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arXiv:1212.4485 · Physical Review B

Mott transitions in the half-filled SU(2 M ) symmetric Hubbard model

Nils Blümer, Elena V. Gorelik

Published Feb 13, 2013• 21 citations
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Abstract

The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali-like atoms. We compute its static properties in the SU($2M$) symmetric limit for up to $M=8$ bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on these unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy $M$ with high accuracy.

DOI
10.1103/physrevb.87.085115

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The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali-like atoms. We compute its static properties in the SU(2M2M2M) symmetric limit for up to M=8M=8M=8 bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on these unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy MMM with high accuracy.
We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U . With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
We investigate the Mott metal-insulator transition in the asymmetric Hubbard model, which may describe the ground states of fermionic atoms trapped in optical lattices. We use the dynamical mean-field theory and the equation of motion approach to calculate the density of states at the Fermi level and the double occupation for various values of the on-site interaction U and the hopping asymmetry r . The critical interaction is also obtained as a function of the hopping asymmetry. Our results are in good agreement with the ones obtained by using the dynamical mean field theory with the exact diagonalization and the quantum Monte Carlo techniques.
Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal repulsive on-site interactions U>0U>0U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., they should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a ``semicompressible'' state observed for large UUU near half filling.