Many-body localization in spin chains with long-range transverse interactions: Scaling of critical disorder with system size Article Swipe
Andrii Maksymov
,
Alexander L. Burin
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1103/physrevb.101.024201
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1103/physrevb.101.024201
We investigate many-body localization in the chain of interacting spins with\na transverse power-law interaction, $J_{0}/r^{\\alpha}$, and random on-site\npotentials, $\\phi_i \\in \\left(-W/2,W/2\\right)$, in the long-range limit,\n$\\alpha< 3/2$, which has been recently examined experimentally on trapped ions.\nThe many-body localization threshold is characterized by the critical\ndisordering, $W_c$, which separates localized ($W > W_c$) and chaotic ($W <\nW_c$) phases. Using the analysis of the instability of localized states with\nrespect to resonant interactions complemented by numerical finite size scaling,\nwe show that the critical disordering scales with the number of spins, $N$, as\n$W_c \\approx [1.37 J_{0}/(4/3 - \\alpha)]N^{4/3 - \\alpha} \\ln N$ for $0 < \\alpha\n\\leq 1$, and as $W_c \\approx [J_{0}/(1-2\\alpha/3)]N^{1-2\\alpha/3} \\ln^{2/3} N$\nfor $1 < \\alpha < 3/2$ while the transition width scales as $\\sigma_{W} \\propto\nW_{c}/N$. We use this result to predict the spin long-term evolution for a very\nlarge number of spins ($N = 50$), inaccessible for exact diagonalization, and\nto suggest the rescaling of hopping interaction with the system size to attain\nthe localization transition at finite disordering in the thermodynamic limit of\ninfinite number of spins.\n
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physrevb.101.024201
- OA Status
- green
- Cited By
- 24
- References
- 66
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- OpenAlex ID
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- OpenAlex ID
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https://openalex.org/W2963486243Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1103/physrevb.101.024201Digital Object Identifier
- Title
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Many-body localization in spin chains with long-range transverse interactions: Scaling of critical disorder with system sizeWork title
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-01-07Full publication date if available
- Authors
-
Andrii Maksymov, Alexander L. BurinList of authors in order
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https://doi.org/10.1103/physrevb.101.024201Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/1905.02286Direct OA link when available
- Concepts
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Physics, Spins, Scaling, Thermodynamic limit, Condensed matter physics, Spin (aerodynamics), Scaling limit, Quantum mechanics, Thermodynamics, Geometry, MathematicsTop concepts (fields/topics) attached by OpenAlex
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24Total citation count in OpenAlex
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2025: 2, 2024: 3, 2023: 5, 2022: 3, 2021: 7Per-year citation counts (last 5 years)
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66Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.the | 5, 22, 41, 56, 59, 76, 81, 114, 127, 146, 152, 163 |
| abstract_inverted_index.use | 122 |
| abstract_inverted_index.$N$, | 85 |
| abstract_inverted_index.$W_c | 103 |
| abstract_inverted_index.> | 48 |
| abstract_inverted_index.< | 98, 109, 111 |
| abstract_inverted_index.3/2$ | 112 |
| abstract_inverted_index.\\in | 19 |
| abstract_inverted_index.\\ln | 94 |
| abstract_inverted_index.been | 28 |
| abstract_inverted_index.show | 74 |
| abstract_inverted_index.size | 72, 154 |
| abstract_inverted_index.spin | 128 |
| abstract_inverted_index.that | 75 |
| abstract_inverted_index.this | 123 |
| abstract_inverted_index.with | 80, 151 |
| abstract_inverted_index.3/2$, | 25 |
| abstract_inverted_index.50$), | 139 |
| abstract_inverted_index.Using | 55 |
| abstract_inverted_index.W_c$) | 49 |
| abstract_inverted_index.[1.37 | 88 |
| abstract_inverted_index.chain | 6 |
| abstract_inverted_index.exact | 142 |
| abstract_inverted_index.limit | 165 |
| abstract_inverted_index.spins | 9, 136 |
| abstract_inverted_index.which | 26, 44 |
| abstract_inverted_index.while | 113 |
| abstract_inverted_index.width | 116 |
| abstract_inverted_index.$W_c$, | 43 |
| abstract_inverted_index.finite | 71, 160 |
| abstract_inverted_index.number | 82, 134, 167 |
| abstract_inverted_index.random | 16 |
| abstract_inverted_index.result | 124 |
| abstract_inverted_index.scales | 79, 117 |
| abstract_inverted_index.spins, | 84 |
| abstract_inverted_index.states | 63 |
| abstract_inverted_index.system | 153 |
| abstract_inverted_index.N$\nfor | 107 |
| abstract_inverted_index.\\alpha | 110 |
| abstract_inverted_index.and\nto | 144 |
| abstract_inverted_index.chaotic | 51 |
| abstract_inverted_index.hopping | 149 |
| abstract_inverted_index.phases. | 54 |
| abstract_inverted_index.predict | 126 |
| abstract_inverted_index.suggest | 145 |
| abstract_inverted_index.trapped | 33 |
| abstract_inverted_index.with\na | 10 |
| abstract_inverted_index.$\\phi_i | 18 |
| abstract_inverted_index.\\alpha} | 93 |
| abstract_inverted_index.\\approx | 87, 104 |
| abstract_inverted_index.analysis | 57 |
| abstract_inverted_index.as\n$W_c | 86 |
| abstract_inverted_index.critical | 77 |
| abstract_inverted_index.examined | 30 |
| abstract_inverted_index.recently | 29 |
| abstract_inverted_index.resonant | 66 |
| abstract_inverted_index.spins.\n | 169 |
| abstract_inverted_index.evolution | 130 |
| abstract_inverted_index.localized | 46, 62 |
| abstract_inverted_index.long-term | 129 |
| abstract_inverted_index.many-body | 2, 35 |
| abstract_inverted_index.numerical | 70 |
| abstract_inverted_index.power-law | 12 |
| abstract_inverted_index.rescaling | 147 |
| abstract_inverted_index.separates | 45 |
| abstract_inverted_index.threshold | 37 |
| abstract_inverted_index.J_{0}/(4/3 | 89 |
| abstract_inverted_index.\\ln^{2/3} | 106 |
| abstract_inverted_index.ions.\nThe | 34 |
| abstract_inverted_index.long-range | 23 |
| abstract_inverted_index.transition | 115, 158 |
| abstract_inverted_index.transverse | 11 |
| abstract_inverted_index.<\nW_c$) | 53 |
| abstract_inverted_index.attain\nthe | 156 |
| abstract_inverted_index.disordering | 78, 161 |
| abstract_inverted_index.instability | 60 |
| abstract_inverted_index.interacting | 8 |
| abstract_inverted_index.interaction | 150 |
| abstract_inverted_index.investigate | 1 |
| abstract_inverted_index.very\nlarge | 133 |
| abstract_inverted_index.$\\sigma_{W} | 119 |
| abstract_inverted_index.complemented | 68 |
| abstract_inverted_index.inaccessible | 140 |
| abstract_inverted_index.interaction, | 13 |
| abstract_inverted_index.interactions | 67 |
| abstract_inverted_index.localization | 3, 36, 157 |
| abstract_inverted_index.of\ninfinite | 166 |
| abstract_inverted_index.scaling,\nwe | 73 |
| abstract_inverted_index.characterized | 39 |
| abstract_inverted_index.thermodynamic | 164 |
| abstract_inverted_index.with\nrespect | 64 |
| abstract_inverted_index.\\alpha\n\\leq | 99 |
| abstract_inverted_index.experimentally | 31 |
| abstract_inverted_index.\\alpha)]N^{4/3 | 91 |
| abstract_inverted_index.diagonalization, | 143 |
| abstract_inverted_index.\\propto\nW_{c}/N$. | 120 |
| abstract_inverted_index.$J_{0}/r^{\\alpha}$, | 14 |
| abstract_inverted_index.limit,\n$\\alpha< | 24 |
| abstract_inverted_index.on-site\npotentials, | 17 |
| abstract_inverted_index.critical\ndisordering, | 42 |
| abstract_inverted_index.\\left(-W/2,W/2\\right)$, | 20 |
| abstract_inverted_index.[J_{0}/(1-2\\alpha/3)]N^{1-2\\alpha/3} | 105 |
| cited_by_percentile_year.max | 98 |
| cited_by_percentile_year.min | 95 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.91304412 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |