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Journal of Physics A Mathematical and Theoretical

Nematic phase transition in a multi-orbital Hubbard model

Giuseppe Guarnaccia, Canio Noce

Published Oct 31, 2014• 0 citations
Publisher

Abstract

By using the reflection positivity method, we rigorously establish some exact properties of a multi-orbital Hubbard model, here adopted to describe a nematic orbital phase transition. We show that, when the on-site intra-orbital Coulomb interaction is equal to the on-site inter-orbital Coulomb interaction, this model supports a staggered nematic orbital order if repulsive or attractive on-site inter-orbital and intra-orbital interactions and off-site repulsive inter-orbital interaction are considered. Depending on the dimensions of the bipartite lattice where the model is defined, we find that, at half-filling, the order may or may not exist. In particular, we prove that the order may exist, in two and three dimensions, at sufficiently low temperatures if the hopping amplitude is small enough.

DOI
10.1088/1751-8113/47/46/465002

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We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH.
We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase transitions such as metal-insulator, magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.
The antiferromagnetic Ne\'el temperature TN{T}_{N}TN​ is calculated as a function of the Coulomb interaction U for a half-filled 3D Hubbard model. Numerical results are given for the specific heat and staggered magnetic suspectibility on periodic lattices ranging from 43{4}^{3}43--103{10}^{3}103 sites, and used to determine TN{T}_{N}TN​. The size dependence of the results suggests that the transition is weakly first order at small to intermediate values of U.
We investigate the phase diagram of the extended Hubbard model on a half-filled honeycomb lattice through determinant quantum Monte Carlo simulations. At zero temperature, the repulsive Hubbard model undergoes a transition to an antiferromagnetic state only for sufficiently strong on-site coupling UUU. However, the inclusion of a repulsive extended interaction VVV between fermions in nearest-neighbor orbitals induces a charge-ordered phase. For attractive interactions, we also identify superconducting and phase-separated phases. We have determined a complete phase diagram with the aid of structure factors associated with various orderings, combined with measurements of double occupancy and the average sign of fermionic determinants. We have established that the semimetallic phase forms a zone from which ordered phases are excluded, preventing the stabilization of a superconducting phase with ddd-wave symmetry, i.e., only sss-wave pairing is allowed.