Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries

Estienne, Benoit; Ikhlef, Yacine; Rotaru, Andrei

doi:10.21468/SciPostPhys.12.4.141

SciPost Physics

Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries

Benoit Estienne, Yacine Ikhlef, Andrei Rotaru

SciPost Phys. 12, 141 (2022) · published 29 April 2022

doi: 10.21468/SciPostPhys.12.4.141
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Abstract

We consider the entanglement entropy in critical one-dimensional quantum systems with open boundary conditions. We show that the second Rényi entropy of an interval away from the boundary can be computed exactly, provided the same conformal boundary condition is applied on both sides. The result involves the annulus partition function. We compare our exact result with numerical computations for the critical quantum Ising chain with open boundary conditions. We find excellent agreement, and we analyse in detail the finite-size corrections, which are known to be much larger than for a periodic system.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.4.141
TI  - Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
PY  - 2022/04/29
UR  - https://scipost.org/SciPostPhys.12.4.141
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 4
SP  - 141
A1  - Estienne, Benoit
AU  - Ikhlef, Yacine
AU  - Rotaru, Andrei
AB  - We consider the entanglement entropy in critical one-dimensional quantum systems with open boundary conditions. We show that the second Rényi entropy of an interval away from the boundary can be computed exactly, provided the same conformal boundary condition is applied on both sides. The result involves the annulus partition function. We compare our exact result with numerical computations for the critical quantum Ising chain with open boundary conditions. We find excellent agreement, and we analyse in detail the finite-size corrections, which are known to be much larger than for a periodic system.
ER  -

@Article{10.21468/SciPostPhys.12.4.141,
	title={{Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries}},
	author={Benoit Estienne and Yacine Ikhlef and Andrei Rotaru},
	journal={SciPost Phys.},
	volume={12},
	pages={141},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.4.141},
	url={https://scipost.org/10.21468/SciPostPhys.12.4.141},
}

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¹ Laboratoire de Physique Théorique et Hautes Energies / Laboratory of Theoretical and High Energy Physics [LPTHE]