We study the phase diagram of the ionic Hubbard model (IHM) at half-filling on a Bethe lattice of infinite connectivity using dynamical mean field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential ∆ and the on-site Hubbard U . We find that for a finite ∆ and at zero temperature, long range antiferromagnetic (AFM) order sets in beyond a threshold U = UAF via a first order phase transition. For U smaller than UAF the system is a correlated band insulator. Both the methods show a clear evidence for a quantum transition to a half-metal phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U . We show that the results obtained within both the methods have good qualitative and quantitative consistency in the intermediate to strong coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first order phase transition at a transition temperature TAF (U, ∆) (or, equivalently, on decreasing U below UAF (T, ∆)), within both the methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T , DMFT+CTQMC shows a second phase transition (not seen within DMFT+IPT) on increasing U beyond UAF . At UN > UAF , when the Neel temperature TN for the effective Heisenberg model becomes lower than T , the AFM order is lost via a second order transition. For2 ) where x = 2∆/U and thus TN increases with increase in ∆/U . In the 3-dimensional parameter space of (U/t, T /t and ∆/t), as T increases, the surface of first order transition at UAF (T, ∆) and that of the second order transition at UN (T, ∆) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first and second order phase transitions.
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