An RVB approach to the Hubbard model (original) (raw)
Thermodynamics and excitations of the one-dimensional Hubbard model
Physics Reports, 2000
We review fundamental issues arising in the exact solution of the one-dimensional Hubbard model. We perform a careful analysis of the Lieb-Wu equations, paying particular attention to so-called 'string solutions'. Two kinds of string solutions occur: Λ strings, related to spin degrees of freedom and k-Λ strings, describing spinless bound states of electrons. Whereas Λ strings were thoroughly studied in the literature, less is known about k-Λ strings. We carry out a thorough analytical and numerical analysis of k-Λ strings. We further review two different approaches to the thermodynamics of the Hubbard model, the Yang-Yang approach and the quantum transfer matrix approach, respectively. The Yang-Yang approach is based on strings, the quantum transfer matrix approach is not. We compare the results of both methods and show that they agree. Finally, we obtain the dispersion curves of all elementary excitations at zero magnetic field for the less than half-filled band by considering the zero temperature limit of the Yang-Yang approach.
Journal of Physics: Condensed Matter, 1999
We have studied the Hubbard model with bond-charge interaction on a triangular lattice for a half-filled band. At the point of particle-hole symmetry the model could be analyzed in detail in two opposite regimes of the parameter space. Using a real space renormalization group we calculate the ground state energy and the local moment over the whole parameter space. The RG results obey the exact results in the respective limits. In the intermediate region of the parameter space the RG results clearly show the effects of the non-bipartite geometry of the lattice as well as the absence of symmetry in the reversal of the sign of the hopping matrix element.
Bound States in the One-dimensional Hubbard Model
1998
The Bethe Ansatz equations for the one-dimensional Hubbard model are reexamined. A new procedure is introduced to properly include bound states. The corrected equations lead to new elementary excitations away from half-filling.
Ground state properties of half-filled Hubbard model
Physics Letters A, 1997
Using the symmetry properties and known exact results on the Hubbard model on a bipartite lattice, we show that at half-filling and for periodic boundary conditions, the ground state has a definite value of the total momentum according to the number of lattice sites both for negative and positive II. @ 1997 Elsevier Science B.V.
Physical Review B, 1990
A resonating-valence-bond (RVB) wave function for the triangular lattice is constructed by following the renormalized Hamiltonian approach (or Gutzwiller approximation) successfully developed for the square lattice. This wave function is then used to ca1culate the ground-state energy by using the variational Monte Carlo method. Comparison with results of other trial wave functions is discussed. Energy of this paramagnetic RVB state is not as low as other antiferromagnetically ordered wave functions. A flux-phase state similar to the RVB state is also presented. This state with one-quarter flux quantum per plaquette breaks time-reversal symmetry.
MAGNETIC COUPLINGS IN THE HUBBARD MODEL
The half-filled Hubbard model can be analyzed in terms of quasi-electron and spin wave excitations; the latter are described by í µí°» í µí°» = − 1 2 ∑ í µí°½ í µí±í µí± í µí°» í µí½ í µí² í µí½ í µí² í µí±í µí± The quantities J mn were calculated and the resulting thermodynamic quantities in the one-dimensional (1D) case are in very good agreement with exact results. We outline here our approximate treatment of the Hubbard [1] hamiltonian, í µí°» ̂ = ∑ ∈ 0 í µí± ̂ í µí±í µí¼ í µí±í µí¼ + ∑ í µí± í µí±í µí±í µí¼ í µí±í µí±í µí¼ í µí»¼ í µí±í µí¼ + í µí± í µí±í µí¼ + í µí± ∑ í µí± ̂ í µí±↑ í µí± ̂ í µí°½↓ í µí± and we summarize our results. For simplicity we take V jjΣ equal to a constant V when the lattice sites i,j are nearest neighbors and zero otherwise. The unperturbed (U= 0) half bandwidth B is proportional to V; e.g. when the site {i} forms a simple cubic lattice B = 6V. In the binary, self-consistent, static approximation (see, e.g., Cyrot's [2] work) one replaces the term í µí±í µí± ̂ í µí±↑ í µí± ̂ í µí± ↓ by í µí± í µí±í µí¼ í µí± ̂ í µí±í µí¼ ; e iς is a random variable which takes the values U(n-μ)/2 and U(n + μ)/2 each with probability 1 2 ;n is the average number of electrons per site and μ is a quantity to be determined self-consistently by the condition í µí¼ = 〈í µí± ̅ í µí±↑ 〉 í µí±= í µí±¢ − 〈 í µí± ̅ í µí± ↓ 〉 í µí± =í µí±¢ where the bar indicates quantum mechanical average and 〈 〉 í µí±= í µí±¢ denotes configurational average under the condition thatí µí± í µí±↑ = U(n — μ)/2 and í µí± í µí±↓ = U(n + μ)/2.. The quantity μ can be interpreted as the magnitude of a local moment, which can take two values ±μ. We call ρ(E) the average density of states corresponding to the effective hamiltonian resulting from the substitution of í µí±í µí± ̂ í µí±↑ í µí± ̂ í µí±↓ by í µí± í µí±í µí¼ í µí± ̂ í µí± í µí¼ .
Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
Physical Review B, 2002
We use a stochastic series expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half filling for small to intermediate values of the on-site (U) and nearest-neighbor (V) repulsions. We confirm the existence of a novel, long-rangeordered bond-order-wave (BOW) phase recently predicted by Nakamura (J. Phys. Soc. Jpn. 68, 3123 (1999)) in a small region of the parameter space between the familiar charge-density-wave (CDW) state for V U/2 and the state with dominant spin-density-wave (SDW) fluctuations for V U/2. We discuss the nature of the transitions among these states and evaluate some of the critical exponents. Further, we determine accurately the position of the multi-critical point, (Um, Vm) = (4.7±0.1, 2.51±0.04) (in energy units where the hopping integral is normalized to unity), above which the two continuous SDW-BOW-CDW transitions are replaced by one discontinuous (first-order) direct SDW-CDW transition. We also discuss the evolution of the CDW and BOW states upon hole doping. We find that in both cases the ground state is a Luther-Emery liquid, i.e., the spin gap remains but the charge gap existing at half-filling is immediately closed upon doping. The charge and bond-order correlations decay with distance r as r −Kρ , where Kρ is approximately 0.5 for the parameters we have considered. We also discuss advantages of using parallel tempering (or exchange Monte Carlo)-an extended ensemble method that we here combine with quantum Monte Carlo-in studies of quantum phase transitions.
Motivated by Mo 3 S 7 (dmit) 3 , we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second-order perturbation theory, that in the molecular limit, the ground state and the low-energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry-protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangular necklace lattice at two-thirds filling is captured by the ferromagnetic Hubbard-Kondo lattice chain at half-filling. This is consistent with and strengthens previous claims that both the half-filled ferromagnetic Kondo lattice model and the two-thirds filled Hubbard model on the triangular necklace lattice are also in the Haldane phase. A connection between Hund's rules and Nagaoka's theorem is also discussed.