We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J=L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a nontrivial flavor selectivity and energy dependence. Furthermore, in the regions near n=2 and n=4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n=4 and discuss the relevance of our results for real materials.
An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region and a suppression in the composite ordered phase. The doping-dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro-orbital order dominates the filling range $2\ensuremath{\lesssim}n\ensuremath{\le}3$ and ferro-orbital order dominates the strongly interacting region for $1\ensuremath{\lesssim}n<2$, we find superconductivity with a remarkably high
Tc around
n=1.5 (quarter filling). Also in the doped system, there is a close connection between the orbital-freezing crossover and superconductivity.
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal)
s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.
We investigate ordered phases (s-wave superconducting (SC), antiferromagnetic (AF) and charge ordered (CO) phases) of the half-filled Holstein-Hubbard model using the dynamical mean-field theory in combination with a continuous time quantum Monte Carlo impurity solver. We particularly focus on the parameter regime where the electron-electron Coulomb interaction and the phonon mediated retarded attractive interaction are both comparable to the bare electron bandwidth to understand the interplay of these interactions and the retardation effects due to finite phonon frequency ω_0. Results for the transition temperatures for SC and AF as a function of the effective interaction U_eff(=U-λwith U the Coulomb repulsion and λthe phonon-mediated attraction) show deviations from the the corresponding results in the anti-adiabatic limit. These are analyzed by comparing with an effective static model in the polaron picture. We also determine the phase diagram around U_eff=0 at low, but nonzero temperatures to show that paramagnetic phases appear between AF and CO when U and λare small or large, while AF and CO directly compete with each other at moderate U and λ.
We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.
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 $\mathrm{\ensuremath{\Delta}}$ and the on-site Hubbard
U. We find that for a finite $\mathrm{\ensuremath{\Delta}}$ 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 methods show a clear evidence for a quantum transition to a half-metal (HM) 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 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 ${T}_{AF}(U,\mathrm{\ensuremath{\Delta}})$ [or, equivalently, on decreasing
U below ${U}_{AF}(T,\mathrm{\ensuremath{\Delta}})$], within both 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. For $U\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}, {T}_{N}\ensuremath{\sim}{t}^{2}/U(1\ensuremath{-}{x}^{2})$, where $x=2\mathrm{\ensuremath{\Delta}}/U$ and thus
TN increases with increase in $\mathrm{\ensuremath{\Delta}}/U$. In the three-dimensional parameter space of $(U/t,\phantom{\rule{0.28em}{0ex}}T/t,\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}\mathrm{\ensuremath{\Delta}}/t)$, as
T increases, the surface of first-order transition at ${U}_{AF}(T,\mathrm{\ensuremath{\Delta}})$ and that of the second-order transition at ${U}_{N}(T,\mathrm{\ensuremath{\Delta}})$ 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.