Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2010-06-08
Phys. Rev. B 82, 125455 (2010)
Physics
Condensed Matter
Strongly Correlated Electrons
8 pages, 6 figures, 2 tables. To be submitted to Physical Review B
Scientific paper
10.1103/PhysRevB.82.125455
We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities $p_i$ to observe a given spin configuration $i$ along a circular section of the cylinder. These probabilities also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson wave-functions. We analyze the subleading constant to the R\'enyi entropy $R_n=1/(1-n) \ln (\sum_i p_i^n)$ and discuss its scaling properties at the critical point. Studying three different microscopic realizations, we provide numerical evidence that it is universal and behaves in a step-like fashion as a function of $n$, with a discontinuity at the Shannon point $n=1$. As a consequence, a field theoretical argument based on the replica trick would fail to give the correct value at this point. We nevertheless compute it numerically with high precision. Two other values of the R\'enyi parameter are of special interest: $n=1/2$ and $n=\infty$ are related in a simple way to the Affleck-Ludwig boundary entropies associated to free and fixed boundary conditions respectively.
Misguich Grégoire
Pasquier Vincent
Stéphan Jean-Marie
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