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Simulating Fermionic Fractional Chern Insulators with Infinite Projected Entangled-Pair States
Hao Chen1, Titus Neupert1, Juraj Hasik1
1University of Zürich, Department of Physics, 8057 Zürich, Switzerland.
Physical Review Letters
|August 10, 2026
Summary
Infinite projected entangled-pair states (iPEPSs) now capture fermionic topological order in fractional Chern insulators. A critical bond dimension was found, enabling accurate variational representation of this complex quantum matter.
Area of Science:
- Quantum Condensed Matter Physics
- Topological Quantum Matter
- Quantum Information Theory
Background:
- Infinite projected entangled-pair states (iPEPSs) are effective for modeling 2D quantum systems.
- Existing iPEPS methods have successfully described bosonic topological order, such as chiral spin liquids.
- Extending iPEPS to fermionic systems is crucial for understanding a broader range of quantum phenomena.
Purpose of the Study:
- To adapt and apply U(1)-symmetric fermionic iPEPS to study fermionic topological order.
- To investigate the fractional Chern insulator (FCI) phase using this extended variational framework.
- To determine the necessary bond dimensions for accurate representation of the FCI state.
Main Methods:
- Variationally optimizing U(1)-symmetric fermionic iPEPS with bond dimensions up to D=9.
- Characterizing the FCI state through bulk observables like Green's functions and pair-correlation functions.
- Analyzing the momentum-resolved edge entanglement spectrum to confirm topological properties.
Main Results:
- Evidence for a critical bond dimension (D_c) was found, above which the iPEPS ansatz accurately represents the FCI phase.
- Bulk observables confirmed the characteristics of the FCI state.
- A compression scheme was developed for efficient entanglement spectrum calculations, showing good convergence at smaller cutoff dimensions.
Conclusions:
- The study successfully extends iPEPS to fermionic topological order, specifically for FCI.
- A critical bond dimension is identified, providing a guideline for future variational studies.
- The developed methods enable robust characterization of fermionic topological phases.
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