The dynamical cluster approximation (DCA) with Betts clusters is used to calculate the antiferromagnetic phase diagram of the three-dimensional Hubbard model at half-filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt et al. [Eur. Phys. J. B 17, 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000.The dynamical cluster approximation (DCA) with Betts clusters is used to calculate the antiferromagnetic phase diagram of the three-dimensional Hubbard model at half-filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt et al. [Eur. Phys. J. B 17, 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000.

arXiv:cond-mat/0506337Physical Review BAug 29, 200579 citations

Thermodynamic properties of the one-dimensional Hubbard model

Norio Kawakami, Tatsuya Usuki, Ayao Okiji

Physics Letters AMay 1, 198959 citations

Applicability and limitations of cluster perturbation theory for Hubbard models

Nicklas Enenkel, Markus Garst, Peter Schmitteckert

We present important use cases and limitations when considering results obtained from cluster perturbation theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of conventional band theory to provide an approximation for the Green’s function in the thermodynamic limit. To this end, we are investigating single-band and multi-band Hubbard models in 1D and 2D systems. A special interest is taken in the supposed pseudogap regime of the 2D square lattice at half-filling and intermediate interaction strength $(U≤3t)$ as well as the metal–insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal–insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.We present important use cases and limitations when considering results obtained from cluster perturbation theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of conventional band theory to provide an approximation for the Green’s function in the thermodynamic limit. To this end, we are investigating single-band and multi-band Hubbard models in 1D and 2D systems. A special interest is taken in the supposed pseudogap regime of the 2D square lattice at half-filling and intermediate interaction strength $(U≤3t)$ as well as the metal–insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal–insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.

arXiv:2309.14035Jan 1, 20230 citations

Thermodynamic Properties of the One-Dimensional Hubbard Model

U. Brandt

Springer eBooksJan 1, 19760 citations

(U≤3t)

as well as the metal–insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal–insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.