Contributor info: Dr Yacine Ikhlef

Benoit Estienne, Yacine Ikhlef, Andrei Rotaru

SciPost Phys. 12, 141 (2022) · published 29 April 2022 | Toggle abstract · pdf

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.

Yacine Ikhlef, Alexi Morin-Duchesne

SciPost Phys. 12, 030 (2022) · published 20 January 2022 | Toggle abstract · pdf

In two-dimensional loop models, the scaling properties of critical random curves are encoded in the correlators of connectivity operators. In the dense O($n$) loop model, any such operator is naturally associated to a standard module of the periodic Temperley-Lieb algebra. We introduce a new family of representations of this algebra, with connectivity states that have two marked points, and argue that they define the fusion of two standard modules. We obtain their decomposition on the standard modules for generic values of the parameters, which in turn yields the structure of the operator product expansion of connectivity operators.

Benoit Estienne, Yacine Ikhlef, Alexi Morin-Duchesne

SciPost Phys. 10, 054 (2021) · published 4 March 2021 | Toggle abstract · pdf

In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

Thomas Dupic, Benoit Estienne, Yacine Ikhlef

SciPost Phys. 4, 031 (2018) · published 18 June 2018 | Toggle abstract · pdf

We present a new method to compute R\'enyi entropies in one-dimensional critical systems. The null-vector conditions on the twist fields in the cyclic orbifold allow us to derive a differential equation for their correlation functions. The latter are then determined by standard bootstrap techniques. We apply this method to the calculation of various R\'enyi entropies in the non-unitary Yang-Lee model.