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 computed from 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.

Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators

“…A similar scenario has been found in d = 1 [15], where it was argued that the result was expected to hold also in higher dimensionality. Nevertheless, we emphasize that this is only true at U U c , whereas the spectral properties at intermediate coupling are highly non-trivial and they require a full dynamical description to be accurately described.…”

“…Even more surprisingly, we observe that the chiral current is typically much larger in the insulating phase than in the metallic phase, and it is maximized at the Mott transition, similarly to what we found in the non-interacting limit. The value of the current is larger for d = 1 than for d = 2 [15].…”

“…The terms in Eq. ( 18) have a non-trivial physical interpretation, as the chiral-current operator ( 16) and the synthetic dimension-current operator (15) can indeed be written as…”

“…Many features of these systems have been investigated both theoretically and experimentally, mostly in the context of (one-dimensional) chains [7,[11][12][13][14][15]. Following the seminal proposal of a synthetic ladder whose plaquettes are pierced by a uniform magnetic flux [7], and the experimental demonstration of chiral states localized on the synthetic edges [12], a number of remarkable effects have been pointed out.…”

Spectrum, Lifshitz transitions and orbital currents in frustrated fermionic ladders with a uniform flux

“…The properties of bosonic and fermionic flux ladders have been the subject of many theoretical and experimental studies [14][15][16][17][18][19][20][21][22][23][24]. Ground state phases and their topological properties, chiral boundary currents and topological Lifshitz transitions taking place in ladders on varying the flux have been investigated.…”