Spacetime Symmetries and Conformal Data in the Continuous Multiscale Entanglement Renormalization Ansatz

Spacetime Symmetries and Conformal Data in the Continuous Multiscale Entanglement Renormalization... The generalization of the multiscale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.100402], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this Letter, we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state |ΨΛ⟩ with finite UV cutoff Λ can capture the spacetime symmetries of the ground state |Ψ⟩. For a free boson conformal field theory (CFT) in 1+1 dimensions, as a concrete example, we build a quasilocal unitary transformation V that maps |Ψ⟩ into |ΨΛ⟩ and show two main results. (i) Any spacetime symmetry of the ground state |Ψ⟩ is also mapped by V into a spacetime symmetry of the cMERA |ΨΛ⟩. However, while in the CFT, the stress-energy tensor Tμν(x) (in terms of which all the spacetime symmetry generators are expressed) is local, and the corresponding cMERA stress-energy tensor TμνΛ(x)=VTμν(x)V† is quasilocal. (ii) From the cMERA, we can extract quasilocal scaling operators OαΛ(x) characterized by the exact same scaling dimensions Δα, conformal spins sα, operator product expansion coefficients Cαβγ, and central charge c as the original CFT. Finally, we argue that these results should also apply to interacting theories. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

Spacetime Symmetries and Conformal Data in the Continuous Multiscale Entanglement Renormalization Ansatz

Preview Only

Spacetime Symmetries and Conformal Data in the Continuous Multiscale Entanglement Renormalization Ansatz

Abstract

The generalization of the multiscale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.100402], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this Letter, we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state |ΨΛ⟩ with finite UV cutoff Λ can capture the spacetime symmetries of the ground state |Ψ⟩. For a free boson conformal field theory (CFT) in 1+1 dimensions, as a concrete example, we build a quasilocal unitary transformation V that maps |Ψ⟩ into |ΨΛ⟩ and show two main results. (i) Any spacetime symmetry of the ground state |Ψ⟩ is also mapped by V into a spacetime symmetry of the cMERA |ΨΛ⟩. However, while in the CFT, the stress-energy tensor Tμν(x) (in terms of which all the spacetime symmetry generators are expressed) is local, and the corresponding cMERA stress-energy tensor TμνΛ(x)=VTμν(x)V† is quasilocal. (ii) From the cMERA, we can extract quasilocal scaling operators OαΛ(x) characterized by the exact same scaling dimensions Δα, conformal spins sα, operator product expansion coefficients Cαβγ, and central charge c as the original CFT. Finally, we argue that these results should also apply to interacting theories.
Loading next page...
 
/lp/aps_physical/spacetime-symmetries-and-conformal-data-in-the-continuous-multiscale-XZK0UUp0T0
Publisher
American Physical Society (APS)
Copyright
Copyright © © 2017 American Physical Society
ISSN
0031-9007
eISSN
1079-7114
D.O.I.
10.1103/PhysRevLett.119.010603
Publisher site
See Article on Publisher Site

Abstract

The generalization of the multiscale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.100402], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this Letter, we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state |ΨΛ⟩ with finite UV cutoff Λ can capture the spacetime symmetries of the ground state |Ψ⟩. For a free boson conformal field theory (CFT) in 1+1 dimensions, as a concrete example, we build a quasilocal unitary transformation V that maps |Ψ⟩ into |ΨΛ⟩ and show two main results. (i) Any spacetime symmetry of the ground state |Ψ⟩ is also mapped by V into a spacetime symmetry of the cMERA |ΨΛ⟩. However, while in the CFT, the stress-energy tensor Tμν(x) (in terms of which all the spacetime symmetry generators are expressed) is local, and the corresponding cMERA stress-energy tensor TμνΛ(x)=VTμν(x)V† is quasilocal. (ii) From the cMERA, we can extract quasilocal scaling operators OαΛ(x) characterized by the exact same scaling dimensions Δα, conformal spins sα, operator product expansion coefficients Cαβγ, and central charge c as the original CFT. Finally, we argue that these results should also apply to interacting theories.

Journal

Physical Review LettersAmerican Physical Society (APS)

Published: Jul 7, 2017

There are no references for this article.

Sorry, we don’t have permission to share this article on DeepDyve,
but here are related articles that you can start reading right now:

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off