Pseudogap, van Hove singularity, maximum in entropy, and specific heat for hole-doped Mott insulators

The first indication of a pseudogap in cuprates came from a sudden decrease of the NMR Knight shift at a doping-dependent temperature $T^{*}\left(\delta \right)$. Since then, experiments have found phase transitions at a lower $T_{\text{phase}}^{*}\left(\delta \right)$. Using plaquette cellular dynamical mean field for the square-lattice Hubbard model at high temperature, where the results are reliable, we show that $T^{*}\left(\delta \right)$ shares many features of $T_{\text{phase}}^{*}\left(\delta \right)$. The remarkable agreement with several experiments, including quantum critical behavior of the electronic specific heat, supports the view that the pseudogap is controlled by a finite-doping extension of the Mott transition. We propose further experimental tests.

Figure 1

For a given value of $U$ at $t^{\prime }=0$ (left) or finite $t^{\prime }$ at $U=9$ (right), the pseudogap $T^{*}$ line is represented by a solid line, the van Hove line by a dashed line, and the zone of maximum entropy by a solid rectangle. The arrows indicate the positions of the van Hove singularities in the noninteracting case for different $t^{\prime }$. Severe sign problems sometimes occurred at low temperature or large doping, especially for $U=36$. The blue temperature axis was obtained from $t\simeq 350$ meV.

Figure 2

Specific heat divided by temperature as a function of temperature for different dopings at $U=9, t^{\prime }=0$ (left) and $U=9, t^{\prime }=-0.3$ (right). After extracting the total energy of the system and fitting it as $E_{\text{tot}}=a+b{T}^{2}lnT+c{T}^2$, the specific heat is extracted as its derivative with respect to temperature, yielding $C/T=2blnT+(b+2c)$. The solid lines are guides to the eye. The temperature in degrees Kelvin and specific heat axes (in blue) were generated using $t\simeq 350$ meV.