Low-energy Green's function of the Gutzwiller-projected Kondo lattice: power-law form, exponent, and spectroscopic test of the non-Fermi-liquid heavy Fermi sea

In a sole-author Physical Review Letters paper, P. W. Anderson argued that the Fermi sea of a heavy-electron metal (a Kondo lattice) can never be a Fermi liquid: because adding an f electron to a Gutzwiller-projected ground state often meets an already occupied site while removing one never violates the constraint, the particle- and hole-addition spectral densities $A(\omega)$ and $B(\omega)$ cannot be equal and nonzero at the Fermi level, which would make the real part of the one-particle Green's function logarithmically singular; the only escape is $A(0)=B(0)=0$, i.e. no jump in occupancy and hence no Landau quasiparticle. He conjectured a power-law Green's function $G(\omega)\sim\omega^{-1+\alpha}$ with a small positive exponent $\alpha$, implying a sharp, deep anomaly of the f-electron density of states at the Fermi energy observable in vacuum tunneling, and proposed a 'hidden Fermi liquid' bottleneck to explain Fermi-liquid-like transport. The paper itself left the power-law form as an unproven conjecture, did not determine $\alpha$ for any realistic Kondo-lattice model, and did not compute the projected f-electron Green's function. The later literature is partial: the cuprate-lineage hidden-Fermi-liquid theory derived an exponent only for the projected t-J Fermi sea; numerical work confirmed the projection-induced electron-hole spectral-weight asymmetry but only in the gapped superconducting state; dynamical mean-field theory (DMFT) studies find heavy Fermi liquids with finite quasiparticle weight and reinterpret 'hidden Fermi liquid' phenomenology without projection; scanning-tunneling and THz experiments on CeCoIn5 test quantum-critical scaling and transport rates but not the predicted zero-temperature density-of-states anomaly. The central problem — establish, refute, or determine by controlled derivation or direct calculation the low-energy form and exponent of the projected f-electron Green's function in a realistic Kondo lattice, and detect or bound the corresponding spectral anomaly experimentally, disentangling it from quantum-critical-point effects — remains open.

Background

Heavy-electron (heavy-fermion) metals are intermetallic compounds of Ce, Yb, or U in which localized f-shell electrons behave at high temperature nearly as magnetic moments hybridized with a conduction band, and cross over at low temperature into itinerant states with very large effective masses. The minimal model is the Kondo lattice (equivalently, the periodic Anderson model): a lattice of f orbitals with a large on-site repulsion $U$ hybridized with conduction electrons. Because double occupation of an f shell costs a large $U$, the low energy f Hilbert space has at most one electron per site, and a faithful wave function is written $\Psi=P_G\Phi$ with the Gutzwiller projector $P_G=\prod_i(1-n^f_{i\uparrow}n^f_{i\downarrow})$ acting on a function $\Phi$ in the full Hilbert space — an approach introduced for heavy electrons by Rice and Ueda. The mainstream quantitative description of the coherent heavy Fermi sea is dynamical mean-field theory (DMFT), a method that maps the lattice problem onto a self-consistent quantum impurity problem (exact in infinite dimensions), which for the paramagnetic Kondo lattice finds heavy Landau Fermi-liquid ground states with a finite, exponentially small quasiparticle residue $Z$ (the weight of the coherent quasiparticle pole) and hence a small but finite jump in the momentum distribution at the Fermi surface.

Anderson's 2010 argument (the source of this problem) challenges the Fermi-liquid assumption itself for projected electrons. The one-particle Green's function $G_{ij}(\omega)$ can be written in terms of the densities $A(\omega)$ and $B(\omega)$ of many-body eigenstates reached by adding, respectively removing, an electron from the ground state. In a Landau Fermi liquid, $A(0)=B(0)\neq 0$ (the electron and hole quasiparticle branches are particle-hole conjugates), which is what keeps the real part of $G$ nonsingular at $\omega=0$ and produces a finite jump in occupancy at the Fermi surface. But adding an f electron to a projected state frequently encounters an already occupied site, while a hole never violates the constraint, so $A$ and $B$ are not symmetric. In the 'Gutzwiller approximation' — treating $\Phi$ as an uncorrelated Slater determinant of Bloch waves, with $x$ the fraction of holes relative to one f electron per site — the weights differ by the ratio $A/B=g=2x/(1+x)<1$. If such a ratio persists at $\omega=0$, the dispersion relation for $\mathrm{Re}\,G$ acquires a logarithmic singularity proportional to $1-g$ at the Fermi level, which is inconsistent; the only escape is $A(0)=B(0)=0$, i.e. no Fermi-liquid discontinuity. This is a lattice cousin of the classic x-ray (Fermi) edge singularity problem, in which a suddenly imposed constraint produces power-law Green's functions rather than quasiparticle poles. Anderson therefore conjectured that $\mathrm{Re}\,G$ and $\mathrm{Im}\,G$ have primarily a power-law dependence on $\omega$ at low energy, $G(\omega)\sim\omega^{-1+\alpha}$ with a small but finite positive exponent $\alpha$, turning the $T=0$ axis into a critical line with continuously variable exponents (while preserving Luttinger's theorem — the statement that the volume enclosed by the Fermi surface counts the total number of particles — and the existence of a Fermi surface), and predicted a sharp, deep anomaly of the f-electron density of states at the Fermi energy that 'will appear in vacuum tunneling and many other experiments'. He had earlier proposed the same projection mechanism for the cuprate strange metal ('the strange metal is a projected Fermi liquid with edge singularities', Nature Physics 2006), and a companion 'hidden Fermi liquid' conjecture — that transport can look Fermi-liquid-like because relaxation is bottlenecked inside a hidden, physically inaccessible Fermi liquid — to explain why heavy-electron transport often appears conventional except near quantum critical points (QCPs), i.e. continuous zero-temperature phase transitions reached by tuning field, pressure, or composition, around which non-Fermi-liquid behavior is widespread. Within the paper, the power-law form is explicitly a conjecture reached 'through more complicated and less rigorous reasoning', the direct measurement of the Green's function 'has not yet been carried out for heavy electron materials', the $A/B$ ratio is obtained only in the uncorrelated-$\Phi$ approximation, and residual occupancy correlations in $\Phi$ beyond a simple Slater determinant ('correlation holes') are asserted to modify the numbers but not the structure, and the relation to QCP physics is posed as a question to be cleared up before speculating about QCPs.

Problem Statement

For the paramagnetic heavy-electron (Kondo-lattice) ground state $\Psi=P_G\Phi$ obtained by projecting out double f-occupancy, establish the true low-energy structure of the single-particle f-electron Green's function and test it against experiment. The common objective is to determine whether the heavy Fermi sea is or is not a Fermi liquid, through four jointly supporting, scientifically linked aspects ((i) and (ii) theoretical, (iii) and (iv) experimental or phenomenological): (i) prove, refute, or make precise Anderson's inconsistency argument — that the particle- and hole-addition spectral densities of projected electrons cannot satisfy $A(0)=B(0)\neq 0$, so that the Fermi surface carries no finite jump in occupancy and the Fermi-liquid assumption fails; (ii) derive or directly calculate the conjectured low-energy form of the site-diagonal (on-site) Green's function $G_{ii}(\omega)\sim\omega^{-1+\alpha}$ with a small positive exponent $\alpha$ for realistic Kondo-lattice models — including the role of occupancy correlations ('correlation holes') in $\Phi$ beyond the uncorrelated-$\Phi$ ratio $A/B=g=2x/(1+x)$, with $x$ the fraction of holes relative to one f electron per site — and determine the value of $\alpha$, or show that a quasiparticle jump survives after all; (iii) confront the prediction with experiment, namely whether the sharp, deep low-energy anomaly of the f-electron density of states at the Fermi energy (with the associated absence of a jump in the momentum distribution) appears in vacuum tunneling or other spectroscopies of heavy-electron materials, or is bounded away by them; and (iv) determine whether the observed non-Fermi-liquid transport anomalies of heavy-electron metals arise predominantly from this projection-induced critical line, including the proposed 'hidden Fermi liquid' bottleneck for relaxation processes, or from proximity to a quantum critical point or competing orders. The question concerns the general Kondo lattice or concrete heavy-electron compounds. It may resolve affirmatively (power-law, no jump, with a determinable exponent) or negatively (consistency of a projected Fermi liquid): a negative resolution settles both (i) and (ii) by identifying where the $A/B$ argument fails, whereas an affirmative resolution requires both the argument of (i) and the form and exponent of (ii).

References

1. P. W. Anderson, 'Fermi Sea of Heavy Electrons (a Kondo Lattice) is Never a Fermi Liquid', Phys. Rev. Lett. 104, 176403 (2010). DOI: 10.1103/PhysRevLett.104.176403, https://doi.org/10.1103/PhysRevLett.104.176403; arXiv:0810.0279, https://arxiv.org/abs/0810.0279.
2. P. W. Anderson, 'The strange metal is a projected Fermi liquid with edge singularities', Nature Physics 2, 626-630 (2006). DOI: 10.1038/nphys388, https://doi.org/10.1038/nphys388; arXiv:cond-mat/0512471, https://arxiv.org/abs/cond-mat/0512471.
3. Philip W. Anderson, Philip A. Casey, 'Transport Anomalies of the Strange Metal: Resolution by Hidden Fermi Liquid Theory', Phys. Rev. B 80, 094508 (2009). DOI: 10.1103/PhysRevB.80.094508, https://doi.org/10.1103/PhysRevB.80.094508; arXiv:0903.0794, https://arxiv.org/abs/0903.0794.
4. Philip A. Casey, Philip W. Anderson, 'Hidden Fermi Liquid: Self-Consistent Theory for the Normal State of High-Tc Superconductors', Phys. Rev. Lett. 106, 097002 (2011). DOI: 10.1103/PhysRevLett.106.097002, https://doi.org/10.1103/PhysRevLett.106.097002; arXiv:1101.3609, https://arxiv.org/abs/1101.3609.
5. Samuel Bieri, Dmitri Ivanov, 'Quasiparticle spectral weights of Gutzwiller-projected high-Tc superconductors', Phys. Rev. B 75, 035104 (2007). DOI: 10.1103/PhysRevB.75.035104, https://doi.org/10.1103/PhysRevB.75.035104; arXiv:cond-mat/0608047, https://arxiv.org/abs/cond-mat/0608047.
6. Wenhu Xu, K. Haule, G. Kotliar, 'Hidden Fermi liquid, scattering rate saturation, and Nernst effect: a dynamical mean-field theory perspective', Phys. Rev. Lett. 111, 036401 (2013). DOI: 10.1103/PhysRevLett.111.036401, https://doi.org/10.1103/PhysRevLett.111.036401; arXiv:1304.7486, https://arxiv.org/abs/1304.7486.
7. Pegor Aynajian, Eduardo H. da Silva Neto, Andras Gyenis, Ryan E. Baumbach, J. D. Thompson, Zachary Fisk, Eric D. Bauer, Ali Yazdani, 'Visualizing heavy fermions emerging in a quantum critical Kondo lattice', Nature 486, 201-206 (2012). DOI: 10.1038/nature11204, https://doi.org/10.1038/nature11204; arXiv:1206.3145, https://arxiv.org/abs/1206.3145.
8. L. Y. Shi, Zhenisbek Tagay, Jiahao Liang, Khoan Duong, Yi Wu, F. Ronning, Darrell G. Schlom, K. M. Shen, N. P. Armitage, 'Low-energy electrodynamics and a hidden Fermi liquid in the heavy-fermion compound CeCoIn5', Phys. Rev. B 111, 165113 (2025). DOI: 10.1103/PhysRevB.111.165113, https://doi.org/10.1103/PhysRevB.111.165113; arXiv:2310.10916, https://arxiv.org/abs/2310.10916.
9. J. Wang, Z. Tagay, L. Shi, J. Liang, N. K. Duong, Y. Wu, P. M. T. Vianez, F. Ronning, D. G. Rickel, D. G. Schlom, K. M. Shen, S. A. Crooker, N. P. Armitage, 'Reconciling strange metal transport in CeCoIn5 through the difference of optical and cyclotron effective masses', arXiv:2603.23740 (2026). arXiv: 2603.23740, https://arxiv.org/abs/2603.23740.
10. Piers Coleman, 'Phil Anderson's Magnetic Ideas in Science', in PWA90: A Lifetime of Emergence (World Scientific, 2016), pp. 187-213. DOI: 10.1142/9789814733632_0017, https://doi.org/10.1142/9789814733632_0017; arXiv:1605.06993, https://arxiv.org/abs/1605.06993.
11. M. S. Laad, S. Koley, A. Taraphder, 'Quantum Critical Phase and Lifshitz Transition in an Extended Periodic Anderson Model', J. Phys.: Condens. Matter 24, 232201 (2012). DOI: 10.1088/0953-8984/24/23/232201, https://doi.org/10.1088/0953-8984/24/23/232201; arXiv:1011.5303, https://arxiv.org/abs/1011.5303.
12. P. Wölfle, Y. Dubi, A. V. Balatsky, 'Tunneling into Clean Heavy Fermion Compounds: Origin of the Fano Line Shape', Phys. Rev. Lett. 105, 246401 (2010). DOI: 10.1103/PhysRevLett.105.246401, https://doi.org/10.1103/PhysRevLett.105.246401; arXiv:1008.4923, https://arxiv.org/abs/1008.4923.
13. Antoine Georges, Gabriel Kotliar, Werner Krauth, Marcelo J. Rozenberg, 'Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions', Rev. Mod. Phys. 68, 13-125 (1996). DOI: 10.1103/RevModPhys.68.13, https://doi.org/10.1103/RevModPhys.68.13.
14. T. M. Rice, K. Ueda, 'Gutzwiller method for heavy electrons', Phys. Rev. B 34, 6420-6427 (1986). DOI: 10.1103/PhysRevB.34.6420, https://doi.org/10.1103/PhysRevB.34.6420.
15. P. W. Anderson, 'Personal history of my engagement with cuprate superconductivity, 1986-2010', Int. J. Mod. Phys. B 25, 1-39 (2011). DOI: 10.1142/S0217979211057013, https://doi.org/10.1142/S0217979211057013; arXiv:1011.2736, https://arxiv.org/abs/1011.2736.