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Quantum entanglement in Tomonaga-Luttinger liquid


The quantum entanglement has recently been recognized as a useful concept in detecting non-trivial correlations existing in many-body
ground states. In particular, it has been found that the scaling of the entanglement entropy - measure of entanglement between a part of
the system and the rest - often contains the information of the universal nature of the system. For instance, in one-dimensional
quantum critical systems, one can determine the central charge - a universal number characterizing the underlying conformal field theory
(CFT) - from such a scaling.

In this talk, after reviewing some basic concepts related to entanglement, I will present our recent work concerning
Tomonaga-Luttinger liquid (TLL). This class of liquid appears in a wide variety of 1D fermionic and bosonic systems, and its critical
nature is characterized by a single number, the boson radius (or Luttinger parameter). Though this radius does not appear in the
scaling of the single-interval entropy, we found that it does appear, in a universal way, in the scaling of the mutual information defined
from the two-interval entanglement entropy. This result allows us to identify the boson radius as a generic structure of the ground state.

Ref. S.F., V. Pasquier, and J. Shiraishi, Phys. Rev. Lett. 102, 170602 (2009).