The Scaling Limit of the Critical One-Dimensional Random Schrödinger Operator

We consider two models of one-dimensional discrete random Schrödinger operators

$(H_n\psi)_\ell =\psi_{\ell -1}+\psi_{\ell +1}+v_\ell \psi_\ell$

, \({\psi_0=\psi_{n+1}=0}\) in the cases \({ v_k=\sigma \omega_k/\sqrt{n}}\) and \({ v_k=\sigma \omega_k/ \sqrt{k}}\) . Here ω _k are independent random variables with mean 0 and variance 1.

We show that the eigenvectors are delocalized and the transfer matrix evolution has a scaling limit given by a stochastic differential equation. In both cases, eigenvalues near a fixed bulk energy E have a point process limit. We give bounds on the eigenvalue repulsion, large gap probability, identify the limiting intensity and provide a central limit theorem.In the second model, the limiting processes are the same as the point processes obtained as the bulk scaling limits of the β-ensembles of random matrix theory. In the first model, the eigenvalue repulsion is much stronger.     

Fermionic Concurrence in the Extended Hubbard Model

We study the fermionic concurrence in an extended Hubbard model. Its behaviour at the ground state and at finite temperatures for general U and V is obtained numerically and analytically for a dimer system. We also investigate the properties of the concurrence under a nonuniform field, and we find that it can be used to modulate and to increase the concurrence.     

Block Entanglement in the Single-Hole Hubbard Model

We investigate the distribution of the entanglement of the one-dimensional single-hole Hubbard model （HM） and study the relationship between the entanglement and quantum phase transition in the model. The von Neumann entropy of a block with neighbouring spins L for a single-hole HM is calculated using the densitymatrix renormalization group. The distributions of the entanglement entropy in the ground state, as a function of block length, show a dramatic effect, i.e. effectively decoupling with the centres, no matter how the Coulomb interaction u 〉0 or u 〈0. Contrarily, for the Coulomb interaction u = 0 or close to zero, the entanglement entropy in the single-hole model reaches a saturation value for a certain block size. For a fixed size L = 40, the ground state entanglement entropy measure, as a function of u1 shows a peak corresponding to the critical quantum phase transition.     

The pairing correlations in the phased t－U Hubbard model

In this paper we have studied the phased t－U Hubbard model. Using the constrained path Monte Carlo method, we investigated the effects of phase factor on pairing correlation functions in the ground state, and we found that the long-range correlations are dependent on the choice of phase factor, and for some special values of phase factor there exist long-range pairing correlations only in the strong coupling region.     

Phase Diagram of the BCS–Hubbard Model in a Magnetic Field

We propose an extended BCS–Hubbard model and investigate its ground state phase diagram in an external magnetic field. By mapping the model onto a model of spinless fermions coupled with conserving Z₂ variables which are mimicked by pseudospins, the model is shown to be exactly solvable along the symmetric lines for an arbitrary on-site Hubbard interaction on the bipartite lattice. In the zero field limit, the ground states exhibit an antiferromagnetic order of pseudospins. In the lar...     

The Critical Properties of One—Dimensional Extended Hubbard Model

In the framework of nonperturbative quantum field theory,the critical phenomena of one-dimensional extended Hubbard model (EHM) at half-filling are discussed from weak to intermediate interactions.After the EHM being mapped into two decoupled sine-Gordon models,the ground state phase diagram of the system is derived in an explicit way.It is confirmed that the coexisting phases appear in different interaction regimes which cannot be found by conventional theoretical methods.The diagram shows that there are seven different phase regions in the ground state,which seems not to be the same as previous discussions,especially the boundary between the phase separation and condensed phase regions.The phase transition properties of the model between various phase regions are studied in detail.     

Exact Solution of the Infinite-Range-Hopping Bose–Hubbard Model

The thermodynamic behavior of the Bose–Hubbard model is solved for any temperature and any chemical potential. It is found that there is a range of critical coupling strengths _c1 < _c2 < _c3 < in this model. For coupling strengths between _c,k and _c,k+1, Bose–Einstein condensation is suppressed at densities near the integer values = 1,...,k with an energy gap. This is known as a Mott insulator phase and was previously shown only for zero temperature. In the context of ultra-cold atoms, this phenomenon was experimentally observed in 2002(1) but, in the Bose–Hubbard model, it manifests itself also in the pressure-volume diagram at high pressures. It is suggested that this phenomenon persists for finite-range hopping and might also be experimentally observable.     

The Energy Spectrum and Optical Properties of Fullerene С36 within the Hubbard Model

Optics and Spectroscopy - The anticommutator Green’s functions and the energy spectra of fullerene С36 and endohedral fullerene La@C36, with both of them belonging to the D6h symmetry...     

The Energy Spectrum and the Optical Absorption Spectrum of С36 Fullerene Within the Hubbard Model

Russian Physics Journal - Using the Hubbard model in an approximation of static fluctuations, analytical relations of anticommutator Green’s functions and energy spectra of С36...     

The B-B′-U Hubbard model in the approximation of static fluctuations

Within the approximation of static fluctuations, the effect of allowing for electron transport from a given site to the second-nearest neighboring site on the energy spectrum of the two-sublattice two-dimensional Hubbard model and on the dependence of the magnetization on the system parameters is investigated. Fiz. Tverd. Tela (St. Petersburg) 41, 951–956 (June 1999)     

Analysis of Polaron Band Formation with the One-Dimensional Holstein Model

We present an analytic result of the polaronic band structure by using the one-dimensional Holstein model on an infinite lattice. The single-phonon effect is used to investigate the ground state properties, such as the polaronic band structure, ground state energy, phonon distribution and effective mass, which agree with the numerical and analytic results obtained recently in the region from the weak coupling to the intermediate coupling.     

Small Denominators and Anomalous Behaviour in the Incommensurate Hubbard–Holstein Model

We consider a system of interacting fermions on a chain in a periodic potential incommensurate with the chain spacing. We derive a convergent perturbative expansion, afflicted by a small denominator problem and based on renormalization group, for the two point Schwinger function. We obtain the large distance behavior of the Schwinger function, which is anomalous and described by critical indices, related to the gap and the wave function renormalization. Received: 20 November 1997 / Accepted: 18 August 1998     

The Langevin Limit of the Nos��-Hoover-Langevin Thermostat

In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the conjugate momentum vector. Numerical experiments with a double well potential corroborate the asymptotic analysis.     

Transition Temperature of Two-Degenerate-Flavour QCD in the Chiral Limit

We present the results for the transition temperature of quantum chromodynamics （QCD） with two degenerate flavours （Nf = 2） of Wilson quarks. On lattice 8^3 × 4 with 4 representing the temporal extent, by using the Ferrenberg-Swendsen reweighting method, we determine the critical β = 6/g^2 where the transition occurs, g is the coupling constant. On lattice 8^2 × 20 × 4, by using the axial vector Ward-Takahashi identity, we calculate the current quark mass amq, a is the lattice spacing. Assuming the O（4） scaling, the critical β in the chiral limit is determined. We calculate the p meson mass amp at zero temperature on lattice 8^3 × 20. By using the experimental p meson mass to set the scale, we obtain 194（1） MeV for the transition temperature in the chiral limit.     

Incommensurate Antiferromagnetism in the Extended t－J Model

The effect of the extra second neighbor hopping t‘ on the incommensurate spin correlation in the t-J model in the underdoped regime is studied within the fermion-spin theory.It is shown that although the extra second neighbor hopping t‘ is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamical spin structure factor,for the physical reasonable small value of t‘ the qualitative behavior of the incommensurate spin correlation in the t-t‘-J model is the same as in the case of t-J model.