Fracton as windows to topology, interaction and constraints in Emerging Phases of Matter

Project Information

fracton

Grant agreement ID: 101019431

DOI

10.3030/101019431

Project terminated on 31 October 2022

EC signature date 11 March 2021

Start date 1 September 2021

End date 31 August 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 212 933,76

EU contribution

€ 212 933,76

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

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

Summary of the context and overall objectives of the project

• 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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

• Interaction-enabled fractonic higher-order topological phases, Julian May-Mann, Yizhi You, Taylor L. Hughes, and Zhen Bi, Phys. Rev. B 105, 245122

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

• 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.

screenshot-2023-01-19-at-08-59-01.png