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arXiv:cond-mat/0105504 · Physical review. B, Condensed matter

Mott-Hubbard transition in infinite dimensions

Ning-Hua Tong, Shun-Qing Shen, Fu‐Cho Pu

Published Nov 27, 2001• 41 citations
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Abstract

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 ${U}_{c1}(T)<U<{U}_{c2}(T).$ The Maxwell construction is performed to evaluate the MIT line ${U}^{*}(T).$ We show how the first-order MIT at ${U}^{*}(T)$ for $T>0$ evolves into the second-order one at ${U}_{c2}(0)$ for $T=0.$ The phase diagram near MIT is presented.

DOI
10.1103/physrevb.64.235109

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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 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 study the Hubbard model in infinite dimension d= infinity within an approximation reproducing simultaneously the atomic limit and the weak-coupling limit up to second order in the interaction strength U. Depending on U we find a paramagnetic metal, a paramagnetic insulator, or an antiferromagnetic insulator. The stability of the antiferromagnetic phase is investigated by calculating the grand canonical potential. We present the phase diagram in the T-U plane and results for the magnetization m as a function of temperature T. For small values of U the antiferromagnetic phase transition is continuous, but for larger values of U the approximation yields a first-order magnetic phase transition. Results for the density of states N( epsilon ) are presented; it either exhibits one single band or an upper and a lower Hubbard band separated by the Mott gap. The upper and lower Hubbard band may exhibit additional magnetic structure, depending on the value of T and 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.
We investigate paramagnetic metal-insulator transitions in the infinite-dimensional ionic Hubbard model at finite temperatures. By means of the dynamical mean-field theory with an impurity solver of the continuous-time quantum Monte Carlo method, we show that an increase in the interaction strength brings about a crossover from a band insulating phase to a metallic one, followed by a first-order transition to a Mott insulating phase. The first-order transition turns into a crossover above a certain critical temperature, which becomes higher as the staggered lattice potential is increased. Further, analysis of the temperature dependence of the energy density discloses that the intermediate metallic phase is a Fermi liquid. It is also found that the metallic phase is stable against strong staggered potentials even at very low temperatures.
Starting from the exact solution of the Hubbard model in the atomic limit, and treating the hopping term as a perturbation by means of a diagram technique, we discuss the electronic structure of the model in some simple approximations. We show that a metal-insulator transition is obtained above a critical value of the on-site Coulomb interaction in a self-consistent evaluation of the one-particle Green's function to one-loop order. A relationship with results in infinite dimensions is briefly discussed.
For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength UUU, temperature TTT, and filling nnn shows that, upon increasing nnn toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T === 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.