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arXiv:1506.06145 · Journal of Physics Condensed Matter

Reliability of the one-crossing approximation in describing the Mott transition

Verónica Laura Vildosola, Leonid V. Pourovskii, L. O. Manuel, P. Roura-Bas

Published Nov 13, 2015• 8 citations
arXivHTMLPDF

Abstract

We assess the reliability of the one-crossing approximation (OCA) approach in a quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds and nanoscale systems. However, several recent studies in the framework of impurity models pointed out serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behaviour is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations of the system away from the particle-hole symmetric case are also presented and discussed.

DOI
10.1088/0953-8984/27/48/485602

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We assess the reliability of the one-crossing approximation (OCA) approach in a quantitative description of the Mott transition in the framework of the dynamical mean field theory (DMFT). The OCA approach has been applied in conjunction with DMFT to a number of heavy-fermion, actinide, transition metal compounds and nanoscale systems. However, several recent studies in the framework of impurity models pointed out serious deficiencies of OCA and raised questions regarding its reliability. Here we consider a single band Hubbard model on the Bethe lattice at finite temperatures and compare the results of OCA to those of a numerically exact quantum Monte Carlo (QMC) method. The temperature-local repulsion U phase diagram for the particle-hole symmetric case obtained by OCA is in good agreement with that of QMC, with the metal-insulator transition captured very well. We find, however, that the insulator to metal transition is shifted to higher values of U and, simultaneously, correlations in the metallic phase are significantly overestimated. This counter-intuitive behaviour is due to simultaneous underestimations of the Kondo scale in the metallic phase and the size of the insulating gap. We trace the underestimation of the insulating gap to that of the second moment of the high-frequency expansion of the impurity spectral density. Calculations of the system away from the particle-hole symmetric case are also presented and discussed.
The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.
We present clear numerical evidence for the coexistence of metallic and insulating dynamical mean-field theory (DMFT) solutions in a half-filled single-band Hubbard model at finite temperature. The quantum Monte Carlo (QMC) method is used to solve the DMFT equation. We discuss important technical aspects of the DMFT-QMC method, which should be properly dealt with in order to obtain reliable DMFT solutions at low temperatures. Among these technical aspects are the critical slowing down near the boundaries of the coexistence region, the convergence criteria for the DMFT iterations, and the correct interpolation of the discretized Green's functions.
We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semimetal and the antiferromagnetic insulator. The aim of this paper is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level, local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations and thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semimetallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point, the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function---waterfall features and narrow spin-polaron bands---is only visible in the lattice QMC approach.
The local moment approach (LMA) has presented itself as a powerful semianalytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low-energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group (NRG) results. However, the most common correlated lattice model, the Hubbard model, has not been explored well within the LMA+DMFT framework beyond the insulating phase. Here in our work, within the framework we complete the filling-interaction phase diagram of the single band Hubbard model at zero temperature. Our formalism is generic to any particle filling and can be extended to finite temperature. We contrast our results with another QIS, namely the iterated perturbation theory (IPT) and show that the second spectral moment sum rule improves better as the Hubbard interaction strength grows stronger in LMA, whereas it severely breaks down after the Mott transition in IPT. For the metallic case, the Fermi liquid (FL) scaling agreement with the NRG spectral density supports the fact that the FL scale emerges from the inherent Kondo physics of the impurity model. We also show that, in the metallic phase, the FL scaling of the spectral density leads to universality which extends to infinite frequency range at infinite correlation strength (strong coupling). At large interaction strength, the off half-filling spectral density forms a pseudogap near the Fermi level and filling-controlled Mott transition occurs as one approaches the half-filling. As a response property, we finally study the zero temperature optical conductivity and find universal features such as absorption peak position governed by the FL scale and a doping independent crossing point, often dubbed the isosbestic point in experiments.
Abstract We propose a minimal effective impurity model that captures the phenomenology of the Mott–Hubbard metal–insulator transition of the half-filled Hubbard model on the Bethe lattice in infinite dimensions as observed by dynamical mean field theory (DMFT). This involves extending the standard Anderson impurity model Hamiltonian to include an explicit Kondo coupling J, as well as a local on-site correlation Ub on the conduction bath site connected directly to the impurity. For the case of attractive local bath correlations ( U b < 0 ), the extended Anderson impurity model (e-SIAM) sheds new light on several aspects of the DMFT phase diagram. For example, the T = 0 metal-to-insulator quantum phase transition (QPT) is preceded by an excited state QPT (ESQPT) where the local moment eigenstates are emergent in the low-lying spectrum. Long-ranged fluctuations are observed near both the QPT and ESQPT, suggesting that they are the origin of the quantum critical scaling observed recently at high temperatures in DMFT simulations. The T = 0 gapless excitations at the quantum critical point display particle-hole interconversion processes, and exhibit power-law behaviour in self-energies and two-particle correlations. These are signatures of non-Fermi liquid behaviour that emerge from the partial breakdown of the Kondo screening.
Wilson's numerical renormalization group method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean-field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real-frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for $T<{T}_{\mathrm{c}}\ensuremath{\approx}0.02W$ (W:(W:(W: bandwidth) we find hysteresis with first-order transitions both at Uc1{U}_{\mathrm{c}1}Uc1​ (defining the insulator to metal transition) and at Uc2{U}_{\mathrm{c}2}Uc2​ (defining the metal to insulator transition), at T>TcT>{T}_{\mathrm{c}}T>Tc​ there is a smooth crossover from metalliclike to insulatinglike solutions.