Phase transition in the Rényi-Shannon entropy of Luttinger liquids
Résumé
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). The replica approach used in previous works fails to predict this transition and turns out to be correct only for $n
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https://hal.science/hal-01586157
Soumis le : mardi 12 septembre 2017-15:06:39
Dernière modification le : vendredi 19 avril 2024-11:44:08
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Identifiants
- HAL Id : hal-01586157 , version 1
- ARXIV : 1104.2544
- DOI : 10.1103/PhysRevB.84.195128
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Jean-Marie Stéphan, Grégoire Misguich, Vincent Pasquier. Phase transition in the Rényi-Shannon entropy of Luttinger liquids. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2011, 84 (19), pp.195128. ⟨10.1103/PhysRevB.84.195128⟩. ⟨hal-01586157⟩
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