Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U _c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U _m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U _c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.     

Three-dimensional folding of the triangular lattice

We study the folding of the regular triangular lattice in three-dimensional embedding space, a model for the crumpling of polymerised membranes. We consider a discrete model, where folds are either planar or form the angles of a regular octahedron. These “octahedral” folding rules correspond simply to a discretisation of the 3d embedding space as a Face Centred Cubic lattice. The model is shown to be equivalent to a 96-vertex model on the triangular lattice. The folding entropy per triangle ln q_3d is evaluated numerically to be q_3d = 1.43(1). Various exact bounds on q_3d are derived.     

Supersolid hard-core bosons on the triangular lattice

We determine the phase diagram of hard-core bosons on a triangular lattice with nearest-neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities rho<1/3 or rho>2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3相似文献   

Cluster-variation method for the triangular lattice gas

A triangular lattice gas with nearest-neighbor repulsions and three-particle attractions is examined in a three-sublattice triangle approximation as a model for lithium intercalation in the transition metals dichalcogenides. Order-disorder phase diagrams and thermodynamic functions are computed. Some peaks in the incremental capacity as function of concentration in the experimental data of Thompson are reproduced in our model.     

Laplacian roughening on a triangular lattice

Monte Carlo simulation of the laplacian roughening model on a triangular lattice indicates that the model has a single first-order phase transition.     

Variational wave-function study of the triangular lattice supersolid

We present a variational wave function which explains the behavior of the supersolid state formed by hard-core bosons on the triangular lattice. The wave function is a linear superposition of only and all configurations minimizing the repulsion between the bosons (which it thus implements as a hard constraint). Its properties can be evaluated exactly--in particular, the variational minimization of the energy yields (i) the surprising and initially controversial spontaneous density deviation from half-filling (ii) a quantitatively accurate estimate of the corresponding density wave (solid) order parameter.     

Singlet and triplet bipolarons on the triangular lattice

We study the Coulomb-Fröhlich model on a triangular lattice, looking in particular at states with angular momentum. We examine a simplified model of crab bipolarons with angular momentum by projecting onto the low energy subspace of the Coulomb-Fröhlich model with large phonon frequency. Such a projection is consistent with large long-range electron-phonon coupling and large repulsive Hubbard U. Significant differences are found between the band structure of singlet and triplet states: The triplet state (which has a flat band) is found to be significantly heavier than the singlet state (which has mass similar to the polaron). We test whether the heavier triplet states persist to lower electron-phonon coupling using continuous time quantum Monte Carlo (QMC) simulation. The triplet state is both heavier and larger, demonstrating that the heavier mass is due to quantum interference effects on the motion. We also find that retardation effects reduce the differences between singlet and triplet states, since they reintroduce second order terms in the hopping into the inverse effective mass.     

The bond bending model on triangular lattice and square lattice

The bond bending model is studied using the series expansion method on a triangular lattice and on a square lattice. The elastic splay susceptibility χ_SR and the elastic compressional susceptibility χ_el are calculated up to 11th order for the triangular lattice and up to 14th order for the square lattice. The elastic splay crossover exponent, ζ_SP, is found to be ζ_SP ≈ 1.26 ± 0.05 for the triangular lattice and ζ_SP = 1.30 ± 0.04 for the square lattice which is close to the conductivity exponent, ζ_Re, of the resistor network. From the scaling relation ? _B = dv + ζ_SP, we found that the bulk modulus exponent ? _B = 3.93 ± 0.05 for the triangular lattice and ? _B = 3.97 ± 0.04 for the square lattice which is in good agreement with the result ? _B = 3.96 ± 0.04, obtained by Zabolitzky et al. using a transfer matrix technique on a honeycomb lattice.     

The effect of lattice strain and antiferromagnetism on superconducting gap in cuprates

The doping of the parent insulating cuprate systems destroys long range antiferromagnetic order and develops superconductivity accompanied by Jahn–Teller type lattice distortion in copper 3d electrons in CuO₂ plane. In the present communication, we propose a microscopic model to study the interplay of these long range orders. The superconducting gap (Δ), staggered magnetic field (h) and lattice strain (e) are calculated from the Green’s functions and solved self-consistently for different sets of model parameters of the system. Finally the temperature dependent density of states helps to calculate the magnitudes of the order parameters.     

Odd-frequency superconductivity on quasi-one-dimensional triangular lattice in the Hubbard model

We study the superconductivity in the Hubbard model on quasi-one-dimensional triangular lattice using random phase approximation (RPA). We find that odd-frequency spin-singlet p-wave pairing can be realized on isosceles quasi-one-dimensional triangular lattice.     

三角晶格磁振子晶体带结构的优化研究

用平面波展开法数值计算了椭圆柱散射体正三角排列的二维磁振子晶体带结构.结果显示,同样的填充率下,带隙的宽度和中心频率随着椭圆两半径之比s的变化出现明显的变化,椭圆柱散射体在三角晶格中可以打开低频带隙或使低频带隙加宽.     

Ground states of a classical triangular lattice

The energies and displacements of a triangular lattice with nearest and next-nearest neighbor interaction are calculated for the groundstates. A nonlinear onsite potential acts perpendicular to the plane. Structures with low periodicity determine the various states in the parameter space. The stability of the different phases is investigated.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Site dilution in the fully frustrated triangular lattice in two dimensions

The Transfermatrix-Method [1, 2] has been adapted to evaluate also the free energy of triangular 2–d-Ising lattices. The present work considers a model with nearest-neighbour antiferromagnetic couplings and a fraction 1–x of spins removed at random sites leading to some frustration effects. It is not yet clear if such a system shows spinglass behaviour [3, 4]. The correlation function s ₀ s _R ² (correlation between two spins with distanceR), which is related to the Edwards-Anderson-Orderparameter, shows such a fast breakdown with distanceR that there is a clear evidence against a phase transition at finiteT. In contrast to other models [1, 2, 5] we still expect an exponential decay of {s ₀ s _R ²} _av with distanceR atT=0.     

RVB theory of the Hubbard model on the triangular lattice

We propose a Green's function technique, to investigate finite-temperature properties of the Hubbard model on the triangular lattice. The lattices are covered by dimers. The method is exact in two limits:U=0 or decoupled dimers. We apply this approximate method to calculate the ground state energy, the specific heat and the single-particle spectral weight for the 1/2-filled case. The largest lattice considered has 16×16 sites. The approximate ground state energy as a function of the on-site interactionU oscillates around the exact energyin the 1/2-filled case. We find two peaks in the specific heat. ForU5t the single-particle spectral weight splits into upper and lower Hubbard bandasymmetrically. Thus in the 1/2-filled case the chemical potential is placed in the upper band leading to a metallic state. The approximate technique yields a finite zero-point entropy for mediumU. All the investigations signal a RVB state in the range of mediumU as formerly proposed by Callaway.     

The dissociated properties of dislocation in two-dimensional triangular lattice

The dissociated core structure of dislocation in two-dimensional triangular lattice is determined by the variational method within lattice theory. The dissociation effect leads to a narrower core width of partial dislocations than the compact one. The equilibrium separation between two partial dislocations is not very sensitive to the intrinsic stacking fault energy and there exists deviation from the intrinsic stacking fault energy criterion in the continuous elastic theory of dislocation. The relationship between the equilibrium separation and intrinsic stacking fault energy is analogous in lattice theory and the Peierls-Nabarro model. But the equilibrium separation obtained in lattice theory is wider than that obtained in the Peierls-Nabarro model for the same intrinsic stacking fault energy.      

Muon spin relaxation in diluted triangular‐lattice antiferromagnet

Zero and longitudinal field μSR measurements on diluted triangular‐lattice antiferromagnet LuFeMgO₄ have revealed gradual and highly anisotropic slowing‐down of spin fluctuation. Relaxation rate \lambda in the condition with initial muon spins perpendicular to the hexagonal c‐plane shows divergent behavior while that in the parallel configuration remains finite. At certain temperature range the fluctuation of spins is suppressed by a small external magnetic field. Monte Carlo calculation suggests that the correlation time for z(c)‐component of spins diverges first on cooling. This revised version was published online in July 2006 with corrections to the Cover Date.