Local classical correlations between physical electrons in Hubbard systems

Abstract

We demonstrate that the local nonfreeness, an unbiased measure of correlation between electrons at a single lattice site, can be computed as the mutual information between local natural spin orbitals. This leads us to prove a general result: local electron correlations in Hubbard-type models are fully classical since the local reduced density matrix is separable in the natural basis and no quantum correlations beyond entanglement are present. Finally, we compare different theoretical descriptions of magnetic and nonmagnetic states, showing that local classical correlations are drastically influenced by nonlocal processes. These results confirm the relation between local classical correlations within an open system and nonlocal entanglement, and they provide a clear path for the study of the relationship between traditional quantum resources and the nonfreeness, in terms of experimentally accessible quantities.

Figures (3)

• Figure 1: Local quasiparticle weight (top) and local nonfreeness (bottom) across the paramagnetic Mott-Hubbard transition on the square lattice, at zero temperature, in the gRISB approximation. The arrows depict the increasing-$U$ and decreasing-$U$ solutions.
• Figure 2: Local magnetization (top), local double occupancy (center) and local nonfreeness (bottom) in the ground state of the Hubbard model on the square lattice, comparing the RISB approximation and the gRISB approximation ($N_\mathrm{ghost}=2$). The dashed green line in the strong-coupling regime marks the exact solution of the isotropic Heisenberg model Sandvik_squareXXX_2002.
• Figure 3: Local magnetization (top), local double occupancy (center) and local nonfreeness (bottom) on the honeycomb lattice, comparing the gRISB approximation ($N_\mathrm{ghost}=2$), the dynamical mean-field theory [DMFT] and auxiliary-field quantum Monte Carlo [AFQMC] data. DMFT data have been generated with the EDIpack library DMFT/ED_CaffarelDMFT/ED_CaponeEDIpackEDIpack2*EDIpack_code. The AFQMC data are taken, with permission, from Ref. DMFT/NRG_HoneyHubbard. The error bars for the local mutual information have been computed with linear propagation of the standard deviation. The dashed green line in the strong-coupling regime marks the numerically exact solution of the isotropic Heisenberg model on the honeycomb lattice, as reported in Ref. Sandvik_honeyXXX_2006.