Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition in the R\'enyi-Shannon entropy of Luttinger liquids   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 $n<n_c$. From the point of view of two-dimensional
Rokhsar-Kivelson states, the transition reveals a rich structure in the
entanglement spectra.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org