We study the lattice counterpart of 't Hooft anomalies of global symmetries using quantum cellular automata (QCA). My contribution includes extracting cohomological invariants using both the symmetry restriction picture and the homotopy/domain wall picture, and exploring the consequences of the anomalies on symmetric commuting projector models. Conclusions in this part include the obstruction to having a trivial symmetric/symmetry broken many-body localized (MBL) phase, and the relationship between the anomaly class, the eigenstate topological order, the structure of its boundary algebra, and the quantum dimensions of the bulk symmetry defects.
Collaborators: David M. Long, Dominic V. Else
We study the dynamics of various disordered spin chains in the prethermal regime, concluding that the previously-observed non-ergodic extended behavior is not related to quasiperiodicity or the mobility edge, but can be perturbatively explained for any potential with regularly spaced deep wells.
Collaborator: David M. Long
Advisor: Sankar Das Sarma
We discuss the linear-in-temperature electronic resistivity due to the scattering by many random phonon modes and the difference between the "apparent asymptote" and the true asymptote, which may have consequences on the interpretation of some recent experiments.
Advisor: Sankar Das Sarma
We compare 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
We simulate 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
We calculate 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
We study the avalanche instability of a quasiperiodic spin chain. My contribution involves calculating the decay rate of bath-coupled small chains numerically to simulate thermal propagation in a large quasiperiodic MBL systems.
Collaborator: DinhDuy Vu (Vũ Trần Đình Duy)
Advisor: Sankar Das Sarma
We consider the properties of the fidelity and fidelity susceptibility in non-Hermitian quantum systems with parity-time symmetry, and its application in numerics to detect quantum phase transitions. My contribution is mainly in the application to the SSH and generalized SSH models.
Collaborators: Iksu Jang (장익수), Po-Yao Chang (張博堯), Yu-Chin Tzeng (曾郁欽)
We generalize the entanglement entropy to non-Hermitian quantum systems such that the scaling properties of conformal field theories are retained at critical points. My contribution is in the theoretical formalism and the numerical confirmation for the SSH and generalized SSH models.
Collaborators: Yu-Chin Tzeng (曾郁欽), Po-Yao Chang (張博堯)
We develop a generalized version of the gauging procedure, and use it to construct non-Abelian fractons and explore 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.
We use the mathematical language of symplectic geometry to reformulate the positive partial transpose criterion in phase space.
Advisor: Ray-Kuang Lee (李瑞光)
