Binding two fermions within a Hubbard lattice predicts the creation of an exceptional point, a specific condition where analytical solutions coalesce. Total momentum selects these special sectors even in isotropic systems, refining understanding beyond previous knowledge of binding thresholds for individual impurities on similar lattices. More broadly, the kinetic structure governing particle movement dictates whether loss-induced binding coincides with such exceptional degeneracy.

Manipulating how particles move within a material’s structure determines if bound pairs also enter an unusual quantum state called an “exceptional point”. This happens because the way particle hops interfere dictates their kinetic energy; when movement along one direction dominates, exceptional points emerge at binding thresholds. These findings refine understanding to predict more complex changes in behaviour, even in uniform materials.

Binding two fermions within a Hubbard lattice, a repeating pattern of atoms acting like a miniature highway system for electrons, creates an exceptional point (EP). An EP represents a special “tuning” point where two normally distinct quantum states become identical, akin to perfectly overlapping waves cancelling each other out but possessing unique symmetry-related properties.

Total momentum can select these unusual sectors even in uniform materials, going beyond identifying when particles bind together. Understanding if and when bound pairs enter such states is key because it refines predictions about complex changes in behaviour within materials; pinpointing exactly when that transition occurs remains vital.

Two-Fermion Binding Predicts Exceptional Points Via Kinetic Energy Control

Precision in predicting exceptional points within Hubbard lattices has increased significantly beyond previous capabilities. Where prior work predicted binding thresholds for single impurities, conditions are now pinpointed for two-fermion binding coinciding with an exceptional point, a vital state indicating dramatic changes to material behaviour. This is achieved through precise calculation of kinetic energy interference from particle hops along different directions and depends on if maximum kinetic energy exceeds transverse maxima within the lattice structure.

Calculations also reveal that even on isotropic lattices, where all directions are equivalent, binding can occur without reaching these exceptional points when no single direction dominates relative motion. Exact diagonalization of finite lattices verified these findings, confirming both thresholds and decay rates across various scenarios. Directional dominance in fermion movement dictates coincidence between pairing and key quantum shifts; specifically, an ‘exceptional threshold’ arises when kinetic energy from particle hops along one direction surpasses transverse maxima within the lattice structure.

Ensuring all scattering channels remain open near the centre of the pair’s energy range leads to purely imaginary local pair functions and restores parity-time symmetry upon loss. However, calculations currently rely on modelling particle interactions on hypercubic lattices, raising questions about whether these findings extend beyond such regular arrangements of atoms into more complex or higher-dimensional materials. Understanding binding at exceptional points remains important regardless of lattice type.

Fermion binding predictions clarify critical transitions in Hubbard lattices

Researchers at Harbin Institute of Technology, Jiangsu University and Shenzhen Key Laboratory of Advanced Functional Carbon Materials have revealed how total momentum governs whether two bound fermions within a lattice structure also exhibit exceptional behaviour. This approach moves past identifying when particles bind by demonstrating the role directional dominance plays in their motion; it provides a foundational principle for predicting dramatic shifts in material properties upon fermion pairing.

Further analysis focused on extending these calculations to more complex lattices or higher dimensional materials, offering valuable insight into real-material behaviour despite being presently limited to hypercubic lattices, regular grids mimicking atomic arrangements. The team plans future investigations exploring whether similar principles apply in systems with disorder or long-range interactions; this will broaden the scope and applicability of their findings beyond idealized models.

Researchers determined that total momentum dictates when two bound fermions within a Hubbard lattice also exhibit exceptional points, critical states where particle properties change dramatically.

They found that restoring parity-time symmetry occurs alongside these changes when kinetic energy from hops along one direction exceeds transverse maxima on hypercubic lattices. The authors intend to expand this research to explore more complex or disordered systems and broaden the applicability of their findings.

👉 More information
🗞 Kinetic competition controls loss-induced exceptional points of Hubbard pairs
✍️ Ho-Kin Tang (Harbin Institute of Technology); Xiaosen Yang (Jiangsu University)
🧠 ArXiv: https://arxiv.org/abs/2610.32123

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