Unusual singular behavior of the entanglement entropy in one dimension
by
Fabio Franchini(SISSA)
→
Europe/Stockholm
132:028
132:028
Description
We study the bipartite entanglement entropy for one-
dimensional systems. Its qualitative behavior is quite well
understood: for gapped systems the entropy saturates to a
finite value, while it diverges logarithmically as the
logarithm of the correlation length as one approaches a
critical, conformal point of phase transition. Using the
example of two integrable models, we argue that close to
non-conformal points the entropy shows a peculiar singular
behavior, characteristic of an essential singularity. At these
non-conformal points the model undergoes a discontinuous
transition, with a level crossing in the ground state and a
quadratic excitation spectrum. We propose the entropy as
an efficient tool to determine the discontinuous or
continuous nature of a phase transition also in more
complicated models.
- F. Franchini, A. R. Its, B.-Q. Jin, V. E. Korepin; J. Phys. A:
Math. Theor. 40 (2007) 8467-8478
- F. Franchini, A. R. Its, V. E. Korepin; J. Phys. A: Math.
Theor. 41 (2008) 025302
- F. Franchini, E. Ercolessi, S. Evangelisti, F. Ravanini;
arXiv:1008.3892
