Hybridization fluctuations in the half-filled periodic Anderson model

Motivated by recent photoemission and pump-probe experiments, we report determinant quantum Monte Carlo simulations of hybridization fluctuations in the half-filled periodic Anderson model. A tentative phase diagram is constructed based solely on hybridization fluctuation spectra and reveals a crossover regime between an unhybridized selective Mott state and a fully hybridized Kondo insulating state. This intermediate phase exhibits quantum hybridization fluctuations and consequentially the so-called “band bending” and a direct hybridization gap as observed in angle-resolved photoemission spectroscopy and optical conductivity. This connects the band bending with the hybridization fluctuations as proposed in a recent ultrafast optical pump-probe experiment. The Kondo insulating state is only established at lower temperatures with the development of sufficiently strong intersite hybridization correlations. Our work suggests a unified picture for interpreting recent photoemission, pump-probe, and optical observations and provides numerical evidences for the importance of hybridization fluctuations in heavy fermion physics.

Figure 1

The real and imaginary parts of the hybridization correlation function $L_{\mathbf{0}}\left(\omega \right)$ with the bare hybridization parameter $V$ and temperature $T$. The insets are enlarged plots of the imaginary part around $\omega =0$, showing the variation of the low-energy slope in $Im{L}_{\mathbf{0}}\left(\omega \right)$ with different parameters.

Figure 2

(a),(b) Comparison of the different features of the real and imaginary parts of $L_{\mathbf{0}}\left(\omega \right)$ in four distinct regimes. (c) The corresponding $f$ electron local density of states. The parameters are $T=2.0, V=0.5$ for regime I; $T=0.6, V=0.25$ for regime II; $T=0.2, V=1.2$ for regime III; and $T=0.05, V=2.0$ for regime IV. (d) Intensity plots of the fermionic spectral function at the Fermi energy in the Brillouin zone evolving with temperature for fixed $V=1.0$; (e) The corresponding plots of the dispersion along a chosen path in the Brillouin zone, showing its evolution across the intermediate regime III.

Figure 3

(a) Comparison of the local and nonlocal contributions to $Re{L}_{\mathbf{0}}\left(\omega \right)$, showing the onset of nonlocal term in regime III and development in regime IV. (b) The normalized hybridization spectral function ${\tilde{A}}_{\mathbf{q}}\left(\omega \right)$, showing the growth of hybridization correlations at $(\pi ,\pi )$. The parameters are the same as in Fig. 2.

Figure 4

A tentative phase diagram constructed based solely on $L_{\mathbf{0}}\left(\omega \right)$. The background colors reflect the low-energy slope $K$ of its imaginary part. The points are estimated from the different features of its real part and the lines are a guide to the eye. The vertical axis at $V=0$ should always belong to regime II at all temperatures, where the $f$ electrons are well localized with two separated Hubbard peaks in their local density of states. The boundary between regimes I and II at small $V$ should in principle extend along the vertical line. From the view of the bubble diagram, one may also consider to multiply a prefactor $V^2$ for the hybridization correlations. The right panel plots the values of $K$ for $V=1.0$, whose nonmonotonic temperature dependence clearly demonstrates the separation of four regimes.