Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm
Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation...
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| description | Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit,
N
→
∞, in terms of the
N spin-
1
/
2 physical spins of the spin-
1
/
2
X
X
Z chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies
Δ
>
1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin-
1
/
2
X
X
Z chain’s continuous
S
U
q
(
2
) symmetry parameterized by
q
=
Δ
+
Δ
2
−
1
∈
]
1
,
∞
] and associated with
q-spin
S
q. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length
n that have no spinon representation, contribute to the dynamical properties of the spin-
1
/
2
X
X
Z chain with anisotropy
Δ
>
1 and for
n
=
1
,
2
,
3 were experimentally identified and realized in the zigzag materials SrCo
2V
2O
8 and BaCo
2V
2O
8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous
S
U
q
(
2
) symmetry reveals that for anisotropy
Δ
>
1 the Bethe strings of length
n
=
1
,
2
,
3
,
… describe a number
n of physical-spins
S
q
=
0 singlet pairs that for
n
>
1 are bound within a
S
q
=
0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin-
1
/
2
X
X
Z chain in a longitudinal magnetic field and the spin chains in SrCo
2V
2O
8 is one of the issues addressed in this paper. In addition, the
S
U
q
(
2
) symmetry imposes that only
2
S
q out of the
N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento [“Diffusive spin |
| doi_str_mv | 10.1063/5.0204689 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_pubme</sourceid><recordid>TN_cdi_proquest_miscellaneous_3075378287</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3075426073</sourcerecordid><originalsourceid>FETCH-LOGICAL-c238t-c6e19bc4e667b1bb87c5f996f0178da68f235085b886100c5ad905ba1b62a0bb3</originalsourceid><addsrcrecordid>eNp90L1OwzAUBWALgSgUBl4ARWIBpLTXcezYI6qAVqrEAlLFEtmO07pKnDZOhm68Bq_Hk5D-wMDAZA_fPTo6CF1hGGBgZEgHEEHMuDhCZxi4CBPGo-Ptn8YhpgA9dO79EgBwROgp6hEuKKdEnKHxxFs3D_zKuhAPo2A2ew_0Qlr39fHpg3UrXdOWwaquVGFKHyizqVwWNAuzO6lcsJK1zOy8vEAnuSy8uTy8ffT29Pg6GofTl-fJ6GEa6ojwJtTMYKF0bBhLFFaKJ5rmQrAccMIzyXjeNQROFecMA2gqMwFUSaxYJEEp0ke3-9yu07o1vklL67UpCulM1fqUQEJJwiOedPTmD11Wbe26djsVRwwS0qm7vdJ15X1t8nRV21LWmxRDup03pelh3s5eHxJbVZrsV_7s2YH7PfDaNrKxlfsn7RsiiICL</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3075426073</pqid></control><display><type>article</type><title>Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm</title><source>AIP Journals Complete</source><creator>Carmelo, J. M. P. ; Sacramento, P. D.</creator><creatorcontrib>Carmelo, J. M. P. ; Sacramento, P. D.</creatorcontrib><description>Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit,
N
→
∞, in terms of the
N spin-
1
/
2 physical spins of the spin-
1
/
2
X
X
Z chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies
Δ
>
1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin-
1
/
2
X
X
Z chain’s continuous
S
U
q
(
2
) symmetry parameterized by
q
=
Δ
+
Δ
2
−
1
∈
]
1
,
∞
] and associated with
q-spin
S
q. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length
n that have no spinon representation, contribute to the dynamical properties of the spin-
1
/
2
X
X
Z chain with anisotropy
Δ
>
1 and for
n
=
1
,
2
,
3 were experimentally identified and realized in the zigzag materials SrCo
2V
2O
8 and BaCo
2V
2O
8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous
S
U
q
(
2
) symmetry reveals that for anisotropy
Δ
>
1 the Bethe strings of length
n
=
1
,
2
,
3
,
… describe a number
n of physical-spins
S
q
=
0 singlet pairs that for
n
>
1 are bound within a
S
q
=
0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin-
1
/
2
X
X
Z chain in a longitudinal magnetic field and the spin chains in SrCo
2V
2O
8 is one of the issues addressed in this paper. In addition, the
S
U
q
(
2
) symmetry imposes that only
2
S
q out of the
N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento [“Diffusive spin transport of the spin-1/2 XXZ chain in the Ising regime at zero magnetic field and finite temperature,” (submitted) (2024)] concerning the vanishing of the contributions to finite-temperature ballistic spin transport at zero magnetic field. Within the physical-spins representation, this merely follows from the absolute value of the elementary spin currents carried by the
M
=
2
S
q spin carriers of all finite-
S
q states that contribute to the spin stiffness being finite. Finally, we discuss deviations of the zigzag materials BaCo
2V
2O
8 and SrCo
2V
2O
8 from the one-dimensional physics described the spin-
1
/
2
X
X
Z chain due to selective interchain couplings.</description><identifier>ISSN: 1054-1500</identifier><identifier>ISSN: 1089-7682</identifier><identifier>EISSN: 1089-7682</identifier><identifier>DOI: 10.1063/5.0204689</identifier><identifier>PMID: 38958539</identifier><identifier>CODEN: CHAOEH</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>Anisotropy ; Couplings ; Effectiveness ; Eigenvectors ; Hilbert space ; Ising model ; Magnetic fields ; Magnetic properties ; Representations ; Stiffness ; Strings ; Structure factor ; Symmetry ; Thermodynamics</subject><ispartof>Chaos (Woodbury, N.Y.), 2024-07, Vol.34 (7)</ispartof><rights>Author(s)</rights><rights>2024 Author(s). Published under an exclusive license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c238t-c6e19bc4e667b1bb87c5f996f0178da68f235085b886100c5ad905ba1b62a0bb3</cites><orcidid>0000-0001-5624-6294 ; 0000-0002-8276-6485</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>313,314,776,780,788,790,4498,27899,27901,27902</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/38958539$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Carmelo, J. M. P.</creatorcontrib><creatorcontrib>Sacramento, P. D.</creatorcontrib><title>Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm</title><title>Chaos (Woodbury, N.Y.)</title><addtitle>Chaos</addtitle><description>Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit,
N
→
∞, in terms of the
N spin-
1
/
2 physical spins of the spin-
1
/
2
X
X
Z chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies
Δ
>
1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin-
1
/
2
X
X
Z chain’s continuous
S
U
q
(
2
) symmetry parameterized by
q
=
Δ
+
Δ
2
−
1
∈
]
1
,
∞
] and associated with
q-spin
S
q. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length
n that have no spinon representation, contribute to the dynamical properties of the spin-
1
/
2
X
X
Z chain with anisotropy
Δ
>
1 and for
n
=
1
,
2
,
3 were experimentally identified and realized in the zigzag materials SrCo
2V
2O
8 and BaCo
2V
2O
8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous
S
U
q
(
2
) symmetry reveals that for anisotropy
Δ
>
1 the Bethe strings of length
n
=
1
,
2
,
3
,
… describe a number
n of physical-spins
S
q
=
0 singlet pairs that for
n
>
1 are bound within a
S
q
=
0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin-
1
/
2
X
X
Z chain in a longitudinal magnetic field and the spin chains in SrCo
2V
2O
8 is one of the issues addressed in this paper. In addition, the
S
U
q
(
2
) symmetry imposes that only
2
S
q out of the
N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento [“Diffusive spin transport of the spin-1/2 XXZ chain in the Ising regime at zero magnetic field and finite temperature,” (submitted) (2024)] concerning the vanishing of the contributions to finite-temperature ballistic spin transport at zero magnetic field. Within the physical-spins representation, this merely follows from the absolute value of the elementary spin currents carried by the
M
=
2
S
q spin carriers of all finite-
S
q states that contribute to the spin stiffness being finite. Finally, we discuss deviations of the zigzag materials BaCo
2V
2O
8 and SrCo
2V
2O
8 from the one-dimensional physics described the spin-
1
/
2
X
X
Z chain due to selective interchain couplings.</description><subject>Anisotropy</subject><subject>Couplings</subject><subject>Effectiveness</subject><subject>Eigenvectors</subject><subject>Hilbert space</subject><subject>Ising model</subject><subject>Magnetic fields</subject><subject>Magnetic properties</subject><subject>Representations</subject><subject>Stiffness</subject><subject>Strings</subject><subject>Structure factor</subject><subject>Symmetry</subject><subject>Thermodynamics</subject><issn>1054-1500</issn><issn>1089-7682</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp90L1OwzAUBWALgSgUBl4ARWIBpLTXcezYI6qAVqrEAlLFEtmO07pKnDZOhm68Bq_Hk5D-wMDAZA_fPTo6CF1hGGBgZEgHEEHMuDhCZxi4CBPGo-Ptn8YhpgA9dO79EgBwROgp6hEuKKdEnKHxxFs3D_zKuhAPo2A2ew_0Qlr39fHpg3UrXdOWwaquVGFKHyizqVwWNAuzO6lcsJK1zOy8vEAnuSy8uTy8ffT29Pg6GofTl-fJ6GEa6ojwJtTMYKF0bBhLFFaKJ5rmQrAccMIzyXjeNQROFecMA2gqMwFUSaxYJEEp0ke3-9yu07o1vklL67UpCulM1fqUQEJJwiOedPTmD11Wbe26djsVRwwS0qm7vdJ15X1t8nRV21LWmxRDup03pelh3s5eHxJbVZrsV_7s2YH7PfDaNrKxlfsn7RsiiICL</recordid><startdate>202407</startdate><enddate>202407</enddate><creator>Carmelo, J. M. P.</creator><creator>Sacramento, P. D.</creator><general>American Institute of Physics</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0001-5624-6294</orcidid><orcidid>https://orcid.org/0000-0002-8276-6485</orcidid></search><sort><creationdate>202407</creationdate><title>Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm</title><author>Carmelo, J. M. P. ; Sacramento, P. D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c238t-c6e19bc4e667b1bb87c5f996f0178da68f235085b886100c5ad905ba1b62a0bb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Anisotropy</topic><topic>Couplings</topic><topic>Effectiveness</topic><topic>Eigenvectors</topic><topic>Hilbert space</topic><topic>Ising model</topic><topic>Magnetic fields</topic><topic>Magnetic properties</topic><topic>Representations</topic><topic>Stiffness</topic><topic>Strings</topic><topic>Structure factor</topic><topic>Symmetry</topic><topic>Thermodynamics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carmelo, J. M. P.</creatorcontrib><creatorcontrib>Sacramento, P. D.</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Carmelo, J. M. P.</au><au>Sacramento, P. D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2024-07</date><risdate>2024</risdate><volume>34</volume><issue>7</issue><issn>1054-1500</issn><issn>1089-7682</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit,
N
→
∞, in terms of the
N spin-
1
/
2 physical spins of the spin-
1
/
2
X
X
Z chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies
Δ
>
1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin-
1
/
2
X
X
Z chain’s continuous
S
U
q
(
2
) symmetry parameterized by
q
=
Δ
+
Δ
2
−
1
∈
]
1
,
∞
] and associated with
q-spin
S
q. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length
n that have no spinon representation, contribute to the dynamical properties of the spin-
1
/
2
X
X
Z chain with anisotropy
Δ
>
1 and for
n
=
1
,
2
,
3 were experimentally identified and realized in the zigzag materials SrCo
2V
2O
8 and BaCo
2V
2O
8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous
S
U
q
(
2
) symmetry reveals that for anisotropy
Δ
>
1 the Bethe strings of length
n
=
1
,
2
,
3
,
… describe a number
n of physical-spins
S
q
=
0 singlet pairs that for
n
>
1 are bound within a
S
q
=
0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin-
1
/
2
X
X
Z chain in a longitudinal magnetic field and the spin chains in SrCo
2V
2O
8 is one of the issues addressed in this paper. In addition, the
S
U
q
(
2
) symmetry imposes that only
2
S
q out of the
N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento [“Diffusive spin transport of the spin-1/2 XXZ chain in the Ising regime at zero magnetic field and finite temperature,” (submitted) (2024)] concerning the vanishing of the contributions to finite-temperature ballistic spin transport at zero magnetic field. Within the physical-spins representation, this merely follows from the absolute value of the elementary spin currents carried by the
M
=
2
S
q spin carriers of all finite-
S
q states that contribute to the spin stiffness being finite. Finally, we discuss deviations of the zigzag materials BaCo
2V
2O
8 and SrCo
2V
2O
8 from the one-dimensional physics described the spin-
1
/
2
X
X
Z chain due to selective interchain couplings.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><pmid>38958539</pmid><doi>10.1063/5.0204689</doi><tpages>26</tpages><orcidid>https://orcid.org/0000-0001-5624-6294</orcidid><orcidid>https://orcid.org/0000-0002-8276-6485</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | Chaos (Woodbury, N.Y.), 2024-07, Vol.34 (7) |
| issn | 1054-1500 1089-7682 1089-7682 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_3075378287 |
| source | AIP Journals Complete |
| subjects | Anisotropy Couplings Effectiveness Eigenvectors Hilbert space Ising model Magnetic fields Magnetic properties Representations Stiffness Strings Structure factor Symmetry Thermodynamics |
| title | Ising spin-1/2 XXZ chain’s quantum problems beyond the spinon paradigm |
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