Ab initioQuantum Monte Carlo Calculations of Spin Superexchange in Cuprates: The Benchmarking Case ofCa2CuO3

Abstract

In view of the continuous theoretical efforts aimed at an accurate microscopic description of the strongly correlated transition metal oxides and related materials, we show that with continuum quantum Monte Carlo (QMC) calculations it is possible to obtain the value of the spin superexchange coupling constant of a copper oxide in a quantitatively excellent agreement with experiment. The variational nature of the QMC total energy allows us to identify the best trial wave function out of the available pool of wave functions, which makes the approach essentially free from adjustable parameters and thus truly ab initio. The present results on magnetic interactions suggest that QMC is capable of accurately describing ground state properties of strongly correlated materials. 02.70.Ss,75.30.Et,75.47.Lx For decades, transition metal oxides have been amongst the most intriguing materials due to the complex correlated behavior of the 3d or 4d electrons of a transition metal ion. In particular, strong electronic correlations often give rise to non-trivial magnetism, such as quantum spin-liquid states in low-dimensional Mott insulating oxides. High-temperature superconductivity in copper oxides (cuprates) is also believed to originate from magnetic spin excitations that bind Cooper pairs [1-3]. Electronic correlations, however, also make this class of materials among the most difficult to describe theoretically, both from model as well as ab initio perspectives.One of the practical challenges of ab initio electronic structure theory is to accurately predict the strength of magnetic coupling between localized spins of transition metal ions [4]. For solids, a natural method of choice is periodic density functional theory (DFT). DFT gives access to the system's ground state energy corresponding to different configurations of localized spins, which can be mapped onto the eigenstates of the a spin model to extract the magnetic couplings J. This approach relies on the accuracy of the description of the ground state. Unfortunately, the presently available approximations to the exchange-correlation functional in DFT either poorly account for the exchange and correlation effects [local density approximation (LDA)] or depend on empirical input parameters (LDA+U, hybrid functionals). Often, the only way to find an appropriate approximation for the system of interest is by comparing theoretical calculations with experiment, compromising the predictive nature of such calculations.This problem is generic to a broad class of transition metal oxides. Let us exemplify the aforementioned limitations of DFT by considering the case of the Mott insulators Ca 2 CuO 3 and Sr 2 CuO 3 . These systems are one of the best realizations of the one-dimensional (1D) spin-1 2 antiferromagnetic Heisenberg chain model, demonstrat-ing spin-liquid behavior and separation of spin and orbital degrees of freedom [11]. The crystal structure of Ca 2 CuO 3 and Sr 2 CuO 3 is similar to that of the superconducting two-dimensional cuprates, with the difference that ...

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