Topological Phase Transitions of Interacting Fermions in the Presence of a Commensurate Magnetic Flux

Abstract

Motivated by recently reported magnetic-field induced topological phases in ultracold atoms and correlated Moiré materials, we investigate topological phase transitions in a minimal model consisting of interacting spinless fermions described by the Hofstadter model on a square lattice. For interacting lattice Hamiltonians in the presence of a commensurate magnetic flux it has been demonstrated that the quantized Hall conductivity is constrained by a Lieb-Schultz-Mattis (LSM)-type theorem due to magnetic translation symmetry. In this work, we revisit the validity of the theorem for such models and establish that a topological phase transition from a topological to a trivial insulating phase can be realized but must be accompanied by spontaneous magnetic translation symmetry breaking caused by charge ordering of the spinless fermions. To support our findings, the topological phase diagram for varying interaction strength is mapped out numerically with exact diagonalization for different flux quantum ratios and band fillings using symmetry indicators. We discuss our results in the context of the LSM-type theorem.

References in corpus (26)

• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Fractional Quantum Hall Effect in Optical Lattices
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Realization of a fractional quantum Hall state with ultracold atoms
• Quantum Phase Diagram of a Moiré-Hubbard Model
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Fractionalization, topological order, and quasiparticle statistics
• Topological charge density waves at half-integer filling of a moiré superlattice
• Direct observation of a magnetic field-induced Wigner crystal
• Generalized Wigner crystallization in moiré materials
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• Universality of Hofstadter butterflies on hyperbolic lattices
• The fidelity approach to the Hubbard model
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries
• Fractional disclination charge and discrete shift in the Hofstadter butterfly
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Optical sensing of fractional quantum Hall effect in graphene
• Moving crystal phases of a quantum Wigner solid in an ultra-high-quality 2D electron system
• Characterization of topological states on a lattice with Chern number
• Landau Levels of the Euler Class Topology
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Symmetry indicators in commensurate magnetic flux
• Particle-Hole Symmetry and the Reentrant Integer Quantum Hall Wigner Solid
• Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands