Periodic Reporting for period 1 - HLQPT (Holographic lattices and quantum phase transitions)
Berichtszeitraum: 2015-06-01 bis 2017-05-31
However, there has been a missing piece in the AdS/CMT realm, which is the dual of topologically nontrivial CM systems. In the CM community, there has been a lot of interest in various topological CM systems recently. The concept of topology in CM systems has been developed in the weakly coupled limit and an immediate question that arises is whether nontrivial topological systems still exist at strong coupling. Does there exist a duality between a certain geometry in weakly coupled gravity theory and topologically nontrivial state? If it exists, is there any novel prediction or hint from the gravity side for the dual topological system? As a first step to answer these question, the objective of the first part of the project is to build a holographic model for a topological gapless Weyl semimetal (WSM) state and study possible implications of the holographic model to the transport behavior of a topological WSM system.
Besides the topological nature of WSM systems, there is another important feature that a WSM possesses, the chiral anomaly, which qualitatively affects the transport behavior of not only the WSM but also other systems which have chiral anomaly. For these systems, there is a special transport behavior called negative magnetoresistivity (NMR). Since the year 2013, there has been a lot of observation of NMR for many different kinds of materials in laboratories. The behavior of NMR could be calculated in the weakly coupled kinetic theory and the result shows that at small magnetic field (B), the DC longitudinal magnetoconductivity has a squared behavior in the magnetic field while at large B, it grows linearly in B. However, in different materials different scaling in B behavior has been found, which could be different from the weakly coupled prediction. There is also evidence showing that the real Dirac/Weyl semimetal systems might be strongly coupled. Thus studying the behavior of NMR for strongly coupled chiral anomalous systems would be very important. The objective of the second part of the project is to study the NMR in strongly coupled holographic chiral anomalous systems, especially its scaling behavior in the magnetic field B and compare with the experimental observations.
These questions lie at the intersection of high energy physics and CM physics, and are important to both CM physics and the better understanding of holography. The importance of the development in CM physics to the society is more straightforward. Better understanding of the transport behavior of novel materials will very likely result in new developments in daily life technologies in the future. In summary, the overall objectives of the project are to build and study the holographic dual of topological nontrivial states, e.g. Weyl semimetals, which are gapless topologically nontrivial states, as well as to study the transport behavior.
Conclusions: we showed that the topological states that are protected from perturbations still exist in the strongly coupled theory. We further showed that the odd viscosities in the strongly coupled holographic WSM are nonvanishing in the quantum critical region due to the existence of mixed axial gravity anomaly. This is a prediction to a transport coefficient induced by the mixed axial gravity anomaly in the quantum critical region of a WSM from holography and can be tested in laboratories.
A lot of seminar talks on these work have been given in different institutes, including the ITP, IHEP and Tsinghua University in China. Work on negative magnetoresistivity was also reported in the conference of Iberian Strings 2016.We also wrote short introducing articles on our two papers that were published in P.R.L in the CSIC social media. We also organized a small workshop on topics in AdS/CMT and invited a lot of experts working in this area to IFT. During the workshop besides listening to their talks and learning from them, I also introduced my work and possible future directions to them. There has been a lot of work done as generalizations or on the basis of our work. For example, a research group in Jena university (Phys. Rev. Lett 118, 201601) studied the surface states of our holographic Weyl semimetal. They observed the appearance of an electric current restricted to the surface in presence of electric chemical potential. The total current is universal in the sense that it only depends on the topology of the phases showing that the bulk-boundary correspondence holds even at strong coupling.