Entanglement and alpha entropies for a massive scalar field in two dimensions

被引:109
作者
Casini, H [1 ]
Huerta, M [1 ]
机构
[1] Ctr Atom Bariloche, RA-8400 San Carlos De Bariloche, Rio Negro, Argentina
来源
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT | 2005年
关键词
Painleve equations; entanglement in extended quantum systems (theory);
D O I
10.1088/1742-5468/2005/12/P12012
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We find the analytic expression of tr rho(n)(L) for a free massive boson field in 1+1 dimensions, where rho(L) is the reduced density matrix corresponding to an interval of length L. This is given exactly ( except for a non-universal factor) in terms of a finite sum of solutions of non-linear differential equations of the Painleve V type. Our method is a generalization of one introduced by Myers and is based on the explicit calculation of quantities related to the Green function on a plane, where boundary conditions are imposed on a finite cut. It is shown that the associated partition function is related to correlators of exponential operators in the sine-Gordon model in agreement with a result by Delfino et al. We also compute the short and long distance leading terms of the entanglement entropy. We find that the bosonic entropic c-function interpolates between the asymptotic limits of the Dirac and Majorana fermion ones given in a previous paper. Finally, we study some universal terms for the entanglement entropy in arbitrary dimensions which, in the case of free fields, can be expressed in terms of the two-dimensional entropy functions.
引用
收藏
页码:291 / 307
页数:17
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