Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
| Autor: | Schossler, Matheus, Bandyopadhyay, Sumanta, Seidel, Alexander |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 105, 155124 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.105.155124 |
| Popis: | We study frustration-free Hamiltonians of fractional quantum Hall (FQH) states from the point of view of the matrix product state (MPS) representation of their ground and excited states. There is a wealth of solvable models relating to FQH physics, which, however, is mostly derived and analyzed from the vantage point of first-quantized "analytic clustering properties". In contrast, one obtains long-ranged frustration-free lattice models when these Hamiltonians are studied in an orbital basis, which is the natural basis for the MPS representation of FQH states. The connection between MPS-like states and frustration-free parent Hamiltonians is the central guiding principle in the construction of solvable lattice models, but thus far, only for short-range Hamiltonians and MPSs of finite bond dimension. The situation in the FQH context is fundamentally different. Here we expose the direct link between the infinite-bond-dimension MPS structure of Laughlin-conformal field theory (CFT) states and their parent Hamiltonians. While focusing on the Laughlin state, generalizations to other CFT-MPSs will become transparent. Comment: published version |
| Databáze: | arXiv |
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