Effect of electron correlation on the electronic structure and spin-lattice coupling of high-$T_c$ cuprates: Quantum Monte Carlo calculations

Electron correlation effects are particularly strong in high-temperature superconducting materials. Devising an accurate description of these materials has long been a challenge, with these strong correlation effects historically being considered impossible or impractical to simulate computationally. Using quantum Monte Carlo techniques, we have explicitly simulated electron correlations in several cuprate materials from first principles. These simulations accurately reproduce many important physical quantities of these materials, including the interaction-induced gap and superexchange coupling between copper spins, with no additional parameters beyond fundamental constants. We further investigate the dimensionless spin-lattice coupling parameter in the parent materials, showing that it varies dramatically, between 0.1 and 1.0, depending on the interlayer. This result indicates that the lattice and magnetic degrees of freedom are not independent in these systems, which may have ramifications for the origin of superconductivity.

Figure 1

The change in frequency upon switching from a checkerboard antiferromagnetic ordering to a ferromagnetic ordering for all $\Gamma$ phonons for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ calculated with the PBE0 density functional. The modes with large changes in frequency are labeled: (a) “cage tilt” is the rotation of the oxygen cage towards the orthorhombic structure; (b) “apical” is a mode involving the apical oxygen atoms; (c) “${\mathrm{B}}_{1g}$” is the $d$-wave oxygen buckling mode; and (d) “half-breathing” is the out-of-phase breathing mode of oxygen atoms in the ${\mathrm{CuO}}_2$ plane.

Figure 2

Controlling the fixed node error by varying the one-particle orbitals. (a) Total FN-DMC energy as a function of the mixing in density functional theory used to generate the orbitals. (b) Energy difference between different magnetic states as a function of the orbitals. (c) Estimated magnetic moments as a function of the orbitals. Lines are guides for the eye, and error bars, when larger than the symbol size, represent 1 standard deviation of the statistical uncertainty.

Figure 3

The energy as a function of the phonon coordinate for all systems considered in this work.

Figure 4

A slice through the $ac$ plane of the three cuprates considered in this study. The column marked “tetragonal” denotes the undistorted $p4$/mmm structure, while the ${\mathrm{A}}_{1g}$ and ${\mathrm{B}}_{1g}$ columns denote frozen phonon vibrations with each of these symmetries. Contour lines are logarithmically spaced, with red denoting down-spin and blue up-spin. The projected positions of the atoms are denoted by filled circles: Cu (yellow), O (red), Ca (magenta), and La (green).