Effect of thermal ground state correlations on the statistical properties of the Lipkin model

The renormalized random phase approximation for hot finite Fermi systems is evaluated with the use of the thermo field dynamics formalism. This approximation treats vibrations of a hot finite Fermi system as harmonic ones but takes into account the Pauli principle in a more proper way than the usual thermal RPA, thus incorporating a new type of correlations in a thermal ground state. To demonstrate advantages of the approximation and to analyze a range of its validity, it is applied to the exactly solvable Lipkin model. A comparison is made with the exact grand canonical ensemble calculations, results of the thermal Hartree – Fock approximation and the thermal random phase approximation. The intrinsic energy of the system, the heat capacity, the average value of the quasispin operator z-projection and the particle number variance are calculated as functions of temperature. On the whole, the thermal renormalized RPA appears to be a better approximation than the other two. Its advantage is especially evident in the vicinity of the phase transition point. It is found that within TRRPA the phase transition occurs at lower temperature than in THFA and TRPA. Received: 4 January 1999 / Revised version: 10 March 1999     

Application of a time-dependent density-matrix formalism

An extended time-dependent Hartree-Fock theory which includes the effects of nucleon-nucleon collisions is presented and applied to the small-amplitude quadrupole motions of¹⁶O and⁴⁰Ca. The collision term of the theory includes not only the Born term but also higher-order terms. It is found that the higher-order terms are essential to the damping of the motions.     

The ground state of the two-leg Hubbard ladder a density-matrix renormalization group study

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin liquid to a band insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes from singlet pairs and the pair field and the “4k_F” density correlations associated with pair-density fluctuations decay as power laws, while the “2k_F” charge density wave correlations decay exponentially. We discuss the behavior of the exponents of the pairing and density correlations within this spin-gapped phase. Additional one-band Luttinger liquid phases which occur in the large interband hopping regime are also discussed.     

The Multimomentum hamiltonian formalism in gauge theory

We extend the jet bundle machinery of gauge theory to the multimomentum Hamiltonian formalism. This enables us to manipulate finite-dimensional momentum spaces of fields. In the framework of this formalism, time and spatial coordinates are regarded on the same footing, and a preliminary (3 + 1) splitting of a world manifold is not required. We get the canonical splitting of a multimomentum Hamiltonian form into a connection part and a Hamiltonian density.     

Multimomentum hamiltonian formalism in quantum field theory

The familiar generating functional in quantum field theory fail to be true measures and make sense only in framework of perturbation theory. In our approach, generating functionals are defined strictly as the Fourier transforms of Gaussian measures in nuclear spaces of multimomentum canonical variables when field momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.     

Spin hamiltonian for which the chiral spin liquid is the exact ground state

We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.     

Correlated ground state of the Hubbard model

The variational many-body approach or, more generally, the method of correlated basis functions initiated for a quantitative analysis of strongly interacting quantum fluids may be adapted with minor modifications for exploring the properties of lattice models. This is demonstrated by performing an explicit analysis of the paramagnetic ground state of the Hubbard model. In a first step of the approximation scheme we represent the correlated state by a spin-dependent wave function of Jastrow-type. We analyze in detail the associated density-matrix elements and set up the corresponding Fermi hypernetted-chain equations which determine the irreducible constituents of these quantities. The solutions are discussed and constructed by iteration in terms of cluster approximants. Specializing the input data and the formal results provides a Fermi hypernetted-chain analysis of the correlations induced by a ground state wave function of the Gutzwiller form.     

Ferromagnetic ground state in the Kondo lattice model

We present a series of rigorous examples of the Kondo lattice model that exhibit full ferromagnetism in the ground state. The models are defined in one-, two- and three-dimensional lattices, and are characterized by a range of hopping terms, specific electron filling, and large ferromagnetic coupling. Our examples show that a sufficient strong but finite exchange coupling between conduction electrons and localized spins could overcome the competition from mobility of a finite density of electrons and drive the system from a paramagnetic phase to a ferromagnetic phase. We also establish a relation of ferromagnetism between the Hubbard model and Kondo lattice model. Meanwhile some rigorous results on ferromagnetism in the corresponding Hubbard model are presented. Received: 10 September 1997 / Revised: 15 October 1997 / Accepted: 17 October 1997     

The ground state of the neutral Hubbard model

The ground state energy of the neutral Hubbard model is calculated by BCS methods for all values of total spinS _z . Numerical results are given for the simple cubic and for the body centred cubic lattice. Antiferromagnetic ordering and a finite paramagnetic susceptibility is found for all values of the coupling constantV ₀.     

Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u=U/(4t) and electron density nc. We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u=3.0 and for arbitrary electron density nc. Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.     

An ab-initio derivation of the pi-electron hamiltonian by a nonperturbative open-shell formalism

A method for generating a pi-electron hamiltonian in an ab-initio manner using the non-perturbative open-shell many-body formalism recently developed by us is presented. The π-hamiltonian thus derived is energy-independent, and is also proved to be spin-independent. A recipe is given with the help of which Goldstone—like matrix-elements ofH _π can be extracted up to three body terms. It has been demonstrated that the use of diagrammatics considerably simplifies the algebra and allows one to keep track of the various quantities involved. Up to a given order of approximation, an explicit form ofH _π containing up to the three body terms has been given, and some of the important physical effects embedded in the hamiltonian are discussed. A comparative analysis of the various formalisms currently in use forms the concluding section of the paper.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Features of the polaron ground state in one-dimensional Holstein model

Applying the method of coherent state orthogonal expansion, we expand the trial wave functions of ground state to the third order. We find that the ground state energy of the system decreases with the increase of expansion orders. Especially, at the zeroth order approximation, the probability distribution of the electron at different sites exhibits a soliton peak. However, the probability distribution of the electron at each site becomes identical, when we expand the trial wave functions of ground state to the higher orders. Supported by the Natural Science Foundation of Sichuan Province, China (Grant No. 2006C028)     

The ground state of the three-dimensional random-field Ising model

We prove that the three-dimensional Ising model in a random magnetic field exhibits long-range order at zero temperature and small disorder. Hence the lower critical dimension for this model is two (or less) and not three as has been suggested by some.Junior Fellow, Society of Fellows. Research supported in part by the National Science Foundation under Grant PHY82-03669     

Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed. Received 20 February 2002 / Received in final form 27 May 2002 Published online 17 September 2002     

Spin quantum number in the ground state of the Mattis-Heisenberg model

Total spin quantum number is rigorously calculated for a quantum version of the Mattis model of random spin systems. Crossover between three universality classes of the Ising model, theXY model, and the Heisenberg model is explicitly worked out in the presence of randomness. The randomness of the type of the Mattis model is shown to have no thermodynamic effects even in quantum systems.     

Fourth order ground state energy in the symmetric Anderson model

By evaluating the ground state energy in the symmetric Anderson model to fourth order in U it is demonstrated that graphs other than ladders and bubbles may give equally important contributions. This supports the doubts raised recently by Iche and Zawadowski against the theory of localized spin fluctuations.