The high-temperature superconducting cuprates are governed by intertwined spin, charge, and superconducting orders. While various state-of-the-art numerical methods have demonstrated that these phases also manifest themselves in doped Hubbard models,
they differ on which is the actual ground state. Finite cluster methods typically indicate that stripe order dominates while embedded quantum cluster methods, which access the thermodynamic limit by treating long-range correlations with a dynamical mean field, conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in the doped single-band Hubbard model using a quantum Monte Carlo dynamical cluster approximation (DCA) method. By resolving both the fluctuating spin and charge orders using DCA, we demonstrate for the first time that they survive in the doped Hubbard model in the thermodynamic limit. This discovery also provides a new opportunity to study the influence of fluctuating stripe correlations on the models pairing correlations within a unified numerical framework.
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the pairing corr
elations in this model using these methods. Specifically, we compute the pair-field susceptibility and study its dependence on temperature, doping, interaction strength, and charge-transfer energy. Using the DCA, we also solve the Bethe-Salpeter equation for the two-particle Greens function in the particle-particle channel to determine the transition temperature to the superconducting phase on smaller clusters. Our calculations reproduce many aspects of the cuprate phase diagram and indicate that there is an optimal value of the charge-transfer energy for the model where $T_c$ is largest. These results have implications for our understanding of superconductivity in both the cuprates and other doped charge-transfer insulators.
The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly c
onsider the orbital degrees of freedom of the relevant CuO$_2$ planes. Here, we use a dynamic cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.
We study the two-dimensional $t$-$J$ model with second neighbor hopping parameter $t$ and in a broad range of doping $delta$ using a closed set of equations from the {em Extremely Correlated Fermi Liquid} (ECFL) theory. We obtain asymmetric energy di
stribution curves and symmetric momentum distribution curves of the spectral function, consistent with experimental data. We further explore the Fermi surface and local density of states for different parameter sets. Using the spectral function, we calculate the resistivity, Hall number and spin susceptibility. The curvature change in the resistivity curves with varying $delta$ is presented and connected to intensity loss in Angle Resolved Photoemission Spectroscopy (ARPES) experiments. We also discuss the role of the super-exchange $J$ in the spectral function and the resistivity in the optimal to overdoped density regimes.
We present theoretical results for the optical conductivity and the non-resonant Raman susceptibilities for three principal polarization geometries relevant to the square lattice. The susceptibilities are obtained using the recently developed extreme
ly correlated Fermi liquid theory for the two-dimensional t-t-J model, where t and t are the nearest and second neighbor hopping. Our results are sensitively depending on t, t. By studying this quartet of related dynamical susceptibilities, and their dependence on t, t, doping and temperature, we provide a useful framework for interpreting and planning future Raman experiments on the strongly correlated matter.
We study the one dimensional t-t-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a
unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.
We present a calculation of the low energy Greens function in $1+epsilon$ dimensions using the method of extended poor mans scaling, developed here. We compute the wave function renormalization $Z(omega)$ and also the decay rate near the Fermi energy
. Despite the lack of $omega^2$ damping characteristic of 3-dimensional Fermi liquids, we show that quasiparticles do exist in $1+epsilon$ dimensions, in the sense that the quasiparticle weight $Z$ is finite and that the damping rate is smaller than the energy. We explicitly compute the crossover from this behavior to a 1-dimensional type Tomonaga-Luttinger liquid behavior at higher energies.
