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2015

A tensor network quotient takes the vacuum to the thermal state

Czech, Bartlomiej, Evenbly, Glen, Lamprou, Lampros et al.

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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, which is explicitly broken by the choice of lattice.

A tensor network quotient takes the vacuum to the thermal state · Around

Built on

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2006
Earlier work this paper cites.

Similar

G. Vidal, “Entanglement renormalization,” Phys. Rev. Lett. 99
2008
Cited alongside, same era.
R. N. C. Pfeifer, G. Evenbly, G. Vidal, “Entanglement renormalization, scale invariance, and quantum criticality,” Phys. Rev. A 79(4), 040301(R) (2009), arXiv:0810.0580
Original
2009
Cited alongside, same era.
B. Swingle, “Entanglement renormalization and holography,” Phys. Rev. D 86
Original
2012
Cited alongside, same era.
B. Czech, G. Evenbly, L. Lamprou, S. McCandlish, X.-L. Qi, J. Sully and G. Vidal, to appear
Cited in the paper.
G. Evenbly and G. Vidal, “Tensor network renormalization,” to appear in Phys. Rev. Lett. [arXiv:1412.0732 [cond-mat.str-el]]
Original
Cited in the paper.
G. Evenbly and G. Vidal, “Tensor network renormalization yields the multi-scale entanglement renormalization ansatz,” arXiv:1502.05385 [cond-mat.str-el]
Original
Cited in the paper.
G. Evenbly and G. Vidal, “Algorithms for tensor network renormalization,” arXiv:1509.07484 [cond-mat.str-el]
Original
Cited in the paper.
G. Evenbly and G. Vidal, “Local scale transformations on the lattice with tensor network renormalization,” arXiv:1510.00689 [cond-mat.str-el]
Original
Cited in the paper.
B. Czech, L. Lamprou, S. McCandlish and J. Sully, “Integral Geometry and Holography,” arXiv:1505.05515 [hep-th]
Original
Cited in the paper.

Then

M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev. D 48
2013
Later among the works it cites.
V. Balasubramanian, B. D. Chowdhury, B. Czech and J. de Boer, “Entwinement and the emergence of spacetime,” JHEP 1501
Original
2015
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