Diagrammatic Monte Carlo for Fermions with Spin-Dependent Hopping Anisotropy

We study attractively interacting fermions on a square lattice whose Fermi surfaces exhibit a spin-dependent anisotropy. Such a system was proposed to harbor several exotic phases, most notably a Cooper-pair Bose-metal featuring a gap for fermionic excitations but gapless, uncondensed pair excitations along a Bose surface in momentum space. We present unbiased numeric results obtained with Diagrammatic Monte Carlo, a new technique for correlated fermionic systems based on sampling Feynman diagrammatic series directly in the thermodynamic limit. For the relevant regime of intermediate coupling strength our data show that the Fermi surface mismatch indeed suppresses the BCS transition to superfluidity. At strong anisotropy we find no sign of an ordering transition down to very low temperature suggesting existence of a quantum-phase transition from the conventional superconductor to an uncondensed state driven by the Fermi surface anisotropy.