Mott transition in one dimension: Benchmarking dynamical cluster approaches

TL;DR

This paper benchmarks the variational cluster approach (VCA) for the one-dimensional Hubbard model, analyzing its accuracy and efficiency in capturing the Mott transition compared to exact and other numerical methods.

Contribution

It provides a comprehensive benchmarking of VCA against exact solutions and other methods, exploring convergence, parameter optimization, and the role of bath sites in one-dimensional systems.

Findings

VCA is computationally efficient and competitive with other cluster methods.

Results converge with increasing cluster size and can access the critical Mott transition regime.

Bath sites improve the description of excitation properties and filling dependence.

Abstract

The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework of the self-energy-functional theory (SFT), different cluster reference systems with and without bath degrees of freedom, in different topologies and with different sets of variational parameters are considered. Static and one-particle dynamical quantities are calculated for half-filling as a function of U as well as for fixed U as a function of the chemical potential to study the interaction- and filling-dependent metal-insulator (Mott) transition. The recently developed Q-matrix technique is used to compute the SFT grand potential. For benchmarking purposes we compare the VCA results with exact results available from the Bethe ansatz, with essentially exact dynamical DMRG data, with (cellular) dynamical mean-field theory and full diagonalization of isolated Hubbard chains. Several issues are discussed including convergence of the results with cluster size, the ability of cluster approaches to access the critical regime of the Mott transition, efficiency in the optimization of correlated-site vs. bath-site parameters and of multi-dimensional parameter optimization. We also study the role of bath sites for the description of excitation properties and as charge reservoirs for the description of filling dependencies. The VCA turns out to be a computationally cheap method which is competitive with established cluster approaches.