Entanglement renormalization of a $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed CFT

Abstract

In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a T$$ \overline{T} $$ T ¯ -deformed scalar CFT on the line, to first order in the deformation parameter. The result is used to find the correction to the correlators of scaling operators of the theory and to the entanglement entropy of a half-line. From the latter, we discuss the non-localities induced by the T$$ \overline{T} $$ T ¯ deformation at short length scales. We find that the kind of non-locality generated by those terms can be considered as a mild-one, in the sense that it does not violate the area law of entanglement. In the context of the conjectured connection between cMERA and holography, we find that at first insight a finite bulk radius can be defined in the putative geometric dual description of cMERA. However, the entropy analysis contradicts the proposal that no geometry can be ascribed to the region outside this radial cutoff.

Entanglement entropy and modular Hamiltonian of free fermion with deformations on a torus

“…Under such duality, the holographic entanglement entropy can be computed by RT surface in JHEP09(2022)247 finite-cutoff geometry [36][37][38][39][40][41][42][43][44]. 1 In field theory side, the entanglement entropy and Rényi entropy of vacuum state and local excited states in deformed theories has been investigated in [45][46][47][48][49][50]. Besides the T T deformation, studying the free field theory with mass deformation is also interesting.…”