Numerical calculations on the relative entanglement entropy in critical spin chains

Abstract

We study the relative entanglement entropy (EE) among various primary excited states in two critical spin chains: the S=1/2 XXZ chain and the transverse field Ising chain at criticality. For the S=1/2 XXZ chain, which corresponds to c=1 free boson conformal field theory (CFT), we numerically calculate the relative EE by exact diagonalization and find a perfect agreement with the predictions by the CFT. For the transverse field Ising chain at criticality, which corresponds to the c=1/2 Ising CFT, we analytically relate its relative EE to that of the S=1/2 XXZ chain and confirm the relation numerically. We also calculate the "sandwiched" Rényi relative EE and again the numerical results agree well with the analytical predictions. Our results are the first direct confirmation of the CFT predictions on the relative EE of the primary excited states in critical spin chains.

arXiv comment16 pages, 5 figures

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• Symmetry resolved relative entropies and distances in conformal field theory
• Subsystem Trace Distance in Quantum Field Theory
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
• Chaos and relative entropy
• Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains
• Quantum Renyi relative entropies on a spin chain with interface defects