3
$\begingroup$

I know that consideration of electrons with disorder can be based on Feynman diagrams with disorder lines. In this approach, only non-crossing diagrams are important and give contribution to self-energy function $\Sigma$ and related quantities. Parameter $p_Fl$ plays the crucial role in this statement ($l$ is mean free path) and it is equivalent to $N$-parameter in field theory. Large-$N$ means that only planar diagrams in theory are important. Assumption $p_Fl\gg 1$ is very similar.

My question: is it possible to show duality between theory of electrons with disorder (EwD) and something like AdS theory? I mean that due to the equivalence of EwD and large-$N$ expansion it seems that one can naively expect that there is a theory which will be dual to EwD in weak coupling limit.

May be my question is not so clear but I would be grateful for any comments which can make it more clear.

$\endgroup$
  • $\begingroup$ Have you heard of the Sachdev-Ye-Kitaev (SYK) model? It is a model of disordered fermions with emergent conformal invariance which is known to fit in the AdS/CFT duality, with much of the intuition coming from diagrams. You may also be interested in this paper which studies the disordered large-$N$ models using AdS/CFT (among other methods): arxiv.org/abs/1509.02547. I do not know of a relation between the usual non-crossing-approximation and AdS/CFT, but SYK is a very similar idea. $\endgroup$ – Seth Whitsitt Dec 14 '19 at 5:27
3
$\begingroup$

I am going to stick my neck out some here, but make this brief so I do not write something wrong. I would say this is a possibility. A quantum spin liquid is a disordered set of quantum spins with long range entanglements. With a topological order in this bulk there may then be edge states with short range entanglements of symmetry protected states. This physics has some parallels to the AdS/CFT correspondence.

$\endgroup$
  • $\begingroup$ Thank you for the answer! In EwD electrons scatterin on impurities gives "interaction lines" in diagrams. What about spin liquid? To be honest, I do not know what means "disordered set"... $\endgroup$ – Artem Alexandrov Aug 25 '19 at 8:33
  • $\begingroup$ A disordered liquid refers to spin states, and these may be electrons in a conduction band that act as a fluid, that are entangled, but that have no magnetic order. There are a few materials with this property, such as $PbCuTe_2O_6$ in a Kagome lattice. Copper is fairly prominent in these materials. These have long range entanglements of spins, but also disordering or frustration of spins. This is the closest thing I could think of with respect to electrons with disorder EwD, which honestly I have never heard of before. $\endgroup$ – Lawrence B. Crowell Aug 25 '19 at 12:31
  • $\begingroup$ @ArtemAlexandrov can correct me if I'm wrong, but I believe he is referring "disorder" specifically as in the concept of "quenched disorder," meaning that the system contains a set of impurities which are not in equilibrium with the rest of the system. The averages over disorder certainly resemble Artem's description of the Feynman diagrams. This is distinct from the concept of "disorder" meaning the absence of long-range magnetic order in a spin liquid. Though of course in any physical spin liquid one should investigate the effects of quenched disorder (and people have done so theoretically). $\endgroup$ – Seth Whitsitt Dec 14 '19 at 5:20
  • $\begingroup$ @SethWhitsitt you are completeley correct. I have found that there is duality between $N$-component scalar field theory with interaction $u(\phi^i\phi_i)^2$. However, I do know about the "solid-state" description of this duality. I know about SYK and its dualities. $\endgroup$ – Artem Alexandrov Dec 14 '19 at 9:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.