Abstract
Ultracold Fermi gases with synthetic gauge field represent an excellent platform to study the combined effect of lattice frustration and an effective magnetic flux close to one flux quantum per particle. The minimal theoretical model to accomplish this task is a system of spinless noninteracting fermions on a triangular two-chain flux ladder. In this paper we consider this model close to half-filling, with interchain hopping amplitudes alternating along the zigzag bonds of the ladder and being small. In such setting qualitative changes in the ground state properties of the model, most notably the flux-induced topological Lifshitz transitions are shifted towards the values of the flux per a diatomic plaquette (f) close to the flux quantum (\(f\sim 1/2\)). Geometrical frustration of the lattice breaks the \(k \rightarrow \pi - k\) particle-hole spectral symmetry present in non-frustrated ladders, and leads to splitting of the degeneracies at metal–insulator transitions. A remarkable feature of a translationally invariant triangular ladder is the appearance of isolated Dirac node at the Brillouin zone boundary, rendering the ground state at \(f=1/2\) semi-metallic. We calculate the flux dependence of the orbital current and identify Lifshitz critical points by the singularities in this dependence at a constant chemical potential \(\mu \) and constant particle density \(\rho \). The absence of the particle-hole symmetry in the triangular ladder leads to the asymmetry between particle (\(\rho >1\)) and hole (\(\rho <1\)) doping and to qualitatively different results for the phase diagram, Lifshitz points and the flux dependence of the orbital current in the settings \(\rho =\textrm{const}\) and \(\mu =\textrm{const}\).
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The authors confirm that the data supporting the findings of this study are available within the article. All data generated or analysed during this study are included in this published article. A preprint of this article has appeared in https://arxiv.org/abs/2210.16814, cond-mat.str-el.
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Notes
In fact, the location of the lowest energy states close to the zone boundary \(k=\pi \) is a robust property of the model valid as long as \(|t_1 - t_2| \ll |t_1 + t_2|\) irrespective of the magnitude of the ratios \(t_{1,2}/t_0\). On the other hand, a local minimum of \(E_k\) at \(k=0\) only exists under the condition \(t_1 t_2 < 4t^2 _0\); otherwise \(E_k\) has a local maximum at \(k=0\).
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Acknowledgements
We thank Marcello Dalmonte for reading the manuscript and making a number of important suggestions. We thank him, Titas Chanda, Pierre Fromholz, Emanuele Tirrito and Mikheil Tsitsishvili for fruitful discussions and cooperation in related projects. We are also grateful to George Japaridze and Oleg Starykh for interesting conversations on the effects of frustration in one-dimensional quantum systems. The authors acknowledge the support from the Shota Rustaveli National Science Foundation of Georgia, SRNSF, Grant No. FR-19-11872.
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Beradze, B., Nersesyan, A. Spectrum, Lifshitz transitions and orbital current in frustrated fermionic ladders with a uniform flux. Eur. Phys. J. B 96, 2 (2023). https://doi.org/10.1140/epjb/s10051-022-00472-0
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DOI: https://doi.org/10.1140/epjb/s10051-022-00472-0