Quantum criticality of loops with topologically constrained dynamics
Quantum fluctuating loops in 2+1 dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.033051 |
| _version_ | 1797211346294538240 |
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| author | Zhehao Dai Adam Nahum |
| author_facet | Zhehao Dai Adam Nahum |
| author_sort | Zhehao Dai |
| collection | DOAJ |
| description | Quantum fluctuating loops in 2+1 dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is that reconnection of a pair of strands is forbidden. This happens at previously studied multicritical points between topologically nontrivial phases. We show that this topologically constrained dynamics leads to universality classes with unusual scaling properties. For example, scaling operators at these fixed points are classified by topology and not only by symmetry. We introduce the concept of the topological operator classification, provide universal scaling forms for correlation functions, and analytical and numerical results for critical exponents. We use an exact correspondence between the imaginary-time dynamics of the 2+1D quantum models and a classical Markovian dynamics for 2D classical loop models with a nonlocal Boltzmann weight (for which we also provide scaling results). We comment on open questions and generalizations of the models discussed for both quantum criticality and classical Markov processes. |
| first_indexed | 2024-04-24T10:25:02Z |
| format | Article |
| id | doaj.art-9433d3f3db26428383db7e51d5b9ed7a |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:25:02Z |
| publishDate | 2020-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-9433d3f3db26428383db7e51d5b9ed7a2024-04-12T16:56:55ZengAmerican Physical SocietyPhysical Review Research2643-15642020-07-012303305110.1103/PhysRevResearch.2.033051Quantum criticality of loops with topologically constrained dynamicsZhehao DaiAdam NahumQuantum fluctuating loops in 2+1 dimensions give gapless many-body states that are beyond current field theory techniques. Microscopically, these loops can be domain walls between up and down spins or chains of flipped spins similar to those in the toric code. The key feature of their dynamics is that reconnection of a pair of strands is forbidden. This happens at previously studied multicritical points between topologically nontrivial phases. We show that this topologically constrained dynamics leads to universality classes with unusual scaling properties. For example, scaling operators at these fixed points are classified by topology and not only by symmetry. We introduce the concept of the topological operator classification, provide universal scaling forms for correlation functions, and analytical and numerical results for critical exponents. We use an exact correspondence between the imaginary-time dynamics of the 2+1D quantum models and a classical Markovian dynamics for 2D classical loop models with a nonlocal Boltzmann weight (for which we also provide scaling results). We comment on open questions and generalizations of the models discussed for both quantum criticality and classical Markov processes.http://doi.org/10.1103/PhysRevResearch.2.033051 |
| spellingShingle | Zhehao Dai Adam Nahum Quantum criticality of loops with topologically constrained dynamics Physical Review Research |
| title | Quantum criticality of loops with topologically constrained dynamics |
| title_full | Quantum criticality of loops with topologically constrained dynamics |
| title_fullStr | Quantum criticality of loops with topologically constrained dynamics |
| title_full_unstemmed | Quantum criticality of loops with topologically constrained dynamics |
| title_short | Quantum criticality of loops with topologically constrained dynamics |
| title_sort | quantum criticality of loops with topologically constrained dynamics |
| url | http://doi.org/10.1103/PhysRevResearch.2.033051 |
| work_keys_str_mv | AT zhehaodai quantumcriticalityofloopswithtopologicallyconstraineddynamics AT adamnahum quantumcriticalityofloopswithtopologicallyconstraineddynamics |