Research

I work on (a) the theoretical studies of strongly interacting problems in quantum magnetism and ultracold atomic systems and (b) the development of new methods for treating such problems in light of quantum information theory.

In quantum magnets, a key concept for finding nontrivial phenomena is frustration, a competition among different magnetic interactions. It occurs, for example, when three spins sit on a triangle and interact antiferromagnetically. In such situations, the system cannot easily find an energetically stable state, leading to quasidegeneracy among a large number of magnetic configurations. Similar quasidegeneracy occurs when flat Landau levels are formed in semiconductors in high magnetic fields. In these situations, effects of quantum fluctuations are significantly enhanced, leading to the destruction of simple orders such as magnetic and density-wave orders. In some cases, the system develops complex orders such as the vector spin chirality characterized by the two-spin order parameter S_ixS_j. It is also possible that topologically ordered states, which allow no characterization in terms of a local order parameter, appear---examples include quantum spin liquids and fractional quantum Hall states. I have worked on the theoretical studies of these exotic states of matter, paying particular attentions to the latest experimental developments that enable the realization and observation of such states. For example, a magnetoelectric coupling in mutiferroics enables the observation of the vector spin chirality through an electric polarization while laser-induced gauge fields for ultracold atoms can provide controllable laboratories for emulating a variety of fractional quantum Hall states. At the same time, I have also been interested in the fresh idea of applying quantum information theory to strongly interacting problems. In particular, I have worked on the applications of the entanglement concept to the studies of quantum critical phenomena and topological phases.

My current and past research topics include:

• Quantum (spin) Hall physics in cold atomic systems in synthetic gauge fields

• Entanglement concepts for probing underlying conformal field theory and topological order

• Frustrated quantum magnets and quantum spin liquids

• Chiral order and multiferroics

My researches are based on the following approaches:

• Analytical methods: bosonization, conformal field theory, slave particle theory, etc.

• Numerical methods: numerical exact diagonalization, matrix product states (iTEBD etc.), etc.

Please see the slides and abstracts of talks here for more information.