We construct an asymptotically solvable model of many-body critical (MBC) phases, the counteparts of single-particle critical (neither localized nor extended) phases in interacting many-body spin chains. The model is based on a phenomenon we found in mirror-symmetric MBL systems, where single-particle mirror resonances are synchronized by interactions. In the simplest model of single-particle criticality from a hierarchy of approximate mirror centers, two thermodynamic phases emerges in the presence of interactions, which resembles the ETH and MBL phases, but with many-body scars, inverted scars, and (in some regime) mobiility edges. I developed the original idea of this project on structural many-body resonances, the freezing/protection intuition, and proved all mathematical results.

Collaborator: Zi-Jian Li (李子健)
Advisor: Sankar Das Sarma

Inspired by a recent experiment on the possible striped superconductivity in rhombohedral hexalayer graphene, we study the interplay between quantum geometry in a parent band and a pre-existing stripe potential in real space, finding two possible forms of SC pairing by a modeled short-range attractive interaction. I contributed to most of the analytical calculation and the numerical works.

Collaborator: Yang-Zhi Chou (周揚智), Yi Huang (黄奕)
Advisor: Sankar Das Sarma

We discuss whether standard Coulomb interaction may give practical s-wave superconductivity. My contribution is to find the strongly attractive regions of dynamically screened Coulomb interaction under various approximations.

Collaborator: Jay D. Sau, Shuyang Wang
Advisor: Sankar Das Sarma

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 numerically study the properties of an interacting model with a potential which varies slower and slower as one goes further away from the origin, showing that it has finite-size MBL behavior and effective criticality.

Collaborator: Zi-Jian Li (李子健)
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