Universal geometric entanglement close to quantum phase transitions

Details Universal geometric entanglement close to quantum phase transitions Universal geometric entanglement close to quantum phase transitions

2007-11-16

arxiv.org/abs/0711.2556v3

Phys.Rev.Lett.100:130502,2008

Physics

Quantum Physics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.100.130502

Under successive Renormalization Group transformations applied to a quantum state $\ket{\Psi}$ of finite correlation length $\xi$, there is typically a loss of entanglement after each iteration. How good it is then to replace $\ket{\Psi}$ by a product state at every step of the process? In this paper we give a quantitative answer to this question by providing first analytical and general proofs that, for translationally invariant quantum systems in one spatial dimension, the global geometric entanglement per region of size $L \gg \xi$ diverges with the correlation length as $(c/12) \log{(\xi/\epsilon)}$ close to a quantum critical point with central charge $c$, where $\epsilon$ is a cut-off at short distances. Moreover, the situation at criticality is also discussed and an upper bound on the critical global geometric entanglement is provided in terms of a logarithmic function of $L$.

Affiliated with

Also associated with

No associations

Rating

Universal geometric entanglement close to quantum phase transitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Universal geometric entanglement close to quantum phase transitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Universal geometric entanglement close to quantum phase transitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-3461