Periodic Reporting for period 1 - fracton (Fracton as windows to topology, interaction and constraints in Emerging Phases of Matter)
Reporting period: 2021-09-01 to 2023-08-31
• We conduct an extensive study of higher-order topological insulators in strongly correlated systems. In particular, we demonstrate a universal way to construct interacting HOTSCs via the coupled wire construction and identify anomalous hinge states from modular tensor categories. We also detect the HOTSCs via entanglement spectra and flux responses, and observe the supersymmetry structure in HOTSC flux states. In addition, we identify a zoology of Kitaev magnetic materials whose fractionalized excitations render emergent Majoranas with HOTSC structures.
• We explore a new type of emergent gauge theory in fracton systems and identify the tensor network realization of these states. In particular, we observe that all discrete fracton gauge theories can be obtained by anyon condensation of conventional Zn gauge theories. We simulate the entanglement entropy and mutual information of these gauge theories and link them to the holonomies of the ground state.
• We explore a new type of emergent gauge theory in fracton systems and identify the tensor network realization of these states. In particular, we observe that all discrete fracton gauge theories can be obtained by anyon condensation of conventional Zn gauge theories. We simulate the entanglement entropy and mutual information of these gauge theories and link them to the holonomies of the ground state.
• Interaction-enabled fractonic higher-order topological phases, Julian May-Mann, Yizhi You, Taylor L. Hughes, and Zhen Bi, Phys. Rev. B 105, 245122
• We identify a protocol to realize a non-CSS code with subdiffusive behavior and slow glassy dynamics that can potentially be useful for quantum information processing. In particular, we propose the realization of non-abelian statistics in these platforms via constructing lattice defect networks.
• We explore the multipolar boson-Hubbard model in 1D that engenders a new type of quantum phase transition that exhibits self-fractal structure. We elucidate the critical exponent of this theory and discover a dimensional duality between the quantum model and the classical close-packed systems.
• We study the disorder effect in various SPT phases and recognize that the quenched disorder in some SPT phases is related to the quantum decoherence of quantum states in open systems.
• We explore the dipolar quantum Hall effect in 2D correlated fermion systems and develop a mathematical no-go theorem that bounds the thermal Hall conductance in dipolar quantum Hall states.
• We explore the multipolar boson-Hubbard model in 1D that engenders a new type of quantum phase transition that exhibits self-fractal structure. We elucidate the critical exponent of this theory and discover a dimensional duality between the quantum model and the classical close-packed systems.
• We study the disorder effect in various SPT phases and recognize that the quenched disorder in some SPT phases is related to the quantum decoherence of quantum states in open systems.
• We explore the dipolar quantum Hall effect in 2D correlated fermion systems and develop a mathematical no-go theorem that bounds the thermal Hall conductance in dipolar quantum Hall states.