We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice.We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem.As our theory describes the evolution from a Slater (U t) to a Mott-Heisenberg (U t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.
The antiferromagnetic phase of two-dimensional (2D) and three-dimensional (3D) Hubbard model with nearest neighbor hopping is studied on a bipartite cubic lattice by means of the quantum $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfy the Mermin-Wagner theorem. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin-quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. An effective action consisting of a spin-charge rotor and a fermionic field is derived as a function of the Coulomb repulsion
U and hopping parameter
t. At zero temperature, our theory describes the evolution from a Slater
(U⪡t) to a Mott-Heisenberg
(U⪢t) antiferromagnet. The results for zero-temperature sublatice magnetization (2D) and finite temperature (3D) phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter
U∕t are presented and the role of the spin Berry phase in the interaction driven crossover is analyzed.
We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.
We study the optical conductivity of the one-band Hubbard model in the Néel state at half filling at T = 0 using the dynamical mean-field theory. For small values of the Coulomb parameter clear signatures of a Slater insulator expected from a weak-coupling theory are found, while the strongly correlated system can be well described in terms of a Mott–Heisenberg picture. However, in contrast to the paramagnet, we do not find any evidence for a transition between these two limiting cases but rather a smooth crossover as a function of the Coulomb interaction.
Abstract We study Hartree–Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x - and y -directions and a possibly different hopping parameter
tz t z in the z -direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases
tz=0 t z = 0 and
tz=t t z = t , respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that
t=1 t = 1 , we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U , and on the hopping parameter
tz t z . We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as
tz→0 t z → 0 . It is found that the asymptotic formulas are qualitatively different for
tz=0 t z = 0 (the two-dimensional case) and
tz>0 t z > 0 (the case of nonzero hopping in the z -direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit
tz→0 t z → 0 in which the three-dimensional model reduces to the two-dimensional model.
We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Riccardo Rossi, Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett. 119, 045701 (2017).PRLTAO0031-900710.1103/PhysRevLett.119.045701]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the Néel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O(3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U/t=4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.