The Kittel–Shore Hamiltonian characterizes N spins with identical long-range interactions, and the [Formula: see text] coalgebra has been proven to be a symmetry of this model, which can be exactly solved. By using quantum groups and, in particular, [Formula: see text], this Hamiltonian was deformed. In this work, we study the thermodynamic properties of this deformed model for spin-[Formula: see text] particles. In particular, we discuss how this deformation affects the specific heat, magnetic susceptibility, magnetization and phase transitions as a function of the parameter q of the deformation and compare them with those of the undeformed model. Deformation was found to shift the thermodynamic behaviors to higher temperatures and alter the phase transitions. Additionally, we extend the framework to complex deformations on the unit circle, [Formula: see text], for q not being a root of unity. For an [Formula: see text] tetrahedral cluster, this phase establishes a thermodynamic equivalence between a second-neighbor spin-Hamiltonian and the q-deformed quantum model. At least, we have found experimental compounds well reproduced by the Kittel–Shore model for [Formula: see text]. Validating our effective algebraic model against exact diagonalization data for the Cu 2 Te 2 O 5 X 2 (X [Formula: see text] Cl, Br) compound family demonstrates that [Formula: see text] accurately reproduces the structural anisotropy.
The Kittel–Shore Hamiltonian characterizes N spins with identical long-range interactions, and the [Formula: see text] coalgebra has been proven to be a symmetry of this model, which can be exactly solved. By using quantum groups and, in particular, [Formula: see text], this Hamiltonian was deformed. In this work, we study the thermodynamic properties of this deformed model for spin-[Formula: see text] particles. In particular, we discuss how this deformation affects the specific heat, magnetic susceptibility, magnetization and phase transitions as a function of the parameter q of the deformation and compare them with those of the undeformed model. Deformation was found to shift the thermodynamic behaviors to higher temperatures and alter the phase transitions. Additionally, we extend the framework to complex deformations on the unit circle, [Formula: see text], for q not being a root of unity. For an [Formula: see text] tetrahedral cluster, this phase establishes a thermodynamic equivalence between a second-neighbor spin-Hamiltonian and the q-deformed quantum model. At least, we have found experimental compounds well reproduced by the Kittel–Shore model for [Formula: see text]. Validating our effective algebraic model against exact diagonalization data for the Cu 2 Te 2 O 5 X 2 (X [Formula: see text] Cl, Br) compound family demonstrates that [Formula: see text] accurately reproduces the structural anisotropy.
Thermodynamics of the q-deformed Kittel--Shore model
The Kittel--Shore Hamiltonian characterizes N spins with identical long-range interactions, and the su(2) coalgebra has been proven to be a symmetry of this model, which can be exactly solved. By using quantum groups and, in particular, suq(2), this Hamiltonian was deformed. In this work, we study the thermodynamic properties of this deformed model for spin-1/2 particles. In particular, we discuss how this deformation affects the specific heat, magnetic susceptibility, magnetisation, and phase transitions as a function of the parameter q of the deformation and compare them with those of the undeformed model. Deformation was found to shift the thermodynamic behaviours to higher temperatures and alter the phase transitions. The potential applications of this q-deformed model for describing few-spin quantum systems with non-identical couplings are discussed.
Thermodynamics of the q-deformed Kittel--Shore model for spin-1 particles
Quantum algebras (q-algebras) have been used in the literature to deform spin-chain models. In particular, in previous works by the present authors, the Kittel--Shore Hamiltonian was deformed using suq(2) algebra. The deformed Hamiltonian was presented for a general spin, and the thermodynamic properties were studied for spin-1/2 particles. In this paper, we focus on the q-deformation of the Kittel--Shore model for spin-1 systems. We analyse the impact of this deformation on the thermodynamic properties and phase transitions of the system as a function of the deformation parameter q. Specifically, we study the specific heat, magnetic susceptibility, and magnetisation, including a detailed analysis of the Curie temperature characterising the ferromagnetic phase. Furthermore, a finite-size scaling analysis is conducted for both the ferromagnetic and antiferromagnetic cases. Results are systematically compared with those of the undeformed model to reveal the physical effects of the q-deformation.
Abstract The Kittel–Shore (KS) Hamiltonian describes N spins with long-range interactions that are identically coupled; therefore, this (mean-field) model is also known as the Heisenberg XXX model on the complete graph. In this paper, the underlying U ( su ( 2 ) ) coalgebra symmetry of the KS model is demonstrated for arbitrary spins, and the quantum deformation of the KS Hamiltonian ( q -KS model) is obtained using the corresponding U q ( su ( 2 ) ) quantum group. By construction, the existence of such a symmetry guarantees that all integrability properties of the KS model are preserved under q -deformation. In particular, the q -KS model for spin- 1 / 2 particles is analysed, the cases with N = 2 and 3 spins are studied in detail, and higher-spin q -KS models are sketched. As a first excursion into the thermodynamic properties of the spin- 1 / 2 q -KS model, the dependence of the Curie temperature on the deformation parameter is studied through numerical analysis.
Quantum deformations of U(sl(2,R)). Part I: Fidelity and experimental benchmarking
This work explores the effects of both the standard quantum q-deformation and the non-standard h-deformation of the Hopf algebra U(sl(2,R)) on multi-qubit systems. By constructing the states of a Hilbert space of N qubits through the Clebsch-Gordan coefficients associated with the deformed algebras, we show that these states naturally coincide with the eigenstates of the Hamiltonian of the q- and h-deformed Kittel-Shore models. We compare the resulting deformed states with those typically targeted in quantum information experiments, providing a bridge between algebraic constructions and experimentally relevant quantum resources. Fidelities with respect to the undeformed states are computed to establish how the quantum correlations are affected, both for few-qubit systems (including Dicke and non-Dicke states), and in the macroscopic limit (N→∞) through closed-form formulas derived for arbitrary Dicke states. The results reveal different behaviors between the two deformations. The q-deformation smoothly modifies the states and maintains a residual overlap with the original configurations, while the h-deformation rapidly makes the states orthogonal to their undeformed counterparts. Both models demand a standard N−1 rescaling to preserve fidelity stability in the macroscopic limit.
The thermodynamic properties of the spin-1/2 diamond quantum Heisenberg chain model have been investigated by means of the transfer matrix renormalization group (TMRG) method. Considering different crystal structures, by changing the interactions among different spins and the external magnetic fields, we first investigate the magnetic susceptibility, magnetization, and specific heat of the distorted diamond chain as a model of ferrimagnetic spin systems. The susceptibility and the specific heat show different features for different ferromagnetic (F) and antiferromagnetic (AF) interactions and different magnetic fields. A 1/3 magnetization plateau is observed at low temperature in a magnetization curve. Then, we discuss the theoretical mechanism of the double-peak structure of the magnetic susceptibility and the three-peak structure of the specific heat of the compound Cu3(CO3)2(OH)2, on which an elegant measurement was performed by Kikuchi et al. [Phys. Rev. Lett. 94, 227201 (2005)]. Our computed results are consistent with the main characteristics of the experimental data. Meanwhile, we find that the double-peak structure of susceptibility can be found in several different kinds of spin interactions in the diamond chain. Moreover, a three-peak behavior is observed in the TMRG results of magnetic susceptibility. In addition, we perform calculations relevant for some experiments and explain the characteristics of these materials.
A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose–Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range [Formula: see text]. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.