Logarithmic corrections in the entanglement entropy

Chanyong Park B

In a $d$-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $\mathrm{\ensuremath{\Delta}}=\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, we can investigate such a logarithmic correction holographically by deforming an AdS space with a massive scalar field dual to the operator with $\mathrm{\ensuremath{\Delta}}=\frac{d+2}{2}$. There are two sources generating the logarithmic correction. One is the metric deformation and the other is the minimal surface deformation. In this work, we investigate the change of the entanglement entropy caused by the minimal surface deformation and find that the second order minimal surface deformation leads to an additional logarithmic correction.

Durrani, Ijaz

Menghan Song, Jiarui Zhao, Zi Yang Meng +2 more

We systematically investigate the finite size scaling behavior of the Rényi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity “subtracted EE” S^s(l) = S(2l) - 2S(l) S s ( l ) = S ( 2 l ) − 2 S ( l ) for each model, which is designed to cancel out the leading perimeter law. We find that (1) for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; (2) for the (2+1)d ( 2 + 1 ) d O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; (3) for the (2+1)d ( 2 + 1 ) d SU(2) J-Q _2 2 and J-Q _3 3 model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.

Siddharth Jindal, Pavan Hosur

The eigenstate thermalization hypothesis (ETH) posits that energy eigenstates encode local properties of the microcanonical ensemble. Motivated by recent interest in the physics of non-commuting conserved charges and the non-Abelian ETH, we study chaotic eigenstates in the presence of symmetries described by general compact Lie groups, such as SU(2). By applying non-Abelian symmetry resolution, we develop a non-Abelian microcanonical entropy and relate this entropy to the entanglement entropy of chaotic eigenstates. We find that microcanonical entropy is closely related to the symmetry-resolved entanglement entropy, which differs from conventional entanglement entropy by a universal logarithmic correction. Our results depend on the global Casimir charge, e.g. total spin. At finite charge density, we find a logarithmic enhancement to conventional entanglement entropy. At zero density, we find no such correction to entanglement entropy, but a logarithmic reduction to microcanonical entropy and symmetry-resolved entanglement entropy. We discuss the implications of our approach for non-Abelian eigenstate thermalization.

William Witczak‐Krempa, Xiaohong Chen, Thomas Faulkner +1 more

Dominik Janzing