Fractional quantum Hall effect, Anyon, Sundance Bilson-Thoompson

In summary: You shouldn't be focussing on the anyons to fix the problems, but rather on the underlying symmetry structures. For instance, maybe try to generalize the notion of quantum groups to higher dimensions. There are models which have been put forth that deal with this type of emergence - models which exhibit topological behavior and in which gauge fields and fermions emerge, rather than being fundamental. Try looking up the Levin and Wen models.
  • #1
ensabah6
695
0
Could Anyons and Fractional quantum Hall effect create 2-D ribbons w/fractional electric charge (e/3) that combine to form fermions or bosons?

Sundance Bilson-Thompson proposed a braiding model of 3's which could account for some particles of the standard model (i.e first generation fermions and bosons)
 
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  • #2
-What do you mean by "A braiding model of 3's" ?

Anyons arise in the Fractional Quantum Hall Effect, yes. But they arise as point particles - not as ribbons. Unless you view them in the complete (2+1)-dimensional space ofcourse. In that case a point particle traces out a world-line, and due to regularization this lineis viewed as a ribbon. Is that what you mean?

So, please, be a bit more specific in your question.
 
  • #3
xepma said:
-What do you mean by "A braiding model of 3's" ?

Anyons arise in the Fractional Quantum Hall Effect, yes. But they arise as point particles - not as ribbons. Unless you view them in the complete (2+1)-dimensional space ofcourse. In that case a point particle traces out a world-line, and due to regularization this lineis viewed as a ribbon. Is that what you mean?

So, please, be a bit more specific in your question.

Could they combine to form fermions or bosons?
 
  • #4
Yes they can. When the anyons are brought together they combine through a process what is called fusion. The mathematical structure underlying this process is called a fusion algebra (related to quantum groups and topological field theories). They fusion algebra is somtehing like a group, in that it closes on itself. It's also finite (i.e. contains a finite number of anyons), and in the FQHE it includes also bosons and fermions. Fusing two anyons gives another anyon. So yea, you it is very well possible that you end up with the boson or fermion upon fusing.

From a more physical persepective this is also quite natural. The anyons arise as collective excitations out of the electrons. So when you mix these excitations together, it should not be too suprising you can construct an electron out of it - it is after all these particles which are the constituents in the first place.
 
  • #5
xepma said:
Yes they can. When the anyons are brought together they combine through a process what is called fusion. The mathematical structure underlying this process is called a fusion algebra (related to quantum groups and topological field theories). They fusion algebra is somtehing like a group, in that it closes on itself. It's also finite (i.e. contains a finite number of anyons), and in the FQHE it includes also bosons and fermions. Fusing two anyons gives another anyon. So yea, you it is very well possible that you end up with the boson or fermion upon fusing.

From a more physical persepective this is also quite natural. The anyons arise as collective excitations out of the electrons. So when you mix these excitations together, it should not be too suprising you can construct an electron out of it - it is after all these particles which are the constituents in the first place.

Is it possible to create an analog system where either space itself or a condensate fluid like field permeating space could create these anyons which can combine to form the SM particles?
 
  • #6
That probably generates more problems than it would solve. You would need the emergence of gauge fields and gauge potentials, different flavor symmetries, and a mechanism that get rids of the anyons as allowed particles.

Let alone the fact that we are talking about a strict 2+1 dimensional system. Anyons are point particles, and the only reason they can exist in the first place is because of this specific dimension. The extension of these condensates to 3+1 dimensions is not a trivial matter (although certain classes exist, that fall under the name of topological insulators).

But the anyons are just a by-product of these types of phases (topological phases). You shouldn't be focussing on the anyons to fix the problems, but rather on the underlying symmetry structures. For instance, maybe try to generalize the notion of quantum groups to higher dimensions. There are models which have been put forth that deal with this type of emergence - models which exhibit topological behavior and in which gauge fields and fermions emerge, rather than being fundamental. Try looking up the Levin and Wen models.
 
  • #7
xepma said:
That probably generates more problems than it would solve. You would need the emergence of gauge fields and gauge potentials, different flavor symmetries, and a mechanism that get rids of the anyons as allowed particles.

Let alone the fact that we are talking about a strict 2+1 dimensional system. Anyons are point particles, and the only reason they can exist in the first place is because of this specific dimension. The extension of these condensates to 3+1 dimensions is not a trivial matter (although certain classes exist, that fall under the name of topological insulators).

But the anyons are just a by-product of these types of phases (topological phases). You shouldn't be focussing on the anyons to fix the problems, but rather on the underlying symmetry structures. For instance, maybe try to generalize the notion of quantum groups to higher dimensions. There are models which have been put forth that deal with this type of emergence - models which exhibit topological behavior and in which gauge fields and fermions emerge, rather than being fundamental. Try looking up the Levin and Wen models.

I'm glad you mention Levin and Wen models, I know he attempts to ground some aspects of the SM in emergence, what do you think of his attempt? Can his attempt explain some of the unknown 18 parameters of the SM, including masses, 3 generations, Weinberg mixing angles? What is it about his emergence models that prevents chiral neutrinos and chiral coupling to W and Z gauge bosons?
 
  • #8
ensabah6 said:
I'm glad you mention Levin and Wen models, I know he attempts to ground some aspects of the SM in emergence, what do you think of his attempt? Can his attempt explain some of the unknown 18 parameters of the SM, including masses, 3 generations, Weinberg mixing angles? What is it about his emergence models that prevents chiral neutrinos and chiral coupling to W and Z gauge bosons?

It's nowhere near, but it's not intended to be. The work is really more a philosophical statement rather than an attempt to re-create the SM. It's saying that there's nothing fundamental about fermions and gauge bosons, and that these can emerge as the low energy excitations of some other _unspecified_ problem. It's showing that universality can extend to these systems, which at one time or another had been felt to be so constrained by their respective symmetries that any underlying microscopic theory had to respect those symmetries also.

In Wen's book, he paints, I think, a rather optimistic view point of how far this can be extended. He identifies a few remaining puzzles, chiefly amongst them the issue of how to get chiral fermions and gravity. But it's important to realize that even if it turns out to be possible to have these emerge (and I do think it's likely --- gravity + bosonic field has been done, not sure about fermions), it only makes constraining the microscopic theory behind SM _harder_, not easier.

Incidentally, the view of gauge theories as lines connecting two fermions has been around for about four or five decades. After all, it's clear that whilst the connection, as a classical variable, is not gauge invariant, various quantities like Wilson loops (and its extension to the non-Abelian case, or open strings terminated by fermions) were realized very early on to be gauge invariant. Further work, mostly using QED (which is unfortunately much simplified from the full case) has shown that it's possible to entirely base the theory on these loop variables --- up to certain mathematical complications due to the need to smear the loops slightly. In fact, this line of attack is what eventually gave string theory (though it can be argued that string theory deviated a little from the spirit of things). Similarly in loop quantum gravity, the idea to to rephrase GR in terms of loop/gauge invariant variables. However, these are all classical variables, and thus suffer from all sorts of rather nasty singular behaviour even when the quantum theory is well-defined.
 
  • #9
ensabah6 said:
What is it about his emergence models that prevents chiral neutrinos and chiral coupling to W and Z gauge bosons?

Probably off on a tangent, but I've wondered if the Nielsen-Ninomiya theorem and the Ginsparg-Wilson relation have anything to do with it.
 
  • #10
genneth said:
It's nowhere near, but it's not intended to be. The work is really more a philosophical statement rather than an attempt to re-create the SM. It's saying that there's nothing fundamental about fermions and gauge bosons, and that these can emerge as the low energy excitations of some other _unspecified_ problem. It's showing that universality can extend to these systems, which at one time or another had been felt to be so constrained by their respective symmetries that any underlying microscopic theory had to respect those symmetries also.

In Wen's book, he paints, I think, a rather optimistic view point of how far this can be extended. He identifies a few remaining puzzles, chiefly amongst them the issue of how to get chiral fermions and gravity. But it's important to realize that even if it turns out to be possible to have these emerge (and I do think it's likely --- gravity + bosonic field has been done, not sure about fermions), it only makes constraining the microscopic theory behind SM _harder_, not easier.

Incidentally, the view of gauge theories as lines connecting two fermions has been around for about four or five decades. After all, it's clear that whilst the connection, as a classical variable, is not gauge invariant, various quantities like Wilson loops (and its extension to the non-Abelian case, or open strings terminated by fermions) were realized very early on to be gauge invariant. Further work, mostly using QED (which is unfortunately much simplified from the full case) has shown that it's possible to entirely base the theory on these loop variables --- up to certain mathematical complications due to the need to smear the loops slightly. In fact, this line of attack is what eventually gave string theory (though it can be argued that string theory deviated a little from the spirit of things). Similarly in loop quantum gravity, the idea to to rephrase GR in terms of loop/gauge invariant variables. However, these are all classical variables, and thus suffer from all sorts of rather nasty singular behaviour even when the quantum theory is well-defined.

interesting. Even string theory suffers from singular behavior? I've not heard this before.
 
  • #11
ensabah6 said:
interesting. Even string theory suffers from singular behavior? I've not heard this before.

No; I mean that attempts to use loop variables for a classical theory leads to singularities. The quantum theories naturally "smear" things enough for a separable Hilbert space to be constructed.
 
  • #12
genneth said:
No; I mean that attempts to use loop variables for a classical theory leads to singularities. The quantum theories naturally "smear" things enough for a separable Hilbert space to be constructed.

One criticism I've heard of LQG is that the Hilbert space is non-separable.

How do you feel about Volvovik's proposal and how does it relate to what Wen is doing?
 

1. What is the fractional quantum Hall effect?

The fractional quantum Hall effect (FQHE) is a phenomenon that occurs in two-dimensional electron systems under strong magnetic fields and low temperatures. It is characterized by the presence of quantized Hall conductance at fractions of the expected value, which is a result of the formation of fractionalized quasiparticles called anyons.

2. What are anyons?

Anyons are exotic quasiparticles that emerge in certain two-dimensional systems, such as the fractional quantum Hall effect. They possess both bosonic and fermionic properties and exhibit fractional statistics, meaning that their exchange behavior is different from traditional particles. Anyons are believed to play a crucial role in the understanding of the FQHE.

3. Who is Sundance Bilson-Thompson and what is their contribution to the study of the FQHE?

Sundance Bilson-Thompson is a theoretical physicist known for their work on topological quantum field theories and their application to condensed matter physics. They have made significant contributions to the understanding of the FQHE, specifically in the development of the anyon model and its connection to topological quantum field theories.

4. How is the FQHE experimentally observed?

The FQHE is observed by measuring the Hall conductance of a two-dimensional electron system at low temperatures and high magnetic fields. The quantized Hall conductance at fractional values is a clear indication of the presence of anyons and the FQHE. Other experimental techniques, such as tunneling spectroscopy, can also provide evidence of anyonic behavior.

5. What are the potential applications of the FQHE and anyons?

The FQHE and anyons have potential applications in quantum computing and topological quantum computation. Anyons are believed to be more robust than traditional qubits, making them promising candidates for quantum information processing. Additionally, the study of anyons and topological quantum field theories has led to a better understanding of topological phases of matter and their potential applications in quantum technologies.

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