Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

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

+ 3 like - 0 dislike
898 views

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 (6,240 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

+ 3 like - 0 dislike

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 (15,787 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...