Clarification: relation spin network/spinfoam and Wen's Qbit lattice

[ensabah6]

Wen has proposed string-net condensation as basis for SM.

http://www.fqxi.org/data/documents/Wen Azores Talk.pdf

he proposes qbit lattice as the basis of space, and his diagram looks similar to spin networks.

What is the relation between his qbit spin-system lattice and spinfoam/spinnetworks?

Can a spin foam model be the basis of qbits, string-net groundstate and topological order?
Can qbits form the basis of spin networks/spin foam?

 

[atyy]

See footnote 4 of http://arxiv.org/abs/cond-mat/0407140

 

[ensabah6]

See footnote 4 of http://arxiv.org/abs/cond-mat/0407140

so qbits are more fundamental than spin networks?

 

[marcus]

so qbits are more fundamental than spin networks?

Did you read footnote 4? It does not say that, but it is interesting on its own.
As it indicates, Penrose introduced the idea of a "spin-network" in 1971, and Wen
gave the mathematical object a new name: "string-net".

==quote Atty's footnote 4 reference ==
4 String-nets with positive integer labeling were first introduced by Penrose (Penrose, 1971), and are known as “spin networks” in the loop quantum gravity community. More recently, researchers in this field considered the generalization to arbitrary labelings (Kauffman and Lins, 1994; Turaev, 1994). These generalized spin networks have the same mathematical structure as string-nets. However, we would like to point out that the physical meaning of spin networks is fundamentally different from that of string-nets. Spin networks are the basic building blocks of loop quantum gravity models. In contrast, string-nets describe the pattern of quantum entanglement in the ground states of certain spin models. In short, spin networks are components of a model while string-nets describe a type of order. The main issue in this paper is to find a kind of ordering in spin models that leads to emergent photons and electrons. We find that “particle” condensation does not work but “string” condensation does work. This is why we introduce the term “string-net”: to stress the stringy character of the ordering.
==endquote==

Here is Penrose 1971 paper. He uses the term "spin network" throughout.
http://math.ucr.edu/home/baez/penrose/Penrose-AngularMomentum.pdf

 

[marcus]

See footnote 4 of http://arxiv.org/abs/cond-mat/0407140

I think I've found the paper where X Wen introduced the term "string-net"
http://arxiv.org/abs/cond-mat/0210040
==quote X Wen 2002 pages 2 and 3==
...
Through our models, we also find that a U(1) gauge theory is actually a dynamical theory of nets of closed strings.[26] The latter will be called the string-net theory whose definition will given in section 2. In other words, gauge theory and string-net theory are dual to each other. This duality is directly connected to the duality between statistical U(1) lattice gauge models and statistical membrane models.[29–31] According to the string-net picture, a gapless gauge boson is a fluctuation of large string-nets and charge is the end of open strings.
In the next a few sections, we will discuss in detail 2D and 3D spin model...
...
We note that the above string operator U(C) can be defined even when the loop C intersects or overlaps with itself. In fact, those self intersecting/overlapping loops are more typical configurations of loops. Such kind of loops looks like nets of closed strings and we will call them closed string-nets. (Nets with open strings will be called open string-nets.) The string operators U(C) will be called string-net operator. The degenerate ground states are formed by closed string-nets.
==endquote==

There is no reference to Penrose in this 2002 paper or any mention of Penrose's idea of "spin network".
X Wen may not have heard about Penrose spin networks at that time, or may not have realized that they were the same thing mathematically (if indeed they are.)

However by 2004 he was saying they are the same math object and, in the footnote 4 we just saw, explaining why he preferred to use his own name rather than the name originally given by Penrose.

So whether or not he made the connection at first, he quickly realized it.

Interesting story.

 

[marcus]

We should make some effort to actually address 'Bah's question which was not about the relation of "string-net" and spin-networks
Atyy's pointer to the 2004 X Wen paper's footnote 4 is about sameness of those two things (which play different roles in different contexts but are the same math object.)

But 'Bah didn't ask about that. He pointed to the qbit lattice which X Wen uses as a model of space and he says that looks similar to LQG spin networks. So is there any relation.

 

[marcus]

We should make some effort to actually address 'Bah's question which was not about the relation of "string-net" and spin-networks
Atyy's pointer to the 2004 X Wen paper's footnote 4 is about sameness of those two things (which play different roles in different contexts but are the same math object.)

But 'Bah didn't ask about that. He pointed to the qbit lattice which X Wen uses as a model of space and he says that looks similar to LQG spin networks. So is there any relation?

I will argue that the two are unrelated. You can think of reasons they are related.

I think X Wen is trying to answer the child-like question "what is space made of?" And following on that "what is everything made of? light? electrons?"

X Wen says space is a regular lattice of identical qbits. Everything else is just patterns of organization of long chains of qbits.
He says the issue is not what is the most fundamental buildingblock, he thinks we know that already, it is qbits. The real issue is how are they organized---the patterns of longrange entanglement. Of course as soon as someone says regular lattice we want to know how many neighbors each vertex has. Six maybe? Like a regular cubical lattice.
If this is offered as the foundation of reality we need to know some details about it.

By contrast LQG is not about what space is made of but about geometric quantum information. The theory does not postulate that space is made of the nodes and links of a vast spin network, or any other material object. One uses a graph to formulate the theory but ultimately one wants to get away from any dependence on any particular graph. There is no assumption that the nodes are all the same (as if they were, like qbits, a fundamental building block.) The aim is a minimalist quantum description of geometric information---related areas angles volumes. Getting away from assumption of some preconceived background. Not about what space IS but about how it responds to measurement.

Spin networks of LQG are not regular lattices of identical nodes. Nodes, their numbers of neighbors and the ways they interconnect can be very different from each other. Just as the various ways you might think of to measure the geometry of something can be radically different. Spin networks are states of geometry. which basically means information an observer might have or might predict. They are not real god-given tinkertoy knobs and sticks.

So I think they are not like X Wen's lattice of qbits. Anyway that's what I think at the moment. Haven't considered it much.

My hunch is that X Wen's lattice gets him into trouble with Lorentz invariance, which is not a problem for LQG. Does anyone know how X Wen handles a black hole (with his regular lattice) or the big bang? or Lorentz covariance?
This could be the reason that it is kind of a oneman show which although intriguing and entertaining has not gone much of anywhere.

 

[atyy]

My hunch is that X Wen's lattice gets him into trouble with Lorentz invariance, which is not a problem for LQG. Does anyone know how X Wen handles a black hole (with his regular lattice) or the big bang? or Lorentz covariance?
This could be the reason that it is kind of a oneman show which although intriguing and entertaining has not gone much of anywhere.

The Levin-Wen string nets are a case emergent QED, not QG. The Lorentz invariance of QED is emergent.

Wen has not tried to use string nets for QG. His attempt at QG shares with string nets emergent gauge bosons due to entanglement. He's got massless spin 2 particles, but not the right dispersion. Xu and Horava recently realized that Wen's and Horava's QG attempts are related http://arxiv.org/abs/1003.0009 .

Three groups have suggested generalizations of string nets. Two of these groups are trying an approach to QG, and they have followed marcus's suggestion of not having a fixed lattice:
http://arxiv.org/abs/1006.5823
http://arxiv.org/abs/0911.5075
http://arxiv.org/abs/1102.0270

 

[marcus]

It's gratifying to hear of some other groups at other places developing Wen-like ideas. Thanks.

 

[atyy]

I should also not neglect to mention Vidal's work which connects to string nets.
http://arxiv.org/abs/0809.2393
http://arxiv.org/abs/1007.4145

You can see the connection between Vidal and Wen's work by comparing the above papers with
http://arxiv.org/abs/0809.2821
http://arxiv.org/abs/1001.4517

That's all condensed matter, which is Wen's and Vidal's day jobs, but of course, Vidal has speculated on a connection between LQG and string theory.
http://www.emergentgravity.org/drupal/sites/default/files/EGIV_presentations/Vidal.pdf

Also interesting is Swingle's http://arxiv.org/abs/0905.1317

 

[ensabah6]

you've answered my question