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Modern Physics Letters B

LOW TEMPERATURE PROPERTIES OF THE MOTT–HUBBARD TRANSITION

Ning-Hua Tong, Shun-Qing Shen

Published Nov 20, 2001• 1 citation
Publisher

Abstract

The unanalytical feature of the Mott–Hubbard metal-insulator transition in infinite dimensions is studied by using a modified self-consistency scheme in the framework of dynamical mean-field theory. For a specific low temperature T=0.0025W (W: half bandwidth), the "Z"-shaped or "S"-shaped curves for double occupancy D, energy per lattice site E, and the quasi-particle weight Z are obtained as functions of U. Direct observation shows that the Fermi-liquid phase changes to the insulating phase through a non-Fermi-liquid phase at the unstable level. Based on our results, a scenario of zero temperature MIT is proposed. The phase diagram for MIT on the T–D plane is also presented.

DOI
10.1142/s0217984901003123

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The unanalytical feature of the Mott–Hubbard metal-insulator transition in infinite dimensions is studied by using a modified self-consistency scheme in the framework of dynamical mean-field theory. For a specific low temperature T=0.0025W (W: half bandwidth), the "Z"-shaped or "S"-shaped curves for double occupancy D, energy per lattice site E, and the quasi-particle weight Z are obtained as functions of U. Direct observation shows that the Fermi-liquid phase changes to the insulating phase through a non-Fermi-liquid phase at the unstable level. Based on our results, a scenario of zero temperature MIT is proposed. The phase diagram for MIT on the T–D plane is also presented.
We analyze the unanalytical structure of metal-insulator transition (MIT) in infinite dimensions. A multiple-valued structure in Green's function and other thermodynamical quantities with respect to the interaction strength U are observed at low temperatures by introducing a transformation into the dynamical mean-field equation of Hubbard model. A complete description of stable, metastable, and unstable phases is established in the regime Uc1(T)<U<Uc2(T).{U}_{c1}(T)<U<{U}_{c2}(T).Uc1​(T)<U<Uc2​(T). The Maxwell construction is performed to evaluate the MIT line U∗(T).{U}^{*}(T).U∗(T). We show how the first-order MIT at U∗(T){U}^{*}(T)U∗(T) for T>0T>0T>0 evolves into the second-order one at Uc2(0){U}_{c2}(0)Uc2​(0) for T=0.T=0.T=0. The phase diagram near MIT is presented.
The dynamical mean-field theory (DMFT) is employed to study the correlation-driven metal-insulator transition in the semi-infinite Hubbard model at half-filling and zero temperature. We consider the low-index surfaces of the three-dimensional simple-cubic lattice, and systematically vary the model parameters at the very surface, the intralayer and interlayer surface hopping, and the surface Coulomb interaction. Within the DMFT the self-energy functional is assumed to be local. Therewith, the problem is self-consistently mapped onto a set of coupled effective impurity models corresponding to the inequivalent layers parallel to the surface. Assuming that the influence of the high-energy Hubbard bands on the low-energy quasiparticle resonance can be neglected at the critical point, a simplified ``linearized DMFT'' becomes possible. The linearized theory, however, is formally equivalent to the Weiss molecular-field theory for the semi-infinite Ising model. This implies that qualitatively the rich phenomenology of the Landau description of second-order phase transitions at surfaces has a direct analog for the surface Mott transition. Motivated by this formal analogy, we work out the predictions of the linearized DMFT in detail. It is found that under certain circumstances the surface of a Mott insulator can be metallic, while a Mott-insulating surface of a normal metal is not possible. We derive the corresponding phase diagrams, the (mean-field) critical exponents and the critical profiles of the quasiparticle weight. The results are confirmed by a fully numerical evaluation of the DMFT equations using the exact-diagonalization (ED) method. By means of the ED approach, we especially investigate the noncritical parts of the phase diagrams and discuss the U and layer dependence of the quasi-particle weight. For strong modifications of the surface model parameters, the surface low-energy electronic structure dynamically decouples from the bulk.
Abstract We present a T = 0 K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possesses the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped phases can be obtained. We find that the normal and insulating phases of the half-filled Hubbard model correspond, for any on-site repulsion, to a marginal Fermi liquid normal phase and a topologically-ordered gapped Mott insulating liquid respectively. The marginal Fermi liquid is found to arise from singular forward scattering in directions normal to the nested Fermi surface, while singular backscattering events lead to Mott liquid state. The transition between these two phases involves passage through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. The pseudogap phase is observed to arise from the electronic differentiation encoded within the nested Fermi surface, and involves the gradual gapping of the Fermi surface from antinodes to nodes via charge and spin excitations that are mutually entangled. We obtain effective Hamiltonians for various phases, as well as wavefunctions for the low-energy many-body eigenstates of the Mott liquid. Benchmarking of the ground-state energy per particle and the double-occupancy fraction for the Mott liquid against existing numerical results yields excellent agreement. Presence of a Néel ordering symmetry-breaking perturbation in the RG leads to an antiferromagnetic spin-ordered charge insulating Mott state. Our results thus offer novel insights on a variety of aspects of the Mott–Hubbard problem, and can be extended to the doped system.
We study the Hubbard model in dimension d= infinity , within an approximation that simultaneously reproduces the atomic limit and the weak-coupling limit up to second order in the interaction strength U. This method, which is a slightly modified version of an approximation suggested by Edwards and Hertz, is applied to the calculation of the self-energy and of the spectral function in the paramagnetic regime for different U, band fillings n, and temperatures T. We find Fermi-liquid behaviour for small U and (for half-filling n=0.5) a metal-insulator (Mott) transition at a critical value U cr , but also a metallic non-Fermi-liquid phase for intermediate values U<U cr . We compare our results with results obtained within the second-order perturbation theory in U and (at finite temperature) with the (essentially exact) quantum Monte Carlo (QMC) results. Qualitatively, the approximation reproduces the correct tendencies obtained by QMC, but in detail there are still discrepancies, in particular for intermediate values of U.
We consider a Mott transition of the Hubbard model in infinite dimensions. The dynamical meanfield theory is employed in combination with a continuous-time quantum Monte Carlo (CTQMC) method for an accurate description at low temperatures. From the double occupancy and the energy density, which are directly measured from the CTQMC method, we construct the phase diagram. We pay particular attention to the construction of the first-order phase transition line (PTL) in the coexistence region of metallic and insulating phases. The resulting PTL is found to exhibit reasonable agreement with earlier finite-temperature results. We also show by a systematic inclusion of low-temperature data that the PTL, which is achieved independently of the previous zero-temperature results, approaches monotonically the transition point from earlier zerotemperature studies.