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Quantum Simulation

Matrix product approximations to conformal field theories

arXiv
Authors: Robert Koenig, Volkher B. Scholz

Year

2015

Paper ID

27061

Status

Preprint

Abstract Read

~2 min

Abstract Words

94

Citations

N/A

Abstract

We establish rigorous error bounds for approximating correlation functions of conformal field theories (CFTs) by certain finite-dimensional tensor networks. For chiral CFTs, the approximation takes the form of a matrix product state. For full CFTs consisting of a chiral and an anti-chiral part, the approximation is given by a finitely correlated state. We show that the bond dimension scales polynomially in the inverse of the approximation error and sub-exponentially in the ultraviolett cutoff. We illustrate our findings using Wess-Zumino-Witten models, and show that there is a one-to-one correspondence between group-covariant MPS and our approximation.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We establish rigorous error bounds for approximating correlation functions of conformal field theories (CFTs) by certain finite-dimensional tensor networks.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.07414 [2] arXiv https://arxiv.org/abs/1509.07414 [3] Publisher https://arxiv.org/abs/1509.07414

Local Citation Graph (Related-Paper Links)

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