Mott physics and the Hubbard model ground state

5 problems

• Universality class of the Mott critical endpoint in organic conductors

  Contested

  Squeezing certain organic salts turns them from Mott insulators into metals through a jump, like liquid turning into gas, that ends at a critical point; the measured critical exponents disagree with the liquid-gas prediction.

• Origin of the Hubbard-model pseudogap at cuprate-like coupling strength

  Partially resolved

  At weak repulsion, computer studies trace the Hubbard model pseudogap to long-range magnetic fluctuations; whether the same holds at the strong repulsion relevant to cuprates is unsettled.

• Does the pure square-lattice Hubbard model superconduct at moderate doping

  Partially resolved

  With only nearest-neighbor hopping, the most accurate computer methods find stripes of charge and spin instead of superconductivity, but competing states lie very close in energy.

• Superconductivity in the Hubbard model with next-nearest-neighbor hopping

  Contested

  Adding a small diagonal hopping t', as in real cuprates, appears to tilt the balance toward superconductivity when electrons are removed.

• Nature of the intermediate phase of the triangular-lattice Hubbard model

  Contested

  On a triangular lattice, between the metal at weak repulsion and the magnet at strong repulsion, there may be a quantum spin liquid, a state in which spins keep fluctuating at zero temperature.