NCTS Taiwan

III. Research Themes:
The common research theme of TG3.2 is novel quantum phenomena in correlated many-body systems. Over the recent decades, many fascinating exotic quantum many-body (collective) phenomena have been observed in condensed matter systems due to strong electron correlations. These phenomena cannot be understood in terms of single-particle picture, and they are made of many-body quantum entangled states. Examples of such kind include: unconventional superconductivity in Fe-based, cuprates and twisted bi-layer graphene, non-Fermi liquid (strange metal) quantum critical behaviors in heavy-fermion metals/superconductors and in high-Tc superconductors, as well as superfluid-Mott transition in cold atoms. Meanwhile, the discovery of symmetry protected topological insulators around 2005 has led to an enormous effort in trying to realize more exotic topological material phases both theoretically and experimentally, including: topological insulators, topological semi-metals, Driac/Weyl semi-metals and topological superconductors. More recently, interest has been shifted to search for topological phases induced/stablized by electron correlation, such as: topological Kondo insulators/semi-metals, magnetic topological insulators/semi-metals. These correlation-driven novel quantum states of matter are of fundamentally important topics in condensed matter systems. There are many new correlated quantum phases of matter have been or yet to be discovered. Meanwhile, the mechanism for many of these exotic correlated quantum states still remain a big mystery and yet to be understood in a new theoretical framework. Therefore, these phenomena are important for understanding fundamental aspects of quantum condensed matter systems as well as for technological applications.

We plan to continue studying the following general topics mentioned in the 2021 NCTS White Paper: Novel quantum phases, quantum phase transitions in and out of equilibrium, and Correlation driven topological phases of matter and Majorana fermions. Meanwhile, we identify a new exciting emerging research topic—Non-Hermitian quantum many-body physics-- in open quantum systems of cold atoms and quantum optics, which leads to new many-body effects.

IV. Activities

V. Expected achievements:
Critical Non-equilibrium Dynamics
The quantum critical models we address feature critical Kondo destruction, where Kondo screening itself is critical invalidating a naive quantum-to-classical mapping. We here proposed to study the problem in the real-time domain.
We expect that this will shed light on how quantum criticality builds up as the long-time limit is approached. Our study of quenches across the critical coupling will indicate if the Kibble-Zurek mechanism works for this class of unconventional quantum phase transitions. Finally, the results of the proposed research will constitute the first step towards a theory of pump-probe spectroscopy in quantum critical matter.
The mechanism of high-Tc superconductivity in cuprtaes emerging from a Planckian strange metal state
Since the strange metal state in both heavy-fermion metals and cuprate superconductors shares striking similar phenomenology in terms of critical charge fluctuations and Fermi surface reconstruction (or Kondo breakdown), it is very promising to expect that ours result can offer a reasonable and accurate description on the superconducting transition temperature Tc in cuprates and account for why Tc is so high in cuprates. Once the mystery of high-Tc superconductivity is revealed, we may find a way to control and enhance Tc. To date, there is no well accepted theory to account for the Planckian metal state in cuprates and how Tc is related to the Planckian metal state though this state is well supported by many convincing experimental evidences. Due to the success of CH Chung’s related work in PNAS 2022 on the strange metal phase in heavy-fermion systems, we are confident that the proposed approach will have a good chance to take the lead in the international community on this topic and make an important impact in the theory of high-Tc superconductivity.
Magneto-optical effects in magnetic Weyl semimetals
We will study electrodynamics in magnetic Weyl semimetals and calculate Kerr and Faraday rotations in respective compounds. The crystalline and
magnetic symmetries will be considered, by which symmetry rules for the Kerr effect will be answered. The interplay between (antiferro)magnetism and Weyl fermions to the optical responses will be examined in consequence.
Topological quantum spin-lquids
Although experimentally, a half-integer quantization in thermal Hall conductance is seen in α-RuCl3. It only exists in a range of finite magnetic field values. It was argued that the onset of the chiral Majorana edge currents coincides with the disappearance of Neel temperature. We expect that our theory can explain the behavior of thermal Hall conductance for the entire range of magnetic field starting from the low-B limit. The issue that in high spin S=3/2 materials, the HDM model fits better to the experiment than the Kitaev interaction-based Hamiltonian will be investigated. 
Finally, we will collaborate with experimentalist on this interesting topic and write a joint paper with the experimental group led by Professor Chun-Liang Lin from National Yang Ming Chiao Tung university on this important aspect to confirm our theoretical results.
The application of superoperator formalism of the Liouville operators to non-Hermitian systems
We would like to use the superoperator formalism of the Liouville operators to introduce the non-Hermicity in the topological system. Most of the recent studies focus on the weakly interacting regime in one-dimensional systems. On top of the single-body physics, we will focus on the higher dimensional generalization, the effect of long-range hoppings, as well as many-body interactions in this platform. Additionally, we can engineer possible Liouville operators to realize the non-Hermitian Chern insulators. The results will be the stepping stone toward the complete understanding of the physics between topology, non-Hermicity and correlation effects.
International collaboration and visibility
We expect via our TG’s activities and strong research collaborations we establish, our research based in NCTS will gain much more international visibility. We are confident that we can form an internationally competitive research team in Taiwan strongly correlated quantum condensed matter and cold atoms. In particular, we expect to establish more international collaborations/ties with experts in world’s leading institutes, such as: Max-Planck Institute, BNL, Princeton U., Rutgers U., U. Cambridge, UIUC, ICTP, KITP at UCSB, RIKEN Lab.…
Collaborations between theorists and experimentalists
We emphasize the importance of theory-experiment collaborations in our proposal. We try to identify the possible experimentalists who can collaborate with us in the sub-topics. We are or have been collaborating with many experimentalists mentioned above.We expect to have stronger and wider collaborations with the experimental groups either in Taiwan or in world’s top institutes/universities.
Cultivate young students and postdocs
We expect that by the solid training we provide, our young students and postdocs will be successful in their physics careers in future. More students will get excellent opportunities to continue their PhD studies at top universities world-wide, and more postdocs will get faculty positions in research universities either in Taiwan or elsewhere.