Broken Luttinger theorem in the two dimensional Fermi Hubbard model

We study the validity of Luttinger's theorem in the two dimensional repulsive Fermi Hubbard model, the parent Hamiltonian for cuprate superconductors, as a function of doping. Using Determinant Quantum Monte Carlo (DQMC) simulations, we compute the single-particle spectral functions and study the Fermi surface of the interacting system. As one approaches the Mott insulating limit, there is a critical doping where the Fermi surface shows a deviation from the Luttinger's volume even in absence of any other broken symmetry. We also conduct a parton mean-field construction (in presence of double occupancies and holes) starting from an effective low-energy Hamiltonian in the large interaction limit, and calculate the Fermi surface of the low-energy Hamiltonian. Our study is also supplemented by the calculation of different transport quantities, like DC Hall coefficient and Seebeck coefficient that capture this phenomenon.