Understanding the nature of collective charge dynamics in the Coulomb gap phase is essential for revealing the existence of many-body localization. However, the corresponding many-particle excitation spectra remain poorly understood. Here, we present a comprehensive investigation of [Formula: see text]Al and [Formula: see text]Cu nuclear magnetic/quadrupole resonance (NMR/NQR), along with specific heat ([Formula: see text]) measurements, in the p-type semiconductor CuAlO[Formula: see text]. Our study unveils distinct changes in charge dynamics at two crossover temperature scales which separate three regimes associated with Anderson localization of charge carriers: thermally activated transport ([Formula: see text] K) → Mott variable-range hopping (VRH) → Efros–Shklovskii (ES) VRH with Coulomb gap formation ([Formula: see text] K). In the ES VRH regime, we observe a striking divergence in the zero-field [Formula: see text]Cu spin-lattice relaxation rate, [Formula: see text], which is strongly suppressed by an applied magnetic field, indicative of quantum critical charge fluctuations. This is further supported by a distinct magnetic field-dependence of [Formula: see text] deep within the Coulomb gap phase. Taken together, these results provide compelling evidence for the emergence of strong, gapless collective charge fluctuations within the Anderson insulating phase where single-particle excitations are gapped.
Interplay of electron correlation and randomness is studied by using the Anderson-Hubbard model within the Hartree-Fock approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions, which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator) and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in one dimension (1D) or even faster in two dimensions (2D) and three dimensions (3D) toward the Fermi energy. We call it soft Hubbard gap. Moreover, exact-diagonalization results in 1D support the formation of the soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to a conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, based on a picture of multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the scaling of Efros and Shklovskii. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results of SrRu_{1-x}Ti_xO_3.
We study electronic transport in Anderson insulators with strong Coulomb interactions in dimensions d>=2. Close to the metal insulator transition where the single particle localization length is much larger than interparticle-distance, the interactions lead to a strongly correlated quantum glass phase. Even though single particle excitations are localized and the system is insulating, there are collective electronic modes which remain delocalized down to parametrically small energies. These collective excitations serve as a continuous bath which can provide the activation energy for variable range hopping transport. This circumvents the energy conservation problem arising when only discrete particle-hole excitations are present. In contrast to the weak and material-dependent phonon-assisted hopping mechanism, the activation by an electronic bath leads to a nearly universal prefactor e^2/h of the Efros-Shklovskii conductance, as is observed in many recent experiments.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a
T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-
Tc cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
An exact study of charge-spin separation, pairing fluctuations, and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature
(T), magnetic field
(h), on-site interaction
(U), and chemical potential $(\ensuremath{\mu})$. Our results, near the average number of electrons $⟨N⟩\ensuremath{\approx}3$, strongly suggest the existence of a critical parameter
Uc(T) for the localization of electrons and a particle-hole binding (positive) gap ${\ensuremath{\Delta}}^{e\text{\ensuremath{-}}h}(T)>0$ at
U>Uc(T), with a zero temperature critical value,
Uc(0)=4.584. For
U<Uc(T), the particle-particle pair binding is found with a (positive) pairing gap ${\ensuremath{\Delta}}^{P}(T)>0$. The ground state degeneracy is lifted at
U>Uc(T) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers $(1\ensuremath{\le}N\ensuremath{\le}8)$ of electrons. In contrast, for $U\ensuremath{\le}{U}_{c}(T)$, we find an electron pair binding instability at finite temperature near $⟨N⟩\ensuremath{\approx}3$, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin pairing, (spin) pseudogap, and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich
(⟨N⟩=2), hole-poor
(⟨N⟩=4), and magnetic
(⟨N⟩=3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high-
Tc cuprates.
We study the tunneling density of states (TDOS) of a disordered electronic system with Coulomb interaction on the insulating side of the Anderson localization transition. The average TDOS shows a critical behavior at high energies, with a crossover to a soft Coulomb gap $\ensuremath{\Delta}$ at low energies. We demonstrate that the single-particle excitations experience a localization transition (which belongs to the noninteracting universality class) at an energy $E=\ifmmode\pm\else\textpm\fi{}{E}_{c}$. The mobility edge
Ec scales with the distance ${\ensuremath{\mu}}_{c}\ensuremath{-}\ensuremath{\mu}$ from the interacting critical point according to ${E}_{c}\ensuremath{\propto}{({\ensuremath{\mu}}_{c}\ensuremath{-}\ensuremath{\mu})}^{\ensuremath{\nu}z}$, where $\ensuremath{\nu}$ and
z are the localization-length and the dynamical critical exponents. Local TDOS shows strong fluctuations and long-range correlations which reflect the multifractality associated with interacting and noninteracting fixed points as well the localization of low-energy excitations.