Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
Numerical studies of the transition between Néel and valence bond solid phases in two-dimensional quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to real...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/100556 https://orcid.org/0000-0002-3488-4532 |
| _version_ | 1811084597233975296 |
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| author | Nahum, Adam Chalker, J. T. Serna, P. Ortuno, M. Somoza, A. M. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Nahum, Adam Chalker, J. T. Serna, P. Ortuno, M. Somoza, A. M. |
| author_sort | Nahum, Adam |
| collection | MIT |
| description | Numerical studies of the transition between Néel and valence bond solid phases in two-dimensional quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realize the universal physics of the Néel–valence-bond-solid (VBS) transition in a three-dimensional classical loop model (this model includes the subtle interference effect that suppresses hedgehog defects in the Néel order parameter). We use the loop model for simulations of unprecedentedly large systems (up to linear size L = 512). Our results are compatible with a continuous transition at which both Néel and VBS order parameters are critical, and we do not see conventional signs of first-order behavior. However, we show that the scaling violations are stronger than previously realized and are incompatible with conventional finite-size scaling, even if allowance is made for a weakly or marginally irrelevant scaling variable. In particular, different approaches to determining the anomalous dimensions η[subscript VBS] and η[subscript Néel] yield very different results. The assumption of conventional finite-size scaling leads to estimates that drift to negative values at large sizes, in violation of the unitarity bounds. In contrast, the decay with distance of critical correlators on scales much smaller than system size is consistent with large positive anomalous dimensions. Barring an unexpected reversal in behavior at still larger sizes, this implies that the transition, if continuous, must show unconventional finite-size scaling, for example, from an additional dangerously irrelevant scaling variable. Another possibility is an anomalously weak first-order transition. By analyzing the renormalization group flows for the noncompact CP[superscript n-1] field theory (the n-component Abelian Higgs model) between two and four dimensions, we give the simplest scenario by which an anomalously weak first-order transition can arise without fine-tuning of the Hamiltonian. |
| first_indexed | 2024-09-23T12:53:41Z |
| format | Article |
| id | mit-1721.1/100556 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:53:41Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1005562022-10-01T11:46:17Z Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models Nahum, Adam Chalker, J. T. Serna, P. Ortuno, M. Somoza, A. M. Massachusetts Institute of Technology. Department of Physics Nahum, Adam Numerical studies of the transition between Néel and valence bond solid phases in two-dimensional quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realize the universal physics of the Néel–valence-bond-solid (VBS) transition in a three-dimensional classical loop model (this model includes the subtle interference effect that suppresses hedgehog defects in the Néel order parameter). We use the loop model for simulations of unprecedentedly large systems (up to linear size L = 512). Our results are compatible with a continuous transition at which both Néel and VBS order parameters are critical, and we do not see conventional signs of first-order behavior. However, we show that the scaling violations are stronger than previously realized and are incompatible with conventional finite-size scaling, even if allowance is made for a weakly or marginally irrelevant scaling variable. In particular, different approaches to determining the anomalous dimensions η[subscript VBS] and η[subscript Néel] yield very different results. The assumption of conventional finite-size scaling leads to estimates that drift to negative values at large sizes, in violation of the unitarity bounds. In contrast, the decay with distance of critical correlators on scales much smaller than system size is consistent with large positive anomalous dimensions. Barring an unexpected reversal in behavior at still larger sizes, this implies that the transition, if continuous, must show unconventional finite-size scaling, for example, from an additional dangerously irrelevant scaling variable. Another possibility is an anomalously weak first-order transition. By analyzing the renormalization group flows for the noncompact CP[superscript n-1] field theory (the n-component Abelian Higgs model) between two and four dimensions, we give the simplest scenario by which an anomalously weak first-order transition can arise without fine-tuning of the Hamiltonian. Engineering and Physical Sciences Research Council (Grant EP/I032487/1) Spain. Ministerio de Economia y Competitividad (FEDER Grant FIS2012-38206) Spain. Ministerio de Educacion, Cultura y Deporte. Formacion de Profesorado Universitario (Grant AP2009-0668) Gordon and Betty Moore Foundation. EPiQS Initiative (Grant GBMF4303) 2015-12-30T02:02:53Z 2015-12-30T02:02:53Z 2015-12 2015-06 2015-12-23T23:00:04Z Article http://purl.org/eprint/type/JournalArticle 2160-3308 http://hdl.handle.net/1721.1/100556 Nahum, Adam, J. T. Chalker, P. Serna, M. Ortuno, and A. M. Somoza. “Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models.” Physical Review X 5, no. 4 (December 23, 2015). https://orcid.org/0000-0002-3488-4532 en http://dx.doi.org/10.1103/PhysRevX.5.041048 Physical Review X Creative Commons Attribution http://creativecommons.org/licenses/by/3.0 authors application/pdf American Physical Society American Physical Society |
| spellingShingle | Nahum, Adam Chalker, J. T. Serna, P. Ortuno, M. Somoza, A. M. Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models |
| title | Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models |
| title_full | Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models |
| title_fullStr | Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models |
| title_full_unstemmed | Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models |
| title_short | Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models |
| title_sort | deconfined quantum criticality scaling violations and classical loop models |
| url | http://hdl.handle.net/1721.1/100556 https://orcid.org/0000-0002-3488-4532 |
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