Testing density functional theory in a quantum Ising chain

Abstract

By using the quantum Ising chain as a test bed and treating the spin polarization along the external transverse field as the "generalized density", we examine the performance of different levels of density functional approximations parallel to those widely used for interacting electrons, such as local density approximation (LDA) and generalized gradient approximation (GGA). We show that by adding the lowest-order and nearest-neighbor density variation correction to the simple LDA, a semi-local energy functional in the spirit of GGA is almost exact over a wide range of inhomogeneous density distribution. In addition, the LDA and GGA error structures bear a high level of resemblance to the quantum phase diagram of the system. These results provide insights into the triumph and failure of these approximations in a general context.

References in corpus (7)

• Quantum Criticality
• DFT: A Theory Full of Holes?
• Linking entanglement and quantum phase transitions via density functional theory
• The 1D Ising model and topological order in the Kitaev chain
• The quasi-periodic quantum Ising transition in 1D
• Spin-distribution functionals and correlation energy of the Heisenberg model
• Density-functional formulations for quantum chains

Cited by in corpus (1)

• Extensibility of Hohenberg-Kohn Theorem to general quantum systems