fermionic quantum particles confined to a two-dimensional box and in presence of an external, uniform magnetic field. The derivation invokes…