Comparing the ground state energy of a 2D bilayer electron-hole system assuming that it is an electron-hole plasma and that it is an exciton gas under various screening assumptions, from which the statbility of the exciton phase can be estimated.

Collaborator: Seth M. Davis

Advisor: Sankar Das Sarma

Simulating a clean spin chain (thermal bath) coupled to an interacting quasiperiodic spin chain with a mobility edge, with the latter initialized in an energy eigenstate, and using the long-time evolution of the system to extract three behaviors: ETH, non-ergodic extended, and localized.

Collaborator: DinhDuy Vu (Vũ Trần Đình Duy)

Advisor: Sankar Das Sarma

Calculating the Lorenz ratio of graphene with a bipolar diffusive Boltzmann transport theory with disorders and phonon scattering, which provides an alternative explanation for the sharp finite-temperature peak of the Lorenz ratio observed in an experimental paper.

Advisor: Sankar Das Sarma

Considering a quasiperiodic spin chain coupling to a thermal bath at one end, and calculating the decay rate numerically to estimate the avalanche stability of large quasiperiodic MBL systems.

Collaborator: DinhDuy Vu (Vũ Trần Đình Duy)

Advisor: Sankar Das Sarma

Generalizing the entanglement entropy to non-Hermitian quantum systems such that the scaling properties of conformal field theories are retained at critical points.

Collaborators: Yu-Chin Tzeng (曾郁欽), Po-Yao Chang (張博堯)

Developing a generalized version of the gauging procedure, using it to construct non-Abelian fractons, and exploring their algebraic properties.

Advisor: Po-Yao Chang (張博堯)

Non-Abelian anyons are the quasiparticles with fascinating properties in two-dimensional topological phases of matter, which are candidates for fault-tolerant quantum computation. Beyond the traditional type of topological phases, fracton orders in three dimensions have the unique feature that some excitations are immobile, making them suitable for quantum memories. Non-Abelian fractons combine the two features above, and are important subjects for theoretical developments and potential applications to quantum information science. However, due to lack of a generic mathematical description of the non-Abelian fractions, a systematical construction of the lattice model is desired. Here, we develop a novel way to construct non-Abelian fractons on lattices based on the gauging principle.

The principle of gauging has a tremendous success in obtaining several topological phases of matters. In electromagnetism, one can start from the symmetry of a matter field, construct the gauge potentials and the gauge transformation, and finally obtain the properties of the electric charge and the magnetic flux. Now, we generalize the construction by starting from a matter field having exotic symmetries, and find that the resulting “electric charges” and “magnetic fluxes” contain non-Abelian fractons. Moreover, we find that, under certain conditions, the algebraic properties of those charges and fluxes are the same as their counterparts in two-dimensional lattice gauge theory for non-Abelian anyons.

Our construction using the gauging principle makes the identification of species and properties of fractons more straightforward. In particular, the correspondence between fractons and anyons from the algebtric structure sheds light on classifying fracton orders.

Using the mathematical language of symplectic geometry to reformulate the positive partial transpose criterion in phase space.

Advisor: Ray-Kuang Lee (李瑞光)