Generalized algebraic transformations and exactly solvable classical-quantum models

Abstract

The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel interesting exact results for the hybrid classical-quantum models, which may for instance describe interacting many-particle systems composed of the classical Ising spins and quantum Heisenberg spins, the localized Ising spins and delocalized electrons, or many other hybrid systems of a mixed classical-quantum nature.

Vigorous thermal excitations in a double-tetrahedral chain of localized Ising spins and mobile electrons mimic a temperature-driven first-order phase transition

“…From this point of view, an exact calculation of the partition function of the spin-electron double-tetrahedral chain is also formally completed. Exact results for other thermodynamic quantities follow directly from the mapping relation (8). Actually, the Gibbs free energy G of the spin-electron doubletetrahedral chain takes the form:…”

“…A particularly fruitful idea for suggesting novel exactly soluble models with peculiar quantum manifestations consists in linking relatively small quantum systems through classical Ising spins. To get a closed-form exact solution for these hybrid classical-quantum models one may take advantage of generalized algebraic transformations, which establish a rigorous mapping correspondence with a simpler (fully classical) lattice-statistical model with the known exact solution [5][6][7][8].…”

“…[8][9][10][11][12] and references therein). However, it has been shown later * Electronic address: galisova.lucia@gmail.com † Electronic address: jozef.strecka@upjs.sk on that this conceptually simple approach is also applicable for spinless fermion models when ignoring the hopping term on particular lattice sites [13,14], or for hybrid spin-electron systems, where finite clusters including a few mobile electrons are mutually inter-connected through the localized Ising spins in order to form either one- [15][16][17][18][19][20][21] or two-dimensional [22][23][24][25] lattice.…”

Entangled state teleportation through a couple of quantum channels composed ofXXZdimers in an Ising-XXZdiamond chain

“…The Ising-XXZ diamond chain was recently studied [15], through a decoration transformation [18,19] and a transfer-matrix approach [20].…”

Magnetic Grüneisen parameter and magnetocaloric properties of a coupled spin–electron double-tetrahedral chain

“…In the present Letter, we will investigate the MCE in a hybrid double-tetrahedral chain composed of the localized Ising spins and mobile electrons, which is exactly solvable by combining the generalized decoration-iteration mapping transformation [21][22][23][24] and the transfer-matrix technique [25,26]. As has been shown in our previous works [15,16], the considered 1D spin-electron system provides a suitable prototype model for theoretical investigation of the relation between the groundstate degeneracy and the cooling efficiency of the system during the adiabatic (de)magnetization.…”