Principle of Maximum Entanglement Entropy and Local Physics of Strongly Correlated Materials

We argue that, because of quantum entanglement, the local physics of strongly correlated materials at zero temperature is described in a very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number of local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits and present numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller approximation that strongly support our theory in general.

Figure 1

Upper panel: quasiparticle renormalization weights of FeSe. The normal-metal phase (small $U$) and the Janus phase (large $U$) are indicatively separated by a vertical shaded line. Lower panel: PMEE trace distances ${\mathrm{\Delta }}_n$ for the reduced density matrix ${\rho }_d$ of FeSe. The series shown in the insets correspond to $U=0.5\mathrm{eV}$, $U=2\mathrm{eV}$, and $U=4\mathrm{eV}$. All the calculations are performed at fixed $J/U=0.224$.

Figure 2

Local configuration probabilities $P_E$ of the eigenstates of ${\widehat{\mathcal{H}}}^{\mathrm{loc}}$ of FeSe, in the sectors $N=5,6,7$, for $U=0.5\mathrm{eV}$, $U=2\mathrm{eV}$, and $U=4\mathrm{eV}$ at fixed $J/U=0.224$. The GA configuration probabilities (red line) are shown in comparison with the local configuration probabilities evaluated by using the PMEE density matrices corresponding to the distances ${\mathrm{\Delta }}_2$ and ${\mathrm{\Delta }}_3$. Within each $N$ sector, the configuration probabilities $P_E$ are sorted in ascending order of energy $E\equiv ⟨{\psi }_E|{\widehat{\mathcal{H}}}^{\mathrm{loc}}|{\psi }_E⟩$, where $|{\psi }_E⟩$ are the eigenstates of ${\widehat{\mathcal{H}}}^{\mathrm{loc}}$.