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What does conventional RG flow analysis miss from a physics point of view compared to an Entanglement RG flow analysis?

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As explained in the context of  this blogpost, Entanglement Renormalization adds to the three steps contained in a "conventional" infinitesimal RG transformation

  • Sume or integrate over small scales (coarse graining)
  • Rescaling
  • Compute the new effective quantitiy (action, Lagrangian, Hamiltonian, etc) that describes the system

the additional step of disentangling the small scale degrees of freedom before they get coarse grained.

The blogpost says that by making use of entanglement renormalization, one may for example reconstruct the small scale wave function from a very small amount of information at large scales.

But what difference does it make from a physics point of view when doing an RG flow analysis, if one uses the "conventional" or entanglement renormalization group?

For example does one meet different (kinds of) fixed points when going from small to large scales?

Or do the fixed points keep the same, but the RG trajectories (or mor generally the RG flow field) in coupling space surrounding them changes?

I always thought that the physics should in principle not depend on the exact renormalization method applied, but maybe it is different when considering entanglement renormalization?

asked May 7, 2015 in Theoretical Physics by Dilaton (4,295 points) [ revision history ]

Maybe @conformal_gk who seems to be interested in RG flow issues knows something about this ;-)?

"the physics should in principle not depend on the exact renormalization method applied" only for renormalizable theories. It's more-or-less a definition that for non-renormalizable theories the regularization method and renormalization scheme do matter.

@Dilaton I don't really know what EE renormalization is. I know about the EE c-function (in 2d QCD see here this paper) which does not add or subtract usual Wilsonian renormalization information or anything like that. All I know is that people disagree about the EE c-function (look at the result of the paper I mention and compare it with the Huertas et. al. results). Sorry for not being of more help.

1 Answer

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Entanglement Renormalization and its variants are a replacement of conventional renormalization techniques adapted to numerical computations. Nothing is ''added'' to the conventional treatment. It is simply a numerical alternative to the standard RG treatments - no ''other'' fixed points can be found, but the existing fixed points can sometimes be found more efficiently. In particular, it enabled people to solve many renormalization problems in one dimensions (effectively quantum wires) that were untractable before. In higher dimensions success is much more limited, due to the poor numerical scaling. 

A paper by Haegeman, Osborne, Verschelde, and Verstraete (Verstraete works here in Vienna) introduced a continuous version cMERA of entanglement renormalization that has some resemblance to the AdS/CFT correspondence. Indeed, the authors write at the end,

It is tempting to speculate [...] that cMERA are a natural candidate to establish a link between entanglement renormalization and the best known realization of the holographic principle, namely the AdS/CFT correspondence.

Some of these speculations have since appeared in print, e.g., here. I don't find them convincing, though.

answered May 7, 2015 by Arnold Neumaier (12,355 points) [ no revision ]

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