BLOCH model wave functions and pseudopotentials for all fractional Chern insulators

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Topological Phases of Matter

Background:

• The fractional quantum Hall (FQH) effect describes exotic states of 2D electron systems in strong magnetic fields.
• Fractional Chern insulators (FCIs) are topological insulators with analogous properties to FQH states but without requiring a magnetic field.
• Existing models for FCI wave functions often lack full lattice translational symmetry or struggle with higher Chern numbers.

Purpose of the Study:

• To introduce a new Bloch-like basis that unifies real and internal degrees of freedom in FQH systems.
• To generate novel wave functions for fractional Chern insulators (FCIs) with arbitrary Chern number C.
• To compare the performance of these new wave functions against existing proposals using numerical methods.

Main Methods:

• Development of a Bloch-like basis preserving N(x)×N(y) lattice translational symmetry for C-component FQH systems.
• Implementation of Haldane pseudopotential Hamiltonians within the new basis.
• Large-size numerical calculations for C=1 and C=3 FCI states, including analysis of energy and entanglement spectra.

Main Results:

• The proposed Bloch basis successfully generates model FQH ground states and allows for the construction of FCI wave functions.
• The new FCI wave functions, particularly for C>1, show relationships to modified Halperin and non-Abelian states.
• Numerical results demonstrate improved overlaps for the new wave functions compared to previous theoretical proposals.

Conclusions:

• The novel Bloch-like basis provides a powerful framework for studying both FQH and FCI states.
• This approach yields improved wave functions for FCIs, offering a new avenue for theoretical and numerical investigations.
• The study highlights the deep connection between FQH and FCI phenomena, elucidated through adiabatic continuation in the Bloch basis.