Superconductivity from repulsion in the doped 2D electronic Hubbard model: an entanglement perspective

We employ the momentum space entanglement renormalization group (MERG) scheme developed in references (Mukherjeeet al2021J. High Energy Phys.JHEP04(2021)148; Patra and Lal 2021Phys. Rev.B104144514) for the study of various insulating, superconducting and normal phases of the doped and the undoped 2D Hubbard model on a square lattice found recently by us (Mukherjee and Lal 2020New J. Phys.22063007; Mukherjee and Lal 2020New J. Phys.22063008). At each MERG step, disentanglement of particular degrees of freedom, transforms the tensor network representation of the many-particle states. The MERG reveals distinct holographic entanglement features for the normal metallic, topologically ordered insulating quantum liquid and Neél antiferromagnetic symmetry-broken ground states of the 2D Hubbard model at half-filling, clarifying the essence of the entanglement phase transitions that separates the three phases. An MERG analysis of the quantum critical point of the hole-doped 2D Hubbard model reveals the evolution of the many-particle entanglement of the quantum liquid ground state with hole-doping, as well as how the collapse of Mottness is concomitant with the emergence of d-wave superconductivity.