Thermal Tensor Network Approach for Spin-Lattice Relaxation in Quantum Magnets
| Title: | Thermal Tensor Network Approach for Spin-Lattice Relaxation in Quantum Magnets |
|---|---|
| Authors: | Xi, Ning, Gao, Yuan, Li, Chengchen, Liang, Shuang, Yu, Rong, Wang, Xiaoqun, Li, Wei |
| Publication Year: | 2024 |
| Collection: | Condensed Matter |
| Subject Terms: | Condensed Matter - Strongly Correlated Electrons |
| More Details: | Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate $1/T_1$, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents $\eta$ and $z\nu$ can be extracted from the low-temperature scalings of the simulated $1/T_1$ near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb$_2$O$_6$ and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba$_8$CoNb$_6$O$_{24}$. We apply the approach to effective model of the family of frustrated magnets AYbCh$_2$ (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields. Comment: 15 pages, 12 figures |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2403.11895 |
| Accession Number: | edsarx.2403.11895 |
| Database: | arXiv |
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| Items | – Name: Title Label: Title Group: Ti Data: Thermal Tensor Network Approach for Spin-Lattice Relaxation in Quantum Magnets – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Xi%2C+Ning%22">Xi, Ning</searchLink><br /><searchLink fieldCode="AR" term="%22Gao%2C+Yuan%22">Gao, Yuan</searchLink><br /><searchLink fieldCode="AR" term="%22Li%2C+Chengchen%22">Li, Chengchen</searchLink><br /><searchLink fieldCode="AR" term="%22Liang%2C+Shuang%22">Liang, Shuang</searchLink><br /><searchLink fieldCode="AR" term="%22Yu%2C+Rong%22">Yu, Rong</searchLink><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xiaoqun%22">Wang, Xiaoqun</searchLink><br /><searchLink fieldCode="AR" term="%22Li%2C+Wei%22">Li, Wei</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2024 – Name: Subset Label: Collection Group: HoldingsInfo Data: Condensed Matter – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Condensed+Matter+-+Strongly+Correlated+Electrons%22">Condensed Matter - Strongly Correlated Electrons</searchLink> – Name: Abstract Label: Description Group: Ab Data: Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate $1/T_1$, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents $\eta$ and $z\nu$ can be extracted from the low-temperature scalings of the simulated $1/T_1$ near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb$_2$O$_6$ and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba$_8$CoNb$_6$O$_{24}$. We apply the approach to effective model of the family of frustrated magnets AYbCh$_2$ (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields.<br />Comment: 15 pages, 12 figures – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2403.11895" linkWindow="_blank">http://arxiv.org/abs/2403.11895</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2403.11895 |
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| RecordInfo | BibRecord: BibEntity: Subjects: – SubjectFull: Condensed Matter - Strongly Correlated Electrons Type: general Titles: – TitleFull: Thermal Tensor Network Approach for Spin-Lattice Relaxation in Quantum Magnets Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Xi, Ning – PersonEntity: Name: NameFull: Gao, Yuan – PersonEntity: Name: NameFull: Li, Chengchen – PersonEntity: Name: NameFull: Liang, Shuang – PersonEntity: Name: NameFull: Yu, Rong – PersonEntity: Name: NameFull: Wang, Xiaoqun – PersonEntity: Name: NameFull: Li, Wei IsPartOfRelationships: – BibEntity: Dates: – D: 18 M: 03 Type: published Y: 2024 |
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