Variational cluster approach to ferromagnetism in infinite dimensions and in one-dimensional chains

TL;DR

This paper applies the variational cluster approach to study ferromagnetism in the Hubbard model across infinite dimensions and one-dimensional chains, providing new insights into phase diagrams and stability of magnetic states.

Contribution

It introduces technical improvements to the VCA implementation and applies it to analyze ferromagnetism in both infinite-dimensional and one-dimensional Hubbard models.

Findings

DIA results benchmarked against previous studies.

Unified picture of ferromagnetism mechanisms in infinite dimensions.

Phase diagrams for one-dimensional chains with various parameters.

Abstract

The variational cluster approach (VCA) is applied to study spontaneous ferromagnetism in the Hubbard model at zero temperature. We discuss several technical improvements of the numerical implementation of the VCA which become necessary for studies of a ferromagnetically ordered phase, e.g. more accurate techniques to evaluate the variational ground-state energy, improved local as well as global algorithms to find stationary points, and different methods to locate the magnetic phase transition. Using the single-site VCA, i.e. the dynamical impurity approximation (DIA), the ferromagnetic phase diagram of the model in infinite dimensions is worked out. The results are compared with previous dynamical mean-field studies for benchmarking purposes. The DIA results provide a unified picture of ferromagnetism in the infinite-dimensional model by interlinking different parameter regimes that are governed by different mechanisms for ferromagnetic order. Using the DIA and the VCA, we then study ferromagnetism in one-dimensional Hubbard chains with nearest and next-nearest-neighbor hopping t2. In comparison with previous results from the density-matrix renormalization group, the phase diagram is mapped out as a function of the Hubbard-U, the electron filling and t2. The stability of the ferromagnetic ground state against local and short-range non-local quantum fluctuations is discussed.