Tensor network quotient takes the vacuum to the thermal state

In 1+1-dimensional conformal-field theory, the thermal state on a circle is related to a certain quotient of the vacuum on a line. We explain how to take this quotient in the MERA tensor network representation of the vacuum and confirm the validity of the construction in the critical Ising model. Th...

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Bibliographic Details
Published in:Physical review. B 2016-08, Vol.94 (8), Article 085101
Main Authors: Czech, Bartłomiej, Evenbly, Glen, Lamprou, Lampros, McCandlish, Samuel, Qi, Xiao-liang, Sully, James, Vidal, Guifré
Format: Article
Language:English
Subjects:
Condensed matter
Mathematical analysis
Networks
Quotients
Representations
Tensors
Transformations (mathematics)
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Summary:In 1+1-dimensional conformal-field theory, the thermal state on a circle is related to a certain quotient of the vacuum on a line. We explain how to take this quotient in the MERA tensor network representation of the vacuum and confirm the validity of the construction in the critical Ising model. This result suggests that the tensors comprising MERA can be interpreted as performing local scale transformations, so that adding or removing them emulates conformal maps. In this sense, the optimized MERA recovers local conformal invariance that is broken by the choice of lattice.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.94.085101