Indicators of conformal field theory: Entanglement entropy and multiple-point correlators
Files
Accepted manuscript
Date
2017-07-27
Authors
Patil, Pranay
Tang, Ying
Katz, Emanuel
Sandvik, Anders W.
Version
Accepted manuscript
OA Version
Citation
Pranay Patil, Ying Tang, Emanuel Katz, Anders W Sandvik. 2017. "Indicators of conformal field theory: Entanglement entropy and multiple-point correlators." Physical Review B, Volume 96, Issue 4, 045140. https://doi.org/10.1103/PhysRevB.96.045140
Abstract
The entanglement entropy (EE) of quantum systems is often used as a test of low-energy descriptions by conformal field theory (CFT). Here we point out that this is not a reliable indicator, as the EE often shows the same behavior even when a CFT description is not correct (as long as the system is asymptotically scale-invariant). We use constraints on the scaling dimension given by the CFT with SU(2) symmetry to provide alternative tests with two- and four-point correlation functions, showing examples for quantum spin models in 1+1 dimensions. In the case of a critical amplitude-product state expressed in the valence-bond basis (where the amplitudes decay as a power law of the bond length and the wave function is the product of all bond amplitudes), we show that even though the EE exhibits the expected CFT behavior, there is no CFT description of this state. We provide numerical tests of the behavior predicted by CFT for the correlation functions in the critical transverse-field Ising chain and the J−Q spin chain, where the conformal structure is well understood. That behavior is not reproduced in the amplitude-product state.