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arXiv:2608.21029

Doping-driven Mott transition from steady-state density functional theory

David Jacob, Stefan Kurth

Published Aug 21, 2026• 0 citations
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Abstract

We describe the doping-driven Mott transition in the Hubbard model within the framework of steady-state density functional theory, or i-DFT. In order to access the many-body spectral function in i-DFT, an approximation to the exchange-correlation (xc) bias at arbitrary density and current is required. By making use of Fermi-liquid theory, we derive conditions on the xc bias of i-DFT in terms of the quasiparticle weight, thus establishing a clear connection between i-DFT and Fermi-liquid theory. The Fermi liquid conditions are then employed to guide the construction of an approximation to the xc bias functional. Numerical results obtained with this functional demonstrate that the doping-driven Mott transition can indeed be captured with i-DFT. More generally, our i-DFT approach to calculate spectral functions establishes an explicit form for the functional relationship between the many-body spectral function and the ground state electronic density.

DOI
10.48550/arxiv.2608.21029

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We describe the doping-driven Mott transition in the Hubbard model within the framework of steady-state density functional theory, or i-DFT. In order to access the many-body spectral function in i-DFT, an approximation to the exchange-correlation (xc) bias at arbitrary density and current is required. By making use of Fermi-liquid theory, we derive conditions on the xc bias of i-DFT in terms of the quasiparticle weight, thus establishing a clear connection between i-DFT and Fermi-liquid theory. The Fermi liquid conditions are then employed to guide the construction of an approximation to the xc bias functional. Numerical results obtained with this functional demonstrate that the doping-driven Mott transition can indeed be captured with i-DFT. More generally, our i-DFT approach to calculate spectral functions establishes an explicit form for the functional relationship between the many-body spectral function and the ground state electronic density.
We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.
The Mott transition is usually considered as resulting from the divergence of the effective mass of the quasiparticle in the Fermi-liquid theory; the dispersion relation around the Fermi level is considered to become flat toward the Mott transition. Here, to clarify the characterization of the Mott transition under the assumption of a Fermi-liquid-like ground state, the electron-addition excitation from the Gutzwiller wavefunction in the $t\text{\ensuremath{-}}J$ model is investigated on a chain, ladder, square lattice, and bilayer square lattice in the single-mode approximation using a Monte Carlo method. The numerical results demonstrate that an electronic mode that is continuously deformed from a noninteracting band at zero electron density loses its spectral weight and gradually disappears toward the Mott transition. It exhibits essentially the magnetic dispersion relation shifted by the Fermi momentum in the small-doping limit as indicated by recent studies for the Hubbard and $t\text{\ensuremath{-}}J$ models, even if the ground state is assumed to be a Fermi-liquid-like state exhibiting gradual disappearance of the quasiparticle weight. This implies that, rather than as the divergence of the effective mass or disappearance of the carrier density that is expected in conventional single-particle pictures, the Mott transition can be better understood as freezing of the charge degrees of freedom while the spin degrees of freedom remain active, even if the ground state is like a Fermi liquid.
We consider a doped Mott insulator in the large dimensionality limit within both the recently developed extremely correlated Fermi liquid (ECFL) theory and the dynamical mean-field theory (DMFT). We show that the general structure of the ECFL sheds light on the rich frequency dependence of the DMFT self-energy. Using the leading Fermi liquid form of the two key auxiliary functions introduced in the ECFL theory, we obtain an analytical ansatz, which provides a good quantitative description of the DMFT self-energy down to hole doping level $\ensuremath{\delta}\ensuremath{\simeq}0.2$. In particular, the deviation from Fermi liquid behavior and the corresponding particle-hole asymmetry developing at a low-energy scale are well reproduced by this ansatz. The DMFT being exact at large dimensionality, our study also provides a benchmark of the ECFL in this limit. We find that the main features of the self-energy and spectral line shape are well reproduced by the ECFL calculations in the $O({\ensuremath{\lambda}}^{2})$ minimal scheme, for not too low doping level $\ensuremath{\delta}\ensuremath{\gtrsim}0.3$. The DMFT calculations reported here are performed using a state-of-the-art numerical renormalization-group impurity solver, which yields accurate results down to an unprecedentedly small doping level $\ensuremath{\delta}\ensuremath{\lesssim}0.001$.
In this paper we investigate the zero-temperature doping-driven evolution of a superconductor toward the Mott insulator in a two-dimensional electron model, relevant for high-temperature superconductivity. To this purpose we use a cluster extension of dynamical mean-field theory. Our results show that a standard ddd-wave superconductor, realized at high doping, is driven into the Mott insulator via an intermediate superconducting state displaying unconventional physical properties. By restoring the translational invariance of the lattice, we give an interpretation of these findings in momentum space. In particular, we show that at a finite doping a strong momentum-space differentiation takes place: non-Fermi liquid and insulatinglike (pseudogap) characters rise in some regions (antinodes), while Fermi liquid quasiparticles survive in other regions (nodes) of momentum space. We describe the consequence of these happenings on the spectral properties, stressing in particular the behavior of the superconducting gap, which reveals two distinct nodal and antinodal energy scales as a function of doping, detected in photoemission and Raman spectroscopy experiments. We study and compare with experimental results the doping-dependent behavior of other physical quantities, such as for instance, the nodal quasiparticle velocity (extracted in angle-resolved photoemission) and the low-energy slopes of the local density of states and of the Raman scattering response. We then propose a description of the evolution of the electronic structure while approaching the Mott transition. We show that, within our formalism, a strong asymmetry naturally arises in the local density of states, measured in scanning tunneling spectroscopy. We investigate in detail the doping evolution of the electronic bands, focusing on the kinklike quasiparticle dispersion observed with angle-resolved photoemission in specific cuts of the momentum-energy space. We finally show the consequences of the properties presented above in the doping dependence of the Hall resistivity, measured in magnetotransport experiments.
Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple excitations, for example, can be easily taken into account in an ensemble), eDFT is not standard, which is essentially due to the lack of reliable approximate exchange-correlation (xcxcxc) functionals for ensembles. Following Smith et al. [Phys. Rev. B 93, 245131 (2016)], we propose in this work to construct an exact eDFT for the nontrivial asymmetric Hubbard dimer, thus providing more insight into the weight dependence of the ensemble xcxcxc energy in various correlation regimes. For that purpose, an exact analytical expression for the weight-dependent ensemble exchange energy has been derived. The complementary exact ensemble correlation energy has been computed by means of Legendre-Fenchel transforms. Interesting features like discontinuities in the ensemble xcxcxc potential in the strongly correlated limit have been rationalized by means of a generalized adiabatic connection formalism. Finally, functional-driven errors induced by ground-state density-functional approximations have been studied. In the strictly symmetric case or in the weakly correlated regime, combining ensemble exact exchange with ground-state correlation functionals gives better ensemble energies than when calculated with the ground-state exchange-correlation functional. However, when approaching the asymmetric equiensemble in the strongly correlated regime, the former approximation leads to highly curved ensemble energies with negative slope which is unphysical. Using both ground-state exchange and correlation functionals gives much better results in that case. In fact, exact ensemble energies are almost recovered in some density domains. The analysis of density-driven errors is left for future work.
We establish that a doping-driven first-order metal-to-metal transition, from a pseudogap metal to Fermi Liquid, can occur in correlated quantum materials. Our result is based on the exact Dynamical Mean Field Theory solution of the Dimer Hubbard Model. This transition elucidates the origin of many exotic features in doped Mott materials, like the pseudogap in cuprates, incoherent bad metals, enhanced compressibility and orbital selective Mott transition. This phenomenon is suggestive to be at the roots of the many exotic phases appearing in the phase diagram of correlated materials.