What is Hubbard potential?

The Hubbard model is a useful approximation for particles in a periodic potential at sufficiently low temperatures, where all the particles may be assumed to be in the lowest Bloch band, and long-range interactions between the particles can be ignored. …

What is model Hamiltonian?

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

What is tight binding approximation?

In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. Tight-binding models are applied to a wide variety of solids.

What is hopping in physics?

In hopping, the hopping particle has to have energy greater than or equal to that of the height of the barrier in order to cross the barrier, in tunnling it can cross the barrier even with energy less than the height of the barrier.

What is particle hole transformation?

Indeed, a particle-hole transformation is an expression of time-reversal, , for a system of fermions (Feynman), and so it is anti-unitary: . Here is a unitary transformation and is complex conjugation. This physics is confirmed by second quantization.

What is Hamiltonian and Lagrangian?

Lagrangian mechanics can be defined as a reformulation of classical mechanics. The key difference between Lagrangian and Hamiltonian mechanics is that Lagrangian mechanics describe the difference between kinetic and potential energies, whereas Hamiltonian mechanics describe the sum of kinetic and potential energies.

What is the purpose of tight binding?

The tight binding or linear combination of atomic orbitals (LCAO) method is a semi-empirical method that is primarily used to calculate the band structure and single-particle Bloch states of a material.

What is the difference between hopping and tunneling?

The difference between the thermally assisted tunnelling and the thermally activated hopping is that the tunnelling occurs at the excited energy levels between the bottom and the top of the barrier, while the hopping always occurs at the top of the barrier.