Gapless Topological Phases and Lifshitz Criticality in 1-D Dipole-Conserving Fermionic Chains

Lattice models with dipolar and other modulated symmetries have emerged as a setting for realizing exotic phases of matter and phase transitions. Motivated by prior explorations of topology in dipole-conserving systems[1], we explore a 1-D dipole-conserving fermionic model inspired by the SSH model. We show that the model exhibits phases where the dipole symmetry is quasi-long range ordered, but they are distinguished by a topological invariant of the mean-field ground state and a resulting edge degeneracy. The critical point separating these topologically inequivalent gapless phases is described by an interacting Lifshitz critical point with a long-range order of the U(1) dipole symmetry. We support our field-theoretic analysis with exactly-solvable lattice models and DMRG simulations.

[1]: AA & Z. Bi (2024). Topological Phases and Phase Transitions with Dipolar Symmetry Breaking. arXiv:2403.19601.