Bicolor loop models and their long range entanglement

Fuente: arXiv
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Main Author: Zhang, Zhao
Format: Preprint
Published: 2023
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_version_ 1866910354226806784
author Zhang, Zhao
author_facet Zhang, Zhao
contents Quantum loop models are well studied objects in the context of lattice gauge theories and topological quantum computing. They usually carry long range entanglement that is captured by the topological entanglement entropy. I consider generalization of the toric code model to bicolor loop models and show that the long range entanglement can be reflected in three different ways: a topologically invariant constant, a sub-leading logarithmic correction to the area law, or a modified bond dimension for the area-law term. The Hamiltonians are not exactly solvable for the whole spectra, but admit a tower of area-law exact excited states corresponding to the frustration free superposition of loop configurations with arbitrary pairs of localized vertex defects. The continuity of color along loops imposes kinetic constraints on the model and results in Hilbert space fragmentation, unless plaquette operators involving two neighboring faces are introduced to the Hamiltonian.
format Preprint
id arxiv_https___arxiv_org_abs_2306_05464
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Bicolor loop models and their long range entanglement
Zhang, Zhao
Quantum Physics
Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
Quantum loop models are well studied objects in the context of lattice gauge theories and topological quantum computing. They usually carry long range entanglement that is captured by the topological entanglement entropy. I consider generalization of the toric code model to bicolor loop models and show that the long range entanglement can be reflected in three different ways: a topologically invariant constant, a sub-leading logarithmic correction to the area law, or a modified bond dimension for the area-law term. The Hamiltonians are not exactly solvable for the whole spectra, but admit a tower of area-law exact excited states corresponding to the frustration free superposition of loop configurations with arbitrary pairs of localized vertex defects. The continuity of color along loops imposes kinetic constraints on the model and results in Hilbert space fragmentation, unless plaquette operators involving two neighboring faces are introduced to the Hamiltonian.
title Bicolor loop models and their long range entanglement
topic Quantum Physics
Statistical Mechanics
High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2306.05464