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.
In this thesis, several aspects of correlation effects in band insulators that were hitherto not addressed, both in equilibrium and non-equilibrium, are studied using the Ionic Hubbard model (IHM) at half-filling and Dynamical mean-field theory (DMFT). The IHM is an extension of the Hubbard model on a bipartite lattice with a staggered on-site “ionic potential Δ added in. The Hubbard model by itself is a tight-binding model of electrons hopping between (orbitals localized on) lattice sites, with amplitudes t and t’ for first neighbor and second neighbor hopping respectively, together with a coulomb repulsion energy cost of U for double occupancy (i.e., with both up and down spin electrons) at any lattice site. The studies in this thesis address strong correlation effects in this model using DMFT techniques which map the lattice problem to a self consistently embedded quantum impurity problem. The impurity problem itself is solved using state of the art continuous time quantum monte-carlo (CTQMC) techniques (Ch.s 3 and 4) as well as the somewhat simpler Iterated Perturbation Theory (IPT) (Ch.s 3, 5 and 6).
Chapter 3 of the thesis is devoted to a detailed analysis of the properties of the half-filled t-U-Δ IHM (i.e., with t’=0) on a Bethe lattice of infinite connectivity. It is shown conclusively here that for a finite Δ and at zero temperature (T=0), the IHM has a first order transition from the Band Insulator (BI) phase to an antiferromagnetic insulating (AFI) phase at a threshold U = UAF (which increases with Δ) such that the BI to AFI transition preempts the transition from the BI to the correlation induced paramagnetic metallic (PM) phase. Evidence is also presented for a quantum transition to a sliver of half-metal (HM) phase just after the AF order turns on, followed by a return to the AFI phase on further increasing U. With increasing T, the AF order is lost via a first-order transition for weak to intermediate U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, the transition from the AFI to the paramagnetic Mott insulating phase (adiabatically connected to the BI phase) is of second order. As T increases, the range of U over which the AF order is stable shrinks, collapsing eventually to a line of tricritical points that separates the surfaces of first- and second-order phase transitions in the T-U-Δ space.
In Chapter 4 of the thesis the t-t’-U-Δ IHM on a square lattice is studied using DMFT+CTQMC. It is shown here that the presence of t’ frustrates the AF order for weak to intermediate correlations, resulting in the stabilization of the correlation induced PM phase over a broad region of the parameter space, although the AFI is always the stable phase for large enough U. In the intermediate coupling regimes, two other interesting phases show up as a result of the competition among U, Δ and t’ : a Ferrimagnetic metallic (FM) phase which has non-zero values of the uniform as well as staggered magnetization; and even more interesting, an…
An unusual metallic phase is argued to develop in the one-dimensional ionic Hubbard model, at half-filling and zero magnetization, at intermediate electron-electron repulsion
U when second-neighbors hopping is allowed and tuned close to a topological Lifshitz transition (connected with a change of the Fermi surface in the noninteracting system). The metallic state lies between a band insulator phase at low repulsion and a correlated (Mott-like) insulator phase at high repulsion. In approaching the latter, the model supports short-range antiferromagnetic order and spontaneous dimerization of both bond charge and nearest-neighbor antiferromagnetic correlations. A combination of mean-field and effective-field theory (bosonization) provides an analytical understanding of the physical processes underlying the argued phase transitions. The ground and low-energy excited states of finite-length chains are explored by density-matrix renormalization-group (DMRG) calculations, providing numerical evidence for the intermediate gapless phase. Such finite systems are attainable by cold atoms in optical lattices for a wide range of the parameter
U.
We investigate the ground-state phase diagram of the half-filled $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ repulsive Hubbard model in the presence of a staggered ionic potential $\ensuremath{\Delta}$ using the continuum-limit bosonization approach. We find that with increasing on-site repulsion
U, depending on the value of the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}$, the model shows three different versions of the ground-state phase diagram. For ${t}^{\ensuremath{'}}<{t}_{c}^{{*}^{\ensuremath{'}}}$, the ground-state phase diagram consists of the following three insulating phases: band insulator at
U<Uc, ferroelectric insulator at
Uc<U<Us, and correlated (Mott) insulator at
U>Uc. For ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ there is only one transition from a spin-gapped metallic phase at
U<Uc to a ferroelectric insulator at
U>Uc. Finally, for intermediate values of the next-nearest-neighbor hopping amplitude ${t}_{c}^{{*}^{\ensuremath{'}}}<{t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$ we find that with increasing on-site repulsion, at
Uc1 the model undergoes a second-order commensurate-incommensurate-type transition from a band insulator into a metallic state and at larger
Uc2 there is a Kosterlitz-Thouless-type transition from a metal to a ferroelectric insulator.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed Gossamer superconductivity. We apply a renormalized mean field theory to approximately take into account the strong correlation effect in partially projected Gutzwiller wave functions. At the half-filling, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion
U from a Gossamer superconductor at small
U. At the critical value
U=Uc, the charge carrier density and the superconducting (SC) order parameter change discontinuously from zero in the Mott insulating phase to finite values in the Gossamer SC phase. The first order transition is due to the interplay of the kinetic and spin exchange energies. As the electron density changes away from half-filling, the Gossamer SC state changes smoothly, while the Mott insulator is evolved into a resonating valence bond (RVB) SC state. The Gossamer and RVB SC states have the same pairing symmetry. The SC order parameter changes smoothly from a RVB SC state at
U>Uc to a Gossamer SC state at
U<Uc at a fixed nonhalf-filled electron density. We argue that the RVB SC state is smoothly connected to the Gossamer SC state, hence to the BCS state.
We investigate the phase diagram of two-dimensional (2D) Hubbard model by employing the optimization variational Monte Carlo method. The 2D Hubbard model is the most simple electronic model for cuprate high-temperature superconductors. The phase diagram consists of three regions; they are antiferromagnetic insulator (AFI) region, superconducting (SC) region and the coexistent region of superconductivity and antiferromgantism. The phase diagram obtained by numerical calculations well agrees with the experimental phase diagram for high-temperature cuprates. We mainly focused on the effect of
t′ on the antiferromagnetic (AF) correlation and the AFI region. The area of the AF phase increases when we include
t′ and thus the pure
d-wave SC phase decreases. The AFI phase near half filling decreases as
∣t′∣ increases.