Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δ_cr = 0.251 for U = ∞ and a critical coupling of U_cr = 77.7t. Both values improve previous variational results considerably.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice

The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δ_cr = 0.29 and we obtain an estimate of U_cr = 63 t for the critical coupling which is considerably better than the best estimate of U_cr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for S _z = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. Received 1st August 2000 and Received in final form 22 December 2000     

Quantum spin liquid near Mott transition with fermionized π-vortices

In this paper, we study the non-magnetic insulator state near Mott transition of 2D π-flux Hubbard model on square lattice and find that such non-magnetic insulator state is quantum spin liquid state with nodal fermionic excitations – nodal spin liquid (NSL). When there exists small easy-plane anisotropic energy, the ground state becomes Z ₂ topological spin liquid (TSL) with full gapped excitations. The U(1) × U(1) mutual-Chern-Simons (MCS) theory is obtained to describe the low energy physics of NSL and TSL.     

State vector evolution localized over the edges of a square tight-binding lattice

We study the time evolution of a state vector in a square tight-binding lattice, focusing on its evolution localized over the system surfaces. In this tight-binding lattice, the energy of atomic orbital centred at surface site is different from that at the interior (bulky) site by an energy shift U. It is shown that for the state vector initially localized on a surface, there exists an exponential law (y=a\e^x/b+y₀) determined by the absolute value of the energy shift, |U|, which describes the transition of the state evolving on the square tight-binding lattice, from delocalized over the whole lattice to localized over the surfaces.     

Influence of spin fluctuations in the ground state on the coherent motion of holes in high-T c superconductors

The coherent two-dimensional motion of a hole generated in a high-T _c superconductor at half-filling is discussed. The system is described by thet-J model which reduces to the Heisenberg antiferromagnet (HAF) at half-filling. Special attention is payed to the influence of spin fluctuations in the ground state on the hole motion. Spin fluctuations can be considered as deviations of the true ground state of the Heisenberg antiferromagnet from the Néel state. The calculations are based on the introduction of a new trial wave function. It generalizes a wave function which was originally proposed by Shraiman and Siggia for the hole motion in the Néel state. As a result, we find that the excitation energy for the hole has a bandwidth which is reduced by a factor 0.7 as compared to the case without spin fluctuations. Moreover, the dispersion relation contains cubic harmonics which are due to effective hopping processes to more distant than second-or third-nearest neighbors. For larger values of the ratiot/J the band is substantially deformed. We compare our theory with results obtained from the exact diagonalization of finite clusters and find good agreement.     

Theory of a single Oxygen hole propagating in Sr2CuO2Cl2: the spin of the quasiparticles in CuO2 planes

Recent photoemission experiments have measured E vs. k for a single hole propagating in antiferromagnetically aligned Sr₂CuO₂Cl₂. Comparisons with (i) the t - t′ - J model, for which the carrier is a spinless vacancy, and (ii) a strong-coupling version of the three-band Emery model, for which the carrier is a S = 1/2 hole moving on the Oxygen sublattice, have demonstrated that if one wishes to describe the quasiparticle throughout the entire first Brillouin zone the three-band model is superior. Here we present a new variational wave function for a single Oxygen hole in the three-band model: it utilizes a classical representation of the antiferromagnetically ordered Cuspin background but explicitly includes the quantum fluctuations of the lowest energy doublet of the Cu-O-Cu bond containing the Oxygen hole. We find that this wave function leads to a quasiparticle dispersion for physical exchange and hopping parameters that is in excellent agreement with the measured ARPES data. We also obtain the average spin of the Oxygen hole, and thus deduce that this spin is only quenched to zero at certain wave vectors, helping to explain the inadequacy of the t - t′ - J model to match the experimentally observed dispersion relation everywhere in the first Brillouin zone.     

Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ ₁+λ ₂=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ ₁+λ ₂=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.     

Infrared conductivity from spin and charge density waves: (TMTSF) 2X

Infrared conductivity from an incommensurate spin density wave occurs due to even-order charge density wave harmonics which interact with the host lattice. Phonon states within the density-wave-induced energy gap for single-particle excitations lead to conductivity much different from that of an incommensurate charge density wave including counter-ion ordering. The conductivity expected for relaxed and quenched states of (TMTSF)₂ClO₄ is discussed.     

Electronic structures of the zinc-blende GaN/Ga1−xAlxN compressively strained superlattices and quantum wells

The electronic structures of the zinc-blende GaN/Ga_0.85Al_0.15N compressively strained superlattices and quantum wells are investigated using a 6×6 Hamiltonian model (including the heavy hole, light hole and spin-orbit splitting band). The energy bands, wavefunctions and optical transition matrix elements are calculated. It is found that the light hole couples with the spin-orbit splitting state even at thek=0 point, resulting in the hybrid states. The heavy hole remains a pure heavy hole state atk=0. The optical transitions from the hybrid valence states to the conduction states are determined by the transitions of the light hole and spin-orbit splitting states to the conduction states. The transitions from the heavy hole, light hole and spin-orbit splitting states to the conduction states obey the selection rule Δn=0. The band structures obtained in this work will be valuable in designing GaN/GaAlN based optoelectronic devices.     

Saturation recovery electron spin–lattice relaxation studies on benzene anion radical and its derivatives: application of Kivelson–Orbach mechanism of electron spin relaxation

The role of low-lying excited states on the spin–lattice relaxation times (T₁) of organic radicals has been investigated. To test the applicability of Kivelson's electric field fluctuation model (D. Kivelson, J. Chem. Phys. 45, 1324 (1966)), based on the Orbach mechanism of spin relaxation, the T₁s of the anion radicals of benzene, benzene-1-d, toluene, ethyl benzene, isopropyl benzene, t-butyl benzene, p-xylene, 1,2,4-trimethyl benzene and 1,3,5-trimethyl benzene in liquid solutions, with potassium cation as the counter ion, have been measured by the pulse saturation recovery technique. The energy gap between the ground and the first excited electronic states changed with the substitutions to different extent. The spin–lattice relaxation rates showed correlation with this energy gap. Anion radicals of benzene and benzene-1-d showed the shortest T₁ among the radicals studied here. A small but measurable energy splitting due to the deuterium substitution in benzene-1-d radical was obtained from the temperature dependence of T₁. Spin–lattice relaxation times of benzene anion measured here decreased monotonically in the range of ?60 to ?125 °C, in contrast to some reported claims of very unusual temperature dependence, based on the continuous wave microwave power saturation studies. Our results also showed that the ion pairing between benzene anion and potassium cation did not significantly influence the spin–lattice relaxation times.     

Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions [A.M. Frolov, Phys. Lett. A 374, 2361 (2010)] is used for variational computations of bound states in three-electron atomic systems. It appears that the semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than was originally anticipated. In particular, the 40-term Larson’s wave function improved with the use of semi-exponential radial basis functions now produces the total energy –7.4780581457 a.u. for the ground 1²S-state in the ^￥Li^\infty{\rm Li} atom (only one spin function c₁\chi_1 = aba\alpha\beta\alpha - baa\beta\alpha\alpha was used in these calculations). This variational energy is very close to the exact ground state energy of the ^￥Li^\infty{\rm Li} atom and is substantially lower than the total energy obtained with the original Larson’s 40-term wave function (–7.477944869 a.u.).     

Low temperature thermodynamical properties of the organic chain conductor (TMTSF)AsF

We report on specific heat measurements of the quasi-one-dimensional organic salt (TMTSF)₂AsF₆ in its spin density wave state between 75 mK and 7 K. Similarly to (TMTSF)₂PF₆, we find discontinuities in the lattice contribution at 1.9 K an d 3.5 K ascribed to sub-spin density wave phases. Time-dependent effects due to dynamics of low-energy excitations in metastable states occur only below 0.2 K which yields an activation energy for the equilibrium energy relaxation process of 0.34 K, 4-5 times smaller than found for (TMTSF)₂PF₆. Finally the reduction of the low-energy excitations contribution to the specific heat in comparison to PF₆ reveals an intermediate cubic-like regime between 0.25 and 0.5 K that we tentatively describe as the phason contribution of the incommensurate spin density wave modulation. Received: 17 March 1998 / Revised: 27 July 1998 / Accepted: 22 September 1998     

Benzoic acid and phenol derivatives of nitronyl nitroxide biradical as building blocks of organic molecule-based ferrimagnets

A crystal-engineering approach to organic ferrimagnets is reported. Coulombic energy between an anionic biradical withS = 1 and a cationic monoradical withS = 1/2 can be utilized as a driving force of cocrystallization of open-shell molecules with different spin quantum numbers, leading to organic salt ferrimagnets. In this study, 3,5-substituted phenol and benzoic acid derivatives of nitronyl nitroxide biradicals were synthesized as an ionizableS = 1 component of organic salt ferrimagnets. The molecular ground states of the biradicals in the neutral state were examined by continuous wave electron spin resonance (ESR) spectroscopy and static paramagnetic susceptibility measurements in the solid state. The molecular ground state of the phenol derivative was found to be triplet (S = 1) with the singlet-triplet energy gap of ΔE/k_B ≈ 25 K, indicating that the biradical can be a building block of organic salt ferrimagnetics. The benzoic acid derivative was found to have a singlet (S = 0) ground state (ΔE/k_B ≧ −5 K), exemplifying thatmeta-(3,5)-linkage of unpaired electrons in π-aromatic rings does not necessarily give a triplet ground state for heteroatomic-substituted π conjugation. The molecular ground states of the biradicals determined in the ESR experiments were confirmed by the susceptibility in the solid state.     

Molecular dynamics study for the thermal conductivity of diatomic liquid

The thermal conductivity of diatomic liquids was analyzed using a nonequilibrium molecular dynamics (NEMD) method. Five liquids, namely, O₂, CO, CS₂, Cl₂ and Br₂, were assumed. The two-center Lennard-Jones (2CLJ) model was used to express the intermolecular potential acting on liquid molecules. First, the equation of state of each liquid was obtained using MD simulation, and the critical temperature, density and pressure of each liquid were determined. Heat conduction of each liquid at various liquid states [metastable (ρ=1.9ρ_cr), saturated (ρ=2.1ρ_cr), and stable (ρ=2.3ρ_cr)] at T=0.7T_cr was simulated and the thermal conductivity was estimated. These values were compared with experimental results and it was confirmed that the simulated results were consistent with the experimental data within 10%. Obtained thermal conductivities at saturated state were reduced by the critical temperature, density and mass of molecules and these values were compared with each other. It was found that the reduced thermal conductivity increased with the increase in the molecular elongation. Detailed analysis of the molecular contribution to the thermal conductivity revealed that the contribution of the heat flux caused by energy transport and by translational energy transfer to the thermal conductivity is independent of the molecular elongation while the contribution of the heat flux caused by rotational energy transfer to the thermal conductivity increases with the increase in the molecular elongation. Moreover, by comparing the reduced thermal conductivity at various states, it was found that the increase of thermal conductivity with the increase in the density, or pressure, was caused by the increase of the contribution of energy transfer due to molecular interaction.