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arXiv:2504.19525 · Physical Review Letters

Spin-Depairing-Induced Exceptional Fermionic Superfluidity

Soma Takemori, Kazuki Yamamoto, Akihisa Koga

Published Dec 2, 2025• 4 citations
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Abstract

We investigate the non-Hermitian (NH) attractive Hubbard model with spin depairing, which is a spin-resolved asymmetric hopping that nonreciprocally operates spins in the opposite direction. We find that spin depairing stabilizes a superfluid state unique to the NH system. This phase is characterized not only by a finite order parameter, but also by the emergence of exceptional points (EPs) in the momentum space-a feature that starkly contrasts with previously discussed NH fermionic superfluidity, where EPs are absent within the superfluid state and emerge only at the onset of the superfluid breakdown. We uncover the rich mechanism underlying this "exceptional fermionic superfluidity" by analyzing the interplay between EPs and the effective density of states of the complex energy dispersion. Furthermore, we reveal that the exceptional superfluid state breaks down induced by strong spin depairing on the cubic lattice, while it remains robust on the square lattice.

DOI
10.1103/ntjf-zb2v

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We investigate the non-Hermitian (NH) attractive Hubbard model with spin depairing, which is a spin-resolved asymmetric hopping that nonreciprocally operates spins in the opposite direction. We find that spin depairing stabilizes a superfluid state unique to the NH system. This phase is characterized not only by a finite order parameter, but also by the emergence of exceptional points (EPs) in the momentum space-a feature that starkly contrasts with previously discussed NH fermionic superfluidity, where EPs are absent within the superfluid state and emerge only at the onset of the superfluid breakdown. We uncover the rich mechanism underlying this "exceptional fermionic superfluidity" by analyzing the interplay between EPs and the effective density of states of the complex energy dispersion. Furthermore, we reveal that the exceptional superfluid state breaks down induced by strong spin depairing on the cubic lattice, while it remains robust on the square lattice.
Non-Hermitian (NH) quantum systems host exceptional points (EPs), where eigenstates and eigenvalues coalesce, leading to unconventional many-body phenomena absent in Hermitian systems. While NH fermionic systems with complex interactions exhibit superfluid (SF) breakdown with EPs, spin-dependent asymmetric hopping can stabilize a NH superfluid (NH-SF) that coexists with EPs. In this work, we investigate the quasi-one-dimensional NH attractive Fermi-Hubbard model by using NH-BCS theory. We demonstrate that, when the system is regarded as weakly-coupled chains, the exceptional SF phase becomes unstable and metastable (exceptional) SF state appears between the stable SF and normal states. In the one-dimensional limit, the exceptional SFs disappear entirely and EPs only appear on the phase boundary between the normal and SF states. These results reveal how dimensional crossover governs the stability of the exceptional SF, providing the insights into the interplay between dimensionality and dissipation, with potential relevance for experimental implications in ultracold atoms.
We study non-Hermitian (NH) fermionic superfluidity subject to dissipation of Cooper pairs on a honeycomb lattice, for which we analyze the attractive Hubbard model with a complex-valued interaction. Remarkably, we demonstrate the emergence of the dissipation-induced superfluid phase that is anomalously enlarged by a cusp on the phase boundary. We find that this unconventional phase transition originates from the interplay between exceptional lines and Van Hove singularity, which has no counterpart in equilibrium. Moreover, we demonstrate that the infinitesimal dissipation induces the nontrivial superfluid solution at the critical point. Our results can be tested in ultracold atoms with photoassociation techniques by postselecting special measurement outcomes with the use of quantum-gas microscopy, and they can lead to an understanding of the NH many-body physics triggered by exceptional manifolds in open quantum systems.
Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of nondiagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.
The two-body loss associated with inelastic interactions between fermions plays a significant role in realistic many-body systems. Here we study a two-component non-Hermitian Bardeen-Cooper-Schrieffer superfluidity with spin imbalance and two-body loss characterized by a complex-valued sss-wave interaction in a square lattice. At the mean-field level, we map out the zero-temperature phase diagram and observe a dissipation-induced transition from superfluid to normal phase as well as a distinctive revival of the superfluid state in the weakly interacting regime applicable to both spin-balanced and spin-imbalanced systems. In the spin-imbalanced case, we find that the effective density of states involving weight functions reduces the regions in k\mathbf{k}k space contributing to pairing, hence leading to a pronounced expansion of the normal phase on the phase diagram. Additionally, we analyze the order parameter, condensate energy, quasiparticle spectra, momentum distribution, and compressibility to characterize the presenting phases and phase transitions.
We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated sss-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the long wavelength sound mode, a sharp roton mode over a wide range of densities and interaction strengths. We compute the sound velocity and the roton gap within a generalized random phase approximation (GRPA) and show that the GRPA results are in good agreement, at strong coupling, with a spin-wave analysis of the appropriate strong-coupling pseudospin model. We also investigate, using this two-pronged approach, the breakdown of superfluidity in the presence of a supercurrent. We find that the superflow can break down at a critical flow momentum via several distinct mechanisms---depairing, Landau instabilities or dynamical instabilities---depending on the dimension, the interaction strength and the fermion density. The most interesting of these instabilities is a charge modulation dynamical instability which is distinct from previously studied dynamical instabilities of Bose superfluids. The charge order associated with this instability can be of two types: (i) a commensurate checkerboard modulation driven by softening of the roton mode at the Brillouin zone corner, or, (ii) an incommensurate density modulation arising from superflow-induced finite momentum pairing of Bogoliubov quasiparticles. We elucidate the dynamical phase diagram showing the critical flow momentum of the leading instability over a wide range of fermion densities and interaction strengths and point out implications of our results for experiments on cold atom fermion superfluids in an optical lattice.
Exceptional points (EPs) have seen substantial advances in both experiment and theory. However, in quantum systems, higher-order EPs remain of great interest and possess numerous intriguing properties yet to be fully explored. Here we describe a parity-time symmetry-protected three-level non-Hermitian system with dissipative spin-orbit-coupled fermions in which a third-order exceptional point (EP3) emerges when both the eigenvalues and eigenstates of the system collapse into one. The band structure and its spin dynamics are explored for the 173Yb^{173}\mathrm{Yb}173Yb fermion. We highlight the enhanced sensitivity to the external perturbation of the EP3 with cubic-root energy dispersion. Additionally, we investigate the second-order EP (EP2) with square-root energy dispersion in a three-level quantum system in the absence of parity symmetry, which proves that the enhanced sensitivity closely relates to the symmetries of the non-Hermitian system. Furthermore, we analyze the encircling behavior of the EP3 in terms of the slowly evolving limit and the nonadiabatic dynamics beyond the slowly evolving limit and discover some results different from those of the EP2.