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Register a new userSpin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
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The $2d$ Hubbard model with nearest-neighbour hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using diagrammatic Monte Carlo in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and non-local fluctuations in both channels are essential.
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We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the textcolor{black}{insulating state}, we find strong spin fluctuations at the K point at low energy corresponding to the textcolor{black}{120$^{circ}$} antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and textcolor{black}{spin-lattice} relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba$_8$CoNb$_6$O$_{24}$ and to the relaxation times on $kappa$-(ET)$_2$Cu$_2$(CN)$_3$. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds.
Two very different methods -- exact diagonalization on finite chains and a variational method -- are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied $d$ sites as a function of various parameters. In the absence of on-site Coulomb interaction ($U_f$) between $f$ electrons, the two methods yield similar results. The double occupancy of $d$ levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite $U_f$, while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ($U_d^c$), which depends on $U_f$ and $V$.
We use an unbiased, continuous-time quantum Monte Carlo method to address the possibility of a zero-temperature phase without charge-density-wave (CDW) order in the Holstein and, by extension, the Holstein-Hubbard model on the half-filled square lattice. In particular, we present results spanning the whole range of phonon frequencies, allowing us to use the well understood adiabatic and antiadiabatic limits as reference points. For all parameters considered, our data suggest that CDW correlations are stronger than pairing correlations even at very low temperatures. These findings are compatible with a CDW ground state that is also suggested by theoretical arguments.
Using a self-consistent Hartree-Fock approximation we investigate the relative stability of various stripe phases in the extended $t$-$t$-$U$ Hubbard model. One finds that a negative ratio of next- to nearest-neighbor hopping $t/t<0$ expells holes from antiferromagnetic domains and reinforces the stripe order. Therefore the half-filled stripes not only accommodate holes but also redistribute them so that the kinetic energy is gained, and these stripes take over in the regime of $t/tsimeq -0.3$ appropriate for YBa$_2$Cu$_3$O$_{6+delta}$.
We study the phase diagram of the ionic Hubbard model (IHM) at half-filling 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 potential $Delta$ and the on-site Hubbard U. In both the methods we find that for a finite $Delta$ and at zero temperature, anti-ferromagnetic (AFM) order sets in beyond a threshold $U=U_{AF}$ via a first order phase transition below which the system is a paramagnetic band insulator. Both the methods show a clear evidence for a 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. On increasing the temperature, the AFM order is lost via a first order phase transition at a transition temperature $T_{AF}(U, Delta)$ within both the methods, for weak to intermediate values of U/t. But 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. As a result, at any finite temperature T, DMFT+CTQMC shows a second phase transition (not seen within DMFT+IPT) on increasing U beyond $U_{AF}$. At $U_N > U_{AF}$, when the Neel temperature $T_N$ for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second order transition. In the 3-dimensonal parameter space of $(U/t,T/t,Delta/t)$, there is a line of tricritical points that separates the surfaces of first and second order phase transitions.
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