A metal conducts because its electrons form a Fermi liquid — a gas of quasiparticles that move freely through the lattice. A Mott insulator doesn't conduct because the electron-electron repulsion is strong enough to localize each electron on its own lattice site, freezing the charge flow. Between these two limits lies the bad metal: a state that conducts, but poorly, with transport properties that violate the standard theory of metals without quite reaching the insulating regime.
Lu, Song, Deng, and He (arXiv 2602.22705, February 2026) map this crossover using auxiliary-field quantum Monte Carlo simulations of the half-filled square-lattice Hubbard model — the simplest model that captures the competition between kinetic energy (which favors delocalization) and on-site repulsion (which favors localization). No mean-field approximations, no truncations, no ansatze — the simulations are numerically exact for the finite-size systems studied.
The crossover is gradual, not sharp. No phase transition separates the Fermi liquid from the Mott insulator at finite temperature. Instead, the bad-metal regime extends across a wide range of interaction strengths, with the spectral function — the energy-resolved probability density for finding an electron at a given momentum — degrading continuously. The quasiparticle peaks that define the Fermi liquid broaden and lose weight. The insulating gap that defines the Mott state hasn't yet opened. The spectral function is neither peaked nor gapped — it's diffuse.
The momentum-space structure is anisotropic. Along the (π,0) direction, the spectral function degrades faster than along the (π/2,π/2) direction. The Fermi surface doesn't dissolve uniformly — it erodes from specific points in momentum space, with some regions retaining their metallicity while others are already insulating. The bad metal is not a homogeneous degradation but a spatially structured loss of coherence in momentum space.
The most striking result is Pomeranchuk cooling. In certain parameter regimes, increasing the interaction strength at constant entropy decreases the temperature. Interactions cool the system. The mechanism is entropic: the Mott insulator has a large spin entropy (each localized electron can point up or down independently), and approaching the Mott state redistributes entropy from charge to spin degrees of freedom, lowering the temperature required to maintain the same total entropy.
Stronger correlations produce a colder system. The electron interactions don't just localize charge — they absorb heat.