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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Chiral graviton modes in fermionic fractional Chern insulators
Min Long1,2, Zeno Bacciconi3,4, Hongyu Lu2,5,6
1Department of Physics and HK Institute of Quantum Science & Technology, The University of Hong Kong, Pokfulam Road, Hong Kong Special Administrative Region of China, People's Republic of China.
Summary
Chiral graviton modes, key excitations in Fractional Quantum Hall (FQH) liquids, are shown to exist in Fractional Chern Insulators (FCI) on a lattice. These modes are long-lived, offering insights for solid-state and cold atom experiments.
Area of Science:
- Condensed Matter Physics
- Quantum Hall Effect
- Topological Phases of Matter
Background:
- Chiral graviton modes are characteristic collective excitations in Fractional Quantum Hall (FQH) liquids.
- Their existence in lattice systems, like Fractional Chern Insulators (FCI), is uncertain due to the loss of continuum symmetries.
- Recent advancements in realizing FCIs in materials like transition metal dichalcogenides and graphene highlight the urgency of this question.
Purpose of the Study:
- To theoretically and numerically investigate the existence and properties of chiral graviton modes in fermionic FCIs.
- To establish a connection between FQH and FCI chiral graviton modes.
- To provide evidence for the long-lived nature of these modes in lattice systems.
Main Methods:
- Derivation of a lattice stress tensor operator within the fermionic Harper-Hofstadter (HH) model.
- Establishing an adiabatic connection between FQH and FCI by interpolating between HH and Checkerboard lattice models.
- Utilizing state-of-the-art matrix product state (MPS) and exact diagonalization (ED) simulations.
- Performing finite-size analysis to determine the graviton mode's decay rate.
Main Results:
- Demonstrated the existence of chiral graviton modes in fermionic FCIs.
- Established a deep connection between lattice stress-tensor operators and correlation hole dynamics.
- Provided strong evidence for long-lived chiral graviton modes in FCIs, even without continuous symmetries.
- Quantified an intrinsic lattice-induced decay rate for the graviton mode, found to be small relative to its energy.
Conclusions:
- Chiral graviton modes persist as long-lived excitations in fermionic FCIs on a lattice.
- The findings bridge the understanding of FQH and FCI systems regarding these modes.
- Results have significant implications for exploring FCI phases in solid-state systems and cold atom experiments, and for diagnosing topological phases.
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