We study bilayer fermionic cold-atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth- and first-order Haldane pseudopotentials, at a total Landau-level filling factor of 1/2. Our numerical results on the TCTP model indicate that a Haldane-Rezayi state describes the critical point between strong and weak $d$ -wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.We study bilayer fermionic cold-atom systems with dipolar interactions, as well as a two-component tunable pseudopotential (TCTP) model which keeps only the zeroth- and first-order Haldane pseudopotentials, at a total Landau-level filling factor of 1/2. Our numerical results on the TCTP model indicate that a Haldane-Rezayi state describes the critical point between strong and weak $d$-wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.

arXiv:1407.7935Physical Review BOct 2, 201412 citations

Properties of higher-order phase transitions

Wolfhard Janke E, Desmond A. Johnston, Ralph Kenna B

arXiv:cond-mat/0512352Nuclear Physics BDec 28, 200523 citations

FOTOC complexity in an extended Lipkin-Meshkov-Glick model

Nitesh Jaiswal, Mamta Gautam, Ankit Gill +1 more

We study fidelity out-of-time-order correlators (FOTOCs) in an extended Lipkin-Meshkov-Glick model and demonstrate that these exhibit distinctive behaviour at quantum phase transitions in both the ground and the excited states. We show that the dynamics of the FOTOC have different behaviour in the symmetric and broken-symmetry phases, and as one approaches phase transition. If we rescale the FOTOC operator with time, then for small times, we establish that it is identical to the Loschmidt echo. We also compute the Nielsen complexity of the FOTOC operator in both phases, and apply this operator on the ground and excited states to obtain the quasi-scrambled state of the model. The FOTOC operator introduces a small perturbation on the original ground and excited states. For this perturbed state, we compute the quantum information metric to first order in perturbation, in the thermodynamic limit. We find that the associated Ricci scalar diverges at the phase transition on the broken-symmetry phase side, in contrast to the zeroth order result. Finally, we comment upon the Fubini-Study complexity in this model.We study fidelity out-of-time-order correlators (FOTOCs) in an extended Lipkin-Meshkov-Glick model and demonstrate that these exhibit distinctive behaviour at quantum phase transitions in both the ground and the excited states. We show that the dynamics of the FOTOC have different behaviour in the symmetric and broken-symmetry phases, and as one approaches phase transition. If we rescale the FOTOC operator with time, then for small times, we establish that it is identical to the Loschmidt echo. We also compute the Nielsen complexity of the FOTOC operator in both phases, and apply this operator on the ground and excited states to obtain the quasi-scrambled state of the model. The FOTOC operator introduces a small perturbation on the original ground and excited states. For this perturbed state, we compute the quantum information metric to first order in perturbation, in the thermodynamic limit. We find that the associated Ricci scalar diverges at the phase transition on the broken-symmetry phase side, in contrast to the zeroth order result. Finally, we comment upon the Fubini-Study complexity in this model.

arXiv:2212.03682Dec 7, 20220 citations

On first order phase transitions

Alain H. Billoire

Nuclear Physics B - Proceedings SupplementsJan 1, 19922 citations

d

-wave pairing quantum Hall phases. Upon further increasing the attractive zeroth-order pseudopotentials, the system transits from the strong-pairing phase to a stripe phase and then to a cluster phase (or phase separation). The dipolar interaction can be mapped onto the TCTP model in the strong-pairing phase if high-order pseudopotentials are ignored. Our numerical results show that this is indeed the case, so the strong-pairing phase exists in the cold-atom system.