Renyi Entropy of the Ideal Gas in Finite Momentum Intervals

Bin Chen, Jiaju Zhang

P. T. Landsberg

Bin Chen, Jie-qiang Wu

In this paper, we calculate the Rényi entropy of one single interval on a circle at finite temperature in 2D CFT. In the low temperature limit, we expand the thermal density matrix level by level in the vacuum Verma module, and calculate the first few leading terms in e −π/T L explicitly. On the other hand, we compute the same Rényi entropy holographically. After considering the dependence of the Rényi entropy on the temperature, we manage to fix the interval-independent constant terms in the classical part of holographic Rényi entropy. We furthermore extend the analysis in [9] to higher orders and find exact agreement between the results from field theory and bulk computations in the large central charge limit. Our work provides another piece of evidence to support holographic computation of Rényi entropy in AdS3/CFT2 correspondence, even with thermal effect.

Howard J. Schnitzer

The $\sun1$ WZW model is constructed on a n-sheeted branched torus, which allows the investigation of the Rényi entropy for a single interval at finite temperature. The small and large interval limits, as well as the low temperature expansion are presented for this theory.

Saurav Pandey, Junaid Majeed Bhat, Abhishek Dhar +5 more

Jiaju Zhang, Rajabpour

We investigate the quasiparticle excited state R\'enyi entropy of single, double and more intervals in the fermionic chain, bosonic chain and XY chain. When the gap of the theory is large or all the momenta of the quasiparticles are large, the R\'enyi Entropy takes a super universal form, which is independent of, among others, the model, the quasiparticle momenta, and the subsystem connectedness. We calculate analytically the R\'enyi Entropy in the extremely gapped limit by writing the excited states in terms of the local excitations and find different additional contributions to the super universal R\'enyi entropy in various models. The additional contributions to the super universal R\'enyi entropy cannot be neglected when the momentum differences of the excited quasiparticles are small, however, they are negligible when all the momentum differences are large. The R\'enyi entropy with additional terms derived in the extremely gapped limit is universal in the sense that it is valid in the slightly gapped and critical models as long as all the momenta of the excited quasiparticles are large. In the case of double interval in the XY chain we find new exact super universal as well as the universal results. In the case of the bosonic chain in the extremely massive limit we find analytically a novel formula, written as a permanent of a certain matrix, for the R\'enyi entropy. We support all of our analytical results with numerical calculations.