The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain

Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable to the Δ=1 isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to anisotropy Δ>1. The aim of this paper is the study of the (k,ω)-plane l...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	José M.P. Carmelo, Pedro D. Sacramento
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2022
Materias:	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/36fdf0410a55416a8320305003b30abb
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:36fdf0410a55416a8320305003b30abb
record_format	dspace
institution	DOAJ
collection	DOAJ
language	EN
topic	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 José M.P. Carmelo Pedro D. Sacramento The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
description	Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable to the Δ=1 isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to anisotropy Δ>1. The aim of this paper is the study of the (k,ω)-plane line shape of the spin dynamical structure factor components S+−(k,ω), S−+(k,ω), and Szz(k,ω) of the Δ>1 spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field near their (k,ω)-plane sharp peaks. However, the extension of the theory to anisotropy Δ>1 requires as a first step the clarification of the nature of a specific type of elementary magnetic configurations in terms of physical spins 1/2. To reach that goal, that the spin SU(2) symmetry of the isotropic Δ=1 point is in the case of anisotropy Δ>1 replaced by a continuous quantum group deformed q-spin SUq(2) symmetry plays a key role. For Δ>1, spin projection Sz remains a good quantum number whereas spin S is not, being replaced by the q-spin Sq in the eigenvalue of the Casimir generator of the continuous SUq(2) symmetry. Based on the isomorphism between the irreducible representations of the Δ=1 spin SU(2) symmetry and Δ>1 continuous SUq(2) symmetry and on their relation to the occupancy configurations of the Bethe-ansatz quantum numbers one finds that the elementary magnetic configurations under study are q-spin neutral. This determines the form of S matrices on which the extended dynamical theory relies. They are found in this paper to describe the scattering of n-particles whose relation to configurations of physical spins 1/2 is established. Specifically, their internal degrees of freedom refer to unbound q-spin singlet pairs of physical spins 1/2 described by n=1 real single Bethe rapidities and to n=2,3,... bound such q-spin singlet pairs described by Bethe n-strings for n>1. There is a relationship between the negativity and the length of the momentum k interval of the k dependent exponents that control the power-law line shape of the spin dynamical structure factor components near the lower threshold of a given (k,ω)-plane continuum and the amount of spectral weight over the latter. Using such a relationship, one finds that in the thermodynamic limit the significant spectral weight contributions from Bethe n-strings at a finite longitudinal magnetic field refer to specific two-parametric (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factor components S+−(k,ω) and Szz(k,ω). In contrast to the Δ=1 isotropic chain, excited energy eigenstates including up to n=3 Bethe n-strings lead to finite spectral-weight contributions to S+−(k,ω). Most spectral weight stems though from excited energy eigenstates whose q-spin singlet Sz=Sq=0 pairs of physical spins 1/2 are all unbound. It is associated with (k,ω)-plane continua in the spectra of the spin dynamical structure factor components that are gapless at some specific momentum values. We derive analytical expressions for the line shapes of S+−(k,ω), S−+(k,ω), and Szz(k,ω) valid in the vicinity of (k,ω)-plane lines of sharp peaks. Those are mostly located at and just above lower thresholds of (k,ω)-plane continua associated with both states with only unbound q-spin singlet pairs and states populated by such pairs and a single n=2 or n=3 n-particle. Our results provide physically interesting and important information on the microscopic processes that determine the dynamical properties of the non-perturbative spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field.
format	article
author	José M.P. Carmelo Pedro D. Sacramento
author_facet	José M.P. Carmelo Pedro D. Sacramento
author_sort	José M.P. Carmelo
title	The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
title_short	The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
title_full	The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
title_fullStr	The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
title_full_unstemmed	The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
title_sort	role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 heisenberg-ising xxz chain
publisher	Elsevier
publishDate	2022
url	https://doaj.org/article/36fdf0410a55416a8320305003b30abb
work_keys_str_mv	AT josempcarmelo theroleofqspinsingletpairsofphysicalspinsinthedynamicalpropertiesofthespin12heisenbergisingxxzchain AT pedrodsacramento theroleofqspinsingletpairsofphysicalspinsinthedynamicalpropertiesofthespin12heisenbergisingxxzchain AT josempcarmelo roleofqspinsingletpairsofphysicalspinsinthedynamicalpropertiesofthespin12heisenbergisingxxzchain AT pedrodsacramento roleofqspinsingletpairsofphysicalspinsinthedynamicalpropertiesofthespin12heisenbergisingxxzchain
_version_	1718415968705708032
spelling	oai:doaj.org-article:36fdf0410a55416a8320305003b30abb2021-11-24T04:26:56ZThe role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain0550-321310.1016/j.nuclphysb.2021.115610https://doaj.org/article/36fdf0410a55416a8320305003b30abb2022-01-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0550321321003072https://doaj.org/toc/0550-3213Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable to the Δ=1 isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to anisotropy Δ>1. The aim of this paper is the study of the (k,ω)-plane line shape of the spin dynamical structure factor components S+−(k,ω), S−+(k,ω), and Szz(k,ω) of the Δ>1 spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field near their (k,ω)-plane sharp peaks. However, the extension of the theory to anisotropy Δ>1 requires as a first step the clarification of the nature of a specific type of elementary magnetic configurations in terms of physical spins 1/2. To reach that goal, that the spin SU(2) symmetry of the isotropic Δ=1 point is in the case of anisotropy Δ>1 replaced by a continuous quantum group deformed q-spin SUq(2) symmetry plays a key role. For Δ>1, spin projection Sz remains a good quantum number whereas spin S is not, being replaced by the q-spin Sq in the eigenvalue of the Casimir generator of the continuous SUq(2) symmetry. Based on the isomorphism between the irreducible representations of the Δ=1 spin SU(2) symmetry and Δ>1 continuous SUq(2) symmetry and on their relation to the occupancy configurations of the Bethe-ansatz quantum numbers one finds that the elementary magnetic configurations under study are q-spin neutral. This determines the form of S matrices on which the extended dynamical theory relies. They are found in this paper to describe the scattering of n-particles whose relation to configurations of physical spins 1/2 is established. Specifically, their internal degrees of freedom refer to unbound q-spin singlet pairs of physical spins 1/2 described by n=1 real single Bethe rapidities and to n=2,3,... bound such q-spin singlet pairs described by Bethe n-strings for n>1. There is a relationship between the negativity and the length of the momentum k interval of the k dependent exponents that control the power-law line shape of the spin dynamical structure factor components near the lower threshold of a given (k,ω)-plane continuum and the amount of spectral weight over the latter. Using such a relationship, one finds that in the thermodynamic limit the significant spectral weight contributions from Bethe n-strings at a finite longitudinal magnetic field refer to specific two-parametric (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factor components S+−(k,ω) and Szz(k,ω). In contrast to the Δ=1 isotropic chain, excited energy eigenstates including up to n=3 Bethe n-strings lead to finite spectral-weight contributions to S+−(k,ω). Most spectral weight stems though from excited energy eigenstates whose q-spin singlet Sz=Sq=0 pairs of physical spins 1/2 are all unbound. It is associated with (k,ω)-plane continua in the spectra of the spin dynamical structure factor components that are gapless at some specific momentum values. We derive analytical expressions for the line shapes of S+−(k,ω), S−+(k,ω), and Szz(k,ω) valid in the vicinity of (k,ω)-plane lines of sharp peaks. Those are mostly located at and just above lower thresholds of (k,ω)-plane continua associated with both states with only unbound q-spin singlet pairs and states populated by such pairs and a single n=2 or n=3 n-particle. Our results provide physically interesting and important information on the microscopic processes that determine the dynamical properties of the non-perturbative spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field.José M.P. CarmeloPedro D. SacramentoElsevierarticleNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENNuclear Physics B, Vol 974, Iss , Pp 115610- (2022)

The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain

Ejemplares similares