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 Ω. 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 ≲ Ω 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.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 Ω. 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 ≲ Ω 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:2112.08763New Journal of PhysicsMar 1, 202212 citations

Dynamical classification of topological quantum phases

Lin Zhang, Long Zhang, Sen Niu +1 more

arXiv:1802.10061中国科学通报：英文版Sep 29, 2018150 citations

Topological phase transition in a two-species fermion system: Effects of a rotating trap potential or a synthetic gauge field

Shiuan-Fan Liou, Zi-Xiang Hu, Kun Yang

We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$ -wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor ${\ensuremath{\nu}}_{f}=2$. We show that the system undergoes a continuous quantum phase transition from a ${\ensuremath{\nu}}_{f}=2$ fermionic integer quantum Hall state formed by atoms to a ${\ensuremath{\nu}}_{b}=1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of $p$ -wave pairing.We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor ${\ensuremath{\nu}}_{f}=2$. We show that the system undergoes a continuous quantum phase transition from a ${\ensuremath{\nu}}_{f}=2$ fermionic integer quantum Hall state formed by atoms to a ${\ensuremath{\nu}}_{b}=1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of $p$-wave pairing.

arXiv:1802.10553Physical review. B./Physical review. BJun 25, 20181 citation

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theories

Luca Barbiero, Schweizer, Christian, Monika Aidelsburger +3 more

Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields.Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields.

arXiv:1810.02777Oct 5, 201814 citations

Non-Abelian topological phases

Michael Hartley Freedman

Bulletin of the American Physical SocietyMar 15, 20060 citations

We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via

s

-wave Feshbach resonance and are subject to rotation or a synthetic gauge field that puts the fermions at Landau level filling factor ${\ensuremath{\nu}}_{f}=2$. We show that the system undergoes a continuous quantum phase transition from a ${\ensuremath{\nu}}_{f}=2$ fermionic integer quantum Hall state formed by atoms to a ${\ensuremath{\nu}}_{b}=1/2$ bosonic fractional quantum Hall state formed by bosonic diatomic molecules. In the disk geometry we use, these two different topological phases are distinguished by their different gapless edge excitation spectra, and the quantum phase transition between them is signaled by the closing of the energy gap in the bulk. Comparisons will be made with field-theoretical predictions and the case of

p

-wave pairing.