Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators

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.

9 pages, 11 figures

References in corpus (8)

• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Some formal results for the valence bond basis
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• Increasing of entanglement entropy from pure to random quantum critical chains
• Master equation approach to computing RVB bond amplitudes
• Berry phase induced dimerization in one-dimensional quadrupolar systems
• Correlated valence-bond states
• Resonating valence-bond physics on the honeycomb lattice

Cited by in corpus (6)

• Consistent scaling exponents at the deconfined quantum-critical point
• First-principle simulations of 1+1d quantum field theories at $\theta =\pi$ and spin-chains
• Numerical Investigations of SO(4) Emergent Extended Symmetry in Spin-1/2 Heisenberg Antiferromagnetic Chains
• Extracting the Luttinger parameter from a single wave function
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Tunable quantum spin chain with three-body interactions