Group theoretically possible spin density waves (SDWs) of the Hubbard model on a triangular lattice are found and classified for ordering vectors q of K and M in the Brillouin zone by finding the maximal subgroups of the symmetry group of the Hamiltonian. It is found that classifications of SDWs with these ordering vectors are reduced to classifications of SDWs on molecules with D 3 and T d symmetries, respectively. From this reduction the authors found two axial-type ASDWs (ASDW) and one plane-type SDW (PSDW) for point K and three ASDWs, two PSDWs and one cubic- (three-dimensional-) type SDW (CSDW) for point M. The standard mean-field Hamiltonians and their invariance groups are listed for each class.
Group theoretically possible spin density waves (SDWs) of the Hubbard model on a triangular lattice are found and classified for ordering vectors q of K and M in the Brillouin zone by finding the maximal subgroups of the symmetry group of the Hamiltonian. It is found that classifications of SDWs with these ordering vectors are reduced to classifications of SDWs on molecules with D 3 and T d symmetries, respectively. From this reduction the authors found two axial-type ASDWs (ASDW) and one plane-type SDW (PSDW) for point K and three ASDWs, two PSDWs and one cubic- (three-dimensional-) type SDW (CSDW) for point M. The standard mean-field Hamiltonians and their invariance groups are listed for each class.
Magnetic structures of the two-dimensional Hubbard model on a uniform triangular lattice are investigated from the viewpoint of quantum fluctuations. First, possible spin density wave (SDW) solutions in the unrestricted Hartree-Fock approximation are group theoretically classified for the ordering vectors of Q1=(Ga+Gb)/4, Q2=C3+Q1, and ${\mathbf{Q}}_{3}={C}_{3}^{\ensuremath{-}}{\mathbf{Q}}_{1}$. Then, to include the electron correlation effects efficiently, we apply the resonating Hartree-Fock method. It is shown that the spin fluctuations in the metallic ground state at $U/t\ensuremath{\sim}4.5$ are reasonably described as hybridization of two different SDW states obtained by the group theoretical classification and their low-energy excited states. These fluctuations make the long-range magnetic order significantly reduced in the correlated ground state.
This paper describes a group-theoretical classification of the mean-field solutions of the t-J model and the extended t-J model on a planar square lattice. It is shown that the mean-field solutions can be classified into four categories, spin density wave (SDW), charge density wave (CDW), bond order wave (BOW) and charve current wave (CCW) with distinct behavior under spatial inversion, spin rotation and time reversal. We derived systematically all types of broken-symmetry solutions, each of which is characterized by a single order parameter, for the ordering vector q= Q≡(π, π) and those for q= q1≡(π, 0). It is shown that for the t-J model there are four states (flux, Peierls, kite and SDW) with q= Q and six states (two CDWs, two BOWs and two CCWs) with q= Q and six states (two CDWs, two BOWs and two CCWs) with q= q1. For the t-J-J′ model including next-nearest-neighbour Heisenberg coupling, other four states (one CDW, one BOW and two CCWs) with q= Q and seven states (three SDWs, two BOWs and two CCWs) with q= q1 are possible. These phases are derived naturally from the irreducible spectral decomposition of the Σ JSiSj term and the self-consistent condition of the renormalized mean-field theory. The role of local SU(2) symmetry present at half filling is also discussed.
This paper describes a group-theoretical classification of the mean-field solutions of the t-J model and the extended t-J model on a planar square lattice. It is shown that the mean-field solutions can be classified into four categories, spin density wave (SDW), charge density wave (CDW), bond order wave (BOW) and charve current wave (CCW) with distinct behavior under spatial inversion, spin rotation and time reversal. We derived systematically all types of broken-symmetry solutions, each of which is characterized by a single order parameter, for the ordering vector q= Q≡(π, π) and those for q= q1≡(π, 0). It is shown that for the t-J model there are four states (flux, Peierls, kite and SDW) with q= Q and six states (two CDWs, two BOWs and two CCWs) with q= Q and six states (two CDWs, two BOWs and two CCWs) with q= q1. For the t-J-J′ model including next-nearest-neighbour Heisenberg coupling, other four states (one CDW, one BOW and two CCWs) with q= Q and seven states (three SDWs, two BOWs and two CCWs) with q= q1 are possible. These phases are derived naturally from the irreducible spectral decomposition of the Σ JSiSj term and the self-consistent condition of the renormalized mean-field theory. The role of local SU(2) symmetry present at half filling is also discussed.
This paper describes group theoretical classification of superconducting states (SC) in the extended Hubbard model with on-site repulsion (U), nearest neighbor attraction (V) and nearest neighbour exchange interaction (J) on the two-dimensional square lattice using the mean field approach. By decomposing the pairing interaction into irreducible parts; A1g, B1g and Eu of D4h point symmetry, we have derived two singlet SCs (s-wave and d-wave) from A1g and B1g, eight triplet SCs from Eu. The first three types of triplet SC have pairing by electrons with antiparallel spin, the second two types have pairing by electrons with equal spin and the last three types are non-unitary and have pairing by only up-spin electrons. We showed that three non-unitary states have to be accompanied with a ferromagnetic order from the structure of the maximal little groups. We performed numerical studies for these SCs. For parameters and electron density favorable for the ferromagnetic order, a non-unitary SC coexistent with ferromagnetism is most stable.
We consider a system of 2D fermions on a triangular lattice with well separated electron and hole pockets of similar sizes, centered at certain high-symmetry points in the Brillouin zone. We first analyze Stoner-type spin-density-wave (SDW) magnetism. We show that SDW order is degenerate at the mean-field level. Beyond mean-field, the degeneracy is lifted and is either ${120}^{\ensuremath{\circ}}$ ``triangular'' order (same as for localized spins), or a collinear order with antiferromagnetic spin arrangement on two-thirds of sites, and nonmagnetic on the rest of sites. We also study a time-reversal symmetric directional spin bond order, which emerges when some interactions are repulsive and some are attractive. We show that this order is also degenerate at a mean-field level, but beyond mean-field the degeneracy is again lifted. We next consider the evolution of a magnetic order in a magnetic field starting from an SDW state in zero field. We show that a field gives rise to a canting of an SDW spin configuration. In addition, it necessarily triggers the directional bond order, which, we argue, is linearly coupled to the SDW order in a finite field. We derive the corresponding term in the free energy. Finally, we consider the interplay between an SDW order and superconductivity and charge order. For this, we analyze the flow of the couplings within parquet renormalization group (pRG) scheme. We show that magnetism wins if all interactions are repulsive and there is little energy space for pRG to develop. However, if system parameters are such that pRG runs over a wide range of energies, the system may develop either superconductivity or an unconventional charge order, which breaks time-reversal symmetry.
Systems of fermions described by the three-dimensional (3D) repulsive Hubbard model on a cubic lattice have recently attracted considerable attention due to their possible experimental realization via cold atoms in an optical lattice. Analytical and numerical results are limited away from half-filling. We study the ground state of the doped system from weak to intermediate interaction strengths within the generalized Hartree-Fock approximation. The exact solution to the self-consistent-field equations in the thermodynamic limit is obtained and the ground state is shown to exhibit antiferromagnetic order and incommensurate spin-density waves (SDW). At low interaction strengths, the SDW has unidirectional character with a leading wavevector along the [100]-direction, and the system is metallic. As the interaction increases, the system undergoes a simultaneous structural and metal-to-insulator transition to a unidirectional SDW state along the [111]-direction, with a different wavelength. We systematically determine the real and momentum space properties of these states. The crossover from 3D to two dimensions (2D) is then studied by varying the inter-plane hopping amplitude, which can be experimentally realized by tuning the distance between a stack of square-lattice layers. Detailed comparisons are made between the exact numerical results and predictions from the pairing model, a variational ansatz based on the pairing of spins in the vicinity of the Fermi surface. Most of the numerical results can be understood quantitatively from the ansatz, which provides a simple picture for the nature of the SDW states.