Matrix Product Approximations to Multipoint Functions in Two-Dimensional Conformal Field Theory
Robert König1, Volkher B Scholz2,3
1Institute for Advanced Study and Zentrum Mathematik, Technische Universität München, 85748 Garching, Germany.
Physical Review Letters
|October 1, 2016
Summary
Matrix product states (MPSs) can accurately approximate correlations in 2D conformal field theories. This study provides quantitative error estimates and an explicit MPS construction, justifying variational methods for critical quantum systems.
Area of Science:
- Quantum Many-Body Physics
- Quantum Field Theory
- Tensor Network States
Background:
- Matrix product states (MPSs) are effective for gapped 1D systems.
- Rigorous analysis of MPSs for critical quantum systems and field theories is lacking.
- Previous evidence suggests tensor networks can approximate correlation functions.
Purpose of the Study:
- To rigorously establish the capability of MPSs in approximating correlations in 2D conformal field theories.
- To provide quantitative estimates for the approximation error.
- To construct an explicit MPS for critical systems.
Main Methods:
- Utilizing properties of 2D conformal field theory.
- Developing a constructive approach to generate an explicit MPS.
- Analyzing approximation errors in correlation functions.
Main Results:
- A complete positive answer regarding MPS approximation of correlations in 2D CFT.
- Quantitative estimates for the approximation error.
- Construction of an explicit MPS ansatz.
Conclusions:
- MPSs rigorously approximate correlations in 2D conformal field theories.
- The explicit MPS provides initial values and justification for variational methods.
- This work bridges a gap in the rigorous understanding of tensor networks for critical quantum systems.
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