Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal

Abstract

The phenomenon of Mott insulation involves the localization of itinerant electrons due to strong local repulsion. Upon doping, a pseudogap (PG) phase emerges - marked by selective gapping of the Fermi surface without conventional symmetry breaking in spin or charge channels. A key challenge is understanding how quasiparticle breakdown in the Fermi liquid gives rise to this enigmatic state, and how it connects to both the Mott insulating and superconducting phases. Here, we develop a renormalization-based construction of strongly correlated lattice models that captures the emergence of the pseudogap phase and its transition to a Mott insulator. Applying a many-body tiling scheme to the fixed-point impurity model uncovers a lattice model with electron interactions and Kondo physics. At half-filling, the interplay between Kondo screening and bath charge fluctuations in the impurity model leads to Fermi liquid breakdown. This reveals a pseudogap phase characterized by a non-Fermi liquid (the Mott metal) residing on nodal arcs, gapped antinodal regions of the Fermi surface, and an anomalous scaling of the electronic scattering rate with frequency. The eventual confinement of holon-doublon excitations of this exotic metal obtains a continuous transition into the Mott insulator. Our results identify the pseudogap as a distinct long-range entangled quantum phase, and offer a new route to Mott criticality beyond the paradigm of local quantum criticality.

Figures (12)

• Figure 1: Schematic representation of (a): flowchart of theoretical framework adopted by us (see main text for explanation of symbols), (b): phases obtained for the extended Hubbard model in two dimensions at $T=0$, and passage between them.
• Figure 2: (a): Phase diagram of impurity model at strong coupling in $U$ in terms of competing dimensionless Kondo ($J/t$) and bath correlation ($W/t$) couplings. Colourbar represents the fraction of states on the Fermi surface replaced by zeros of the Greens function (Luttinger surface). A pseudogap phase (shaded region) is observed between the local Fermi liquid (red region) and local moment (blue region) phases (b): $k$-space-resolved spin-spin correlation $\chi_s(d,{\bf k}) = \braket{{\bf S}_d\cdot{\bf S}_{\bf k}}$ in the pseudogap phase of the impurity model. Antinodal regions are observed to decouple from Kondo screening of the impurity. (c): Upon tiling, this leads to a $k$-space-resolved antinodal gap in the electronic density of states of the lattice model, corresponding to Luttinger surfaces of zeros. (d)-(f): Initiation of the decoupling of $J_{{\bf k}, {\bf k'}}$ (positive, negative and zeros shown in red, blue and white respectively), with ${\bf k}$ (black circle) at low-energies for ${\bf k}$ corresponding to the node, antinode and a point mid-way between them on the top right arm of the FS respectively with tuning $W/J$. As dictated by the symmetry of $J_{{\bf k}, {\bf k'}}$, the decoupling for a given ${\bf k}$ proceeds via the appearance of zeros (white patches) of $J_{{\bf k}, {\bf k'}}$ for ${\bf k'}$ initially on the nodal regions of adjacent arms, and progresses gradually towards the antinodes. The decoupling ends with the onset of the pseudogap.
• Figure 3: (a): Enhanced charge correlations $\chi_c({\bf k}_1, {\bf k}_2) = \braket{c^\dagger_{{\bf k}_1\uparrow}c^\dagger_{{\bf k}_1\downarrow}c_{{\bf k}_2\downarrow}c_{{\bf k}_2\uparrow} + \text{h.c.}}$ between the nodal and antinodal regions, signalling Kondo breakdown in the pseudogap phase of the impurity model. (b): In turn, the breakdown leads to the gapping of the antinodal regions in the lattice model, seen from the appearance of poles in the imaginary part of the self-energy. (c): The imaginary part of the impurity self-energy $\Sigma^{\prime\prime}(\omega >0)$ possesses a pole at non-zero $\omega$ in the PG that moves towards $\omega=0$ as the Mott transition is approached.
• Figure 4: (a): Suppression of quasiparticle residue ($Z_\text{imp}$) as the impurity model is tuned towards the Mott transition. An initial drastic fall in $Z_\text{imp}$ is observed for $W/J \lesssim (W/J)_\text{PG}$ from $0.3$ to around $0.05$, signalling the destruction of the FL with unravelling of Kondo screening. A steady decrease in $Z_{imp}$ is observed in passage through the PG, and is vanishingly small close to the Mott transition due to a divergent self-energy. (b): Growth of unscreened impurity magnetic moment in the pseudogap phase, signalling the breakdown of Kondo screening. (c): The central (Kondo) resonance of the impurity spectral function in the Fermi liquid phase splits into a pseudogap in the PG phase, with its height diminishing rapidly as the Mott transition is approached.
• Figure 5: (a): Imaginary part of impurity self-energy $\Sigma^{\prime\prime}(\omega)$ as a function of frequency $\omega$ for Fermi liquid (FL, $|W/J| < 1.79$) and pseudogapped phases (NFL, $|W/J| \geq 1.79$). $\Sigma"(\omega)$ falls to zero as $\omega\to 0$ for the FL, while it attains a peak in the pseudogap. All $\Sigma"(\omega)$ for the NFL are observed to lie above the Mott-Ioffe-Regel (MIR) bound (dashed blue line), while those for the FL lie below. (b): Scaling of $\Sigma^{\prime\prime}(\omega)$ with frequency for Fermi liquid and pseudogapped phases. The FL self-energy fits to $\Sigma^{\prime\prime} \sim \omega^{\alpha}$ with $\alpha\approx 2$, vanishing as $\omega\to 0$, while the NFL self-energy grows as $\Sigma^{\prime\prime} \approx a + b\omega^{\beta}$ for small $\omega$, with $\beta\approx 2$. Remarkably, the NFL exponent remains mostly unchanged through the entirety of the PG phase. (c): Variation of the zero-frequency imaginary self-energy $-\Sigma"(\omega=0)$ with $\omega$ in the FL and pseudogap phases (entry into the PG is marked by the vertical dashed line). The inset shows the same but in linear scale, in order to display the dramatic rise (by almost 30 times) on entering the PG.