Topological Lifshitz Transitions, Orbital Currents, and Interactions in Low-dimensional Fermi Gases in Synthetic Gauge Fields

Abstract

Low-dimensional systems of interacting fermions in a synthetic gauge field have been experimentally realized using two-component ultra-cold Fermi gases in optical lattices. Using a two-leg ladder model that is relevant to these experiments, we have studied the signatures of topological Lifshitz transitions and the effects of the inter-species interaction $U$ on the gauge-invariant orbital current in the regime of large intra-leg hopping $\Omega$. Focusing on non-insulating regimes, we have carried out numerically exact density-matrix renormalization-group (DMRG) calculations to compute the orbital current at fixed particle number as a function of the interaction strength and the synthetic gauge flux per plaquette. Signatures of topological Lifshitz transitions where the number Fermi points changes are found to persist even in the presence of very strong repulsive interactions. This numerical observation suggests that the orbital current can be captured by an appropriately renormalized mean-field band structure, which is also described here. Quantitative agreement between the mean-field and the DMRG results in the intermediate interaction regime where $U\lesssim \Omega$ is demonstrated. We also have observed that interactions can change the sign of the current susceptibility at zero field and induce Lifshitz transitions between two metallic phases, which is also captured by the mean-field theory. Correlation effects beyond mean-field theory in the oscillations of the local inter-leg current are also reported. We argue that the observed robustness against interactions makes the orbital current a good indicator of the topological Lifshitz transitions.

arXiv comment18 pages, 16 figures; v2: typos corrected and references updated

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• Spectrum, Lifshitz transitions and orbital currents in frustrated fermionic ladders with a uniform flux
• Measuring Hall voltage and Hall resistance in an atom-based quantum simulator
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Mott insulating states of the anisotropic SU(4) Dirac fermions
• Coexisting Néel and charge density wave orders in attractive three-color fermions
• Repulsion driven metallic phase in the ground state of the half-filled $t-t^{\prime }$ ionic Hubbard chain
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux
• Fermi surface as a quantum critical manifold: gaplessness, order parameter, and scaling in $d$-dimensions