Condensed Matter Hamiltonian

Domenico Finco

Franz Wegner

Sivasubramanian, S., A. Widom, Yogendra Narain Srivastava

Electromagnetic superradiant field coherence exists in a condensed matter system if the electromagnetic field oscillators undergo a mean displacement. Transitions into thermal states with ordered superradiant phases have been shown to theoretically exist in Dicke-Preparata models. The theoretical validity of these models for condensed matter has been called into question due to non-relativistic diamagnetic terms in the electronic Hamiltonian. The microscopic bases of Dicke-Preparata thermal superradiance for realistic macroscopic systems are explored in this work. The impossibility of diaelectric correlations in condensed matter systems (via the Landau-Lifshitz theorem) provides a strong theoretical basis for understanding the physical reality of condensed matter thermodynamic superradiant phases.

Valdir C. Aguilera-Navarro

M. S. Ramkarthik, Payal D. Solanki

Hamiltonians of one dimensional spin half models in condensed matter physics are expounded in this chapter. Hamiltonian of spins interacting with an external magnetic field and separate Hamiltonians for the direct exchange spin-spin interactions in X, Y, Z directions, Heisenberg Hamiltonian and the Dzyaloshinskii-Moriya interaction are dealt with in detail. It is emphasized here that the Hamiltonians are not only for the nearest-neighbour interaction but it is for the rth nearest-neighbour interaction, this increases the scope and usability of the recipies. Other important variants such as the Ising model, transverse Ising model, Majumdar-Ghosh model and a plethora of other spin chain models can be easily constructed using our recipes given and it has been highlighted via examples.

Ali Hussain Resak