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arXiv:1505.08091 · Physical Review B

Ground state of doped cuprates from first-principles quantum Monte Carlo calculations

Lucas K. Wagner

Published Oct 30, 2015• 35 citations
arXivHTMLPDF

Abstract

The author reports on high-fidelity simulations of charge carriers in the high-${T}_{c}$ cuprate materials using quantum Monte Carlo techniques applied to the first-principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in x-ray, EELS, and neutron experiments.

DOI
10.1103/physrevb.92.161116

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The author reports on high-fidelity simulations of charge carriers in the high-Tc{T}_{c}Tc​ cuprate materials using quantum Monte Carlo techniques applied to the first-principles Hamiltonian. With this high accuracy technique, the doped ground state is found to be a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface and charge inhomogeneity in these materials. The spin polaron has some unique features that should be visible in x-ray, EELS, and neutron experiments.
The author reports on new high-fidelity simulations of charge carriers in the high-Tc_cc​ cuprate materials using quantum Monte Carlo techniques applied to the first principles Hamiltonian. With this new application of this high accuracy technique, the doped ground state is found to be in the form of a spin polaron, in which charge is localized through a strong interaction with the spin. This spin polaron has calculated properties largely similar to the phenomenology of the cuprates, and may be the object which forms the Fermi surface in these materials. The results contained in this paper comprise an accurate first principles derived paradigm from which to study superconductivity in the cuprates.
There is growing evidence that the hole-doped single-band Hubbard and t - J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.
We perform extensive auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in order to study the ground-state properties of copper-oxygen planes in the cuprates. Employing cutting-edge AFQMC techniques with a self-consistent gauge constraint in auxiliary-field space to control the sign problem, we reach supercells containing $\ensuremath{\approx}500$ atoms to capture collective modes in the charge and spin orders and characterize the behavior in the thermodynamic limit. The self-consistency scheme interfacing with generalized Hartree-Fock calculations allows high accuracy in AFQMC to resolve small energy scales, which is crucial for determining the complex candidate orders in such a system. We present detailed information on the charge order, spin order, momentum distribution, and localization properties as a function of charge-transfer energy for the the underdoped regime. In contrast with the stripe and spiral orders under hole doping, we find that the corresponding 1/81/81/8 electron-doped system exhibits purely antiferromagnetic order in the three-band model, consistent with the asymmetry between electron and hole doping in the phase diagram of cuprates.
We present an advanced ab initio quantum Monte Carlo (QMC) calculation of the ground state of undoped CaCuO2{\mathrm{CaCuO}}_{2}CaCuO2​. We extend the traditional single-determinant Slater-Jastrow approach to include multideterminant wave functions, inhomogeneous Jastrow factors, and orbital optimization. Our results demonstrate not only an improvement in the variational bound of the ground state energy---2.3 eV per formula unit lower than previous state-of-the-art techniques---but also confirm the presence of spin fluctuations in multideterminant wave functions in a strongly correlated cuprate system, which is integral to understanding high-Tc{T}_{c}Tc​ superconductivity. This is a demonstration of capturing spin fluctuations in QMC wave functions on a cuprate, establishing the groundwork for studies on doped cuprates in the superconducting state, where spin fluctuations require more accurate characterization.
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A classical Monte Carlo algorithm based on the quasi-classical approximation is applied to the pseudospin Hamiltonian of the model cuprate. The model takes into account both local and non-local correlations, Heisenberg spin-exchange interaction, single-particle and correlated two-particle transfer. We define the state selection rule that gives both the uniform distribution of states in the phase space and the doped charge conservation. The simulation results show a qualitative agreement of a phase diagrams with the experimental ones.