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Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states in multiband lattices

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By considering an on-site attraction between a spin-up arrow and a spin-down arrow fermion in a multiband tight-binding lattice, here we study the two-body spectrum and derive an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states. In addition to the intraband (or the so-called conventional) contribution that depends only on the single-particle spectrum and the interband (or the so-called geometric) contribution that is controlled by the quantum metric, our generalized relation has an additional interband contribution that depends on the so-called band-resolved quantum metric. All of our analytical expressions are applicable to those multiband lattices that simultaneously exhibit time-reversal symmetry and fulfill the condition on spatially uniform pairing. As a nontrivial illustration we analyze the two body problem in a Kagome lattice with nearest-neighbor hoppings, and we show that the exact relation provides a perfect benchmark.

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American Physical Society (APS)

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Optics, Physics, atomic, molecular and chemical

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Physical Review A

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10.1103/PhysRevA.105.023312

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