We restrict ourselves to ground states of translationally invariant 1d quantum systems.

I understand that there is the scale invariant MERA(multiscale entanglement renormalization ansatz) which describes quantum critical points in which the tensors ("isometries" and "disentaglers") are the same across different levels. I also understand that away from a quantum critical point, these tensors must vary across different levels (and are same within a level due to translational invariance). Is there a way to obtain an RG flow equation based on the details of how these tensors must vary across adjacent layers. Also, is it possible to go backwards: i.e., to obtain conditions for these tensors across adjacent levels from the correct flow equation. More generally, what are the techniques used to obtain these tensors?

A commentary about where I can find answers to these question in the literature will be very helpful. Thank you.

  • 1
    $\begingroup$ Comment to the question (v1): Consider spelling out abbreviations to increase accessibility. $\endgroup$
    – Qmechanic
    Aug 29, 2014 at 18:53
  • $\begingroup$ I don't know the answer. However I found this nice presentation where some RG flows are described, and some refs, ref1, ref2, ref3. $\endgroup$
    – Trimok
    Aug 30, 2014 at 9:42
  • $\begingroup$ In ref3, page $9$, I found this interesting paragraph : "In the present formulation of bosonic modes, in which the representation of the state is given by a covariance matrix as opposed to a density matrix, this rule imposes that only modes in a block that can be identifyed as being in a product state with the rest of the system can be truncated and safely removed from the description of the state. Thus in comparison with Hamiltonian RG, which was optimised to truncate modes such that effective theory had minimal energy.... $\endgroup$
    – Trimok
    Aug 30, 2014 at 9:43
  • $\begingroup$ ..... here we optimise for (u;w) so that the truncated modes have minimal entanglement with the rest of the system.". So it seems that it is the way where isometries $w$ and disantenglers $u$ are choosen. $\endgroup$
    – Trimok
    Aug 30, 2014 at 9:44
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    $\begingroup$ Thank you very much Trimok. That talk is indeed a great bibliographic guide. $\endgroup$ Aug 30, 2014 at 15:07


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