Regensburg 2025 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 35: Topology: Poster

TT 35.9: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P3

Variational Trial States for Fractional Chern Insulators — •Giacomo Amadore — LMU, Munich, Germany

Early on, Laughlin's wave functions and other variational trial states provided deep physical insights into the nature of fractional quantum Hall (FQH) systems. One particularly fruitful approach in motivating such trial states is based on the composite fermion description of the FQH problem in the continuum. In contrast, variational states describing fractional Chern insulators in lattice systems remained scarce. While existing methods can construct lattice analogs of familiar FQH states, these states are not generally expected to be the ground state of simple discretized FQH Hamiltonians, but instead a parent Hamiltonian is only constructed a posteriori. To address this limitation, we propose a conceptually different approach motivated by the possibility to study FQH physics in optical lattice experiments realizing the Hofstadter-Bose-Hubbard model. We derive trial states for the ground state of this specific Hamiltonian by turning hard-core bosons into composite fermions through the attachment of a single flux quantum and deriving an effective Hamiltonian for the composite fermions coupled to a dynamical gauge field. To benchmark our findings, we compare the variational energies of different ansätze to (quasi-)exact numerical results. We anticipate that our preliminary results provide a promising starting point for further variational studies and investigations of lattice analogs of FQH systems.

Keywords: FQH system; Hofstadter-Bose-Hubbard model; lattice theory; variational methods