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2011

Phase transition in the R\'enyi-Shannon entropy of Luttinger liquids

Stéphan, Jean-Marie, Misguich, Grégoire, Pasquier, Vincent

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The R\'enyi-Shannon entropy associated to critical quantum spins chain with central charge $c=1$ is shown to have a phase transition at some value $n_c$ of the R\'enyi parameter $n$ which depends on the Luttinger parameter (or compactification radius R).

Using a new replica-free formulation, the entropy is expressed as a combination of single-sheet partition functions evaluated at $n-$ dependent values of the stiffness.
The transition occurs when a vertex operator becomes relevant at the boundary.
Our numerical results (exact diagonalizations for the XXZ and $J_1-J_2$ models) are in agreement with the analytical predictions: above $n_c=4/R^2$ the subleading and universal contribution to the entropy is $\ln(L)(R^2-1)/(4n-4)$ for open chains, and $\ln(R)/(1-n)$ for periodic ones (R=1 at the free fermion point).

Phase transition in the R\'enyi-Shannon entropy of Luttinger liquids · Around

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J.-M. Stéphan et al
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