Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Δ in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Δ on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N _a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)_c for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)_c=0.300±0.005, agrees with the value (t/U)_c=0.304±0.002 obtained previously by the combined “exact diagonalization + renormalization-group analysis” method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Δ∼exp[−b(1−t/t _c)^−1/2]. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 92–96 (25 July 1996)     

Running coupling: does the coupling between dark energy and dark matter change sign during the cosmological evolution?

In this paper we put forward a running coupling scenario for describing the interaction between dark energy and dark matter. The dark sector interaction in our scenario is free of the assumption that the interaction term Q is proportional to the Hubble expansion rate and the energy densities of dark sectors. We only use a time-variable coupling b(a) (with a the scale factor of the universe) to characterize the interaction Q. We propose a parametrization form for the running coupling b(a)=b ₀ a+b _e (1−a) in which the early-time coupling is given by a constant b _e , while today the coupling is given by another constant, b ₀. For investigating the feature of the running coupling, we employ three dark energy models, namely, the cosmological constant model (w=−1), the constant w model (w=w ₀), and the time-dependent w model (w(a)=w ₀+w ₁(1−a)). We constrain the models with the current observational data, including the type Ia supernova, the baryon acoustic oscillation, the cosmic microwave background, the Hubble expansion rate, and the X-ray gas mass fraction data. The fitting results indicate that a time-varying vacuum scenario is favored, in which the coupling b(z) crosses the noninteracting line (b=0) during the cosmological evolution and the sign changes from negative to positive. The crossing of the noninteracting line happens at around z=0.2–0.3, and the crossing behavior is favored at about 1σ confidence level. Our work implies that we should pay more attention to the time-varying vacuum model and seriously consider the phenomenological construction of a sign-changeable or oscillatory interaction between dark sectors.     

Bounds on the Minimal Energy of Translation Invariant N-Polaron Systems

For systems of N charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fröhlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U > 0 and α > 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition ${\sqrt{2}\alpha < U}For systems of N charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fr?hlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U > 0 and α > 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition ?2a < U{\sqrt{2}\alpha < U}, which follows from the dependence of U and α on electrical properties of the crystal. We show that the large N asymptotic behavior of the minimal energy E _N changes at ?2a = U{\sqrt{2}\alpha=U} and that ?2a ￡ U{\sqrt{2}\alpha\leq U} is necessary for thermodynamic stability: for ${\sqrt{2}\alpha > U}${\sqrt{2}\alpha > U} the phonon-mediated electron-electron attraction overcomes the Coulomb repulsion and E _N behaves like −N ^7/3.     

Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutions with size-dissimilar ions

Modern theories of electrolyte solutions are physically accurate but difficult to apply for real-life systems; a need therefore exists to theoretically derive simplified and practically useful mathematical expressions for thermodynamic excess functions. This can be done by incorporating ion-size dissimilarity into the classical Debye-Hückel model [Physik Z. 24, 185 (1923)], under conditions at which non-electrostatic contributions are negligible. If the contact distance between the central (β) ion and a cloud (α) ion is a for counter-ions and b for co-ions, two basic cases exist, b < a and b > a. In both, a ‘smaller-ion shell’ (SiS) at the edge of the ionic cloud, bordered by the spherical surfaces of radius b and a, admits only the smaller α ions [Thomlinson and Outhwaite, Mol. Phys. 47, 1113 (1982)]. In the b < a case, the SiS contributes an ionic repulsion effect and the overall extra-electrostatic potential energy, Ψ _{b < a} (κ) ? κ, reciprocal screening length–exhibits a minimum. For b > a, the SiS contributes an ‘extra ionic attraction’ and the overall extra-electrostatic energy, Ψ _{b > a} (κ) declines monotonically with increasing κ. The entire Ψ contribution, Ψ_±, is a linear combination of the Ψs of the two counter β ions. The effectiveness of Ψ_± is demonstrated for real-life electrolyte systems, based on experimental mean ionic activity coefficients and their concentration dependencies. Fitting theory with experiment generates ion-size parameters that represent realistic interionic collision distances in solution, unlike parallel parameters based on other simplified theories.     

Neutron,x-ray and lattice dynamical studies of paraelectric Sb2S3

Neutron and x-ray diffraction studies of Sb₂S₃ indicate extensive diffuse scattering in the plane perpendicular to the chain axis of polymer-like (Sb₄S₆) _n molecules. The crystal structure of the paraelectric phase is said to be orthorhombic with space group D _2h ¹⁶ with four molecules per unit cell. The observed diffuse scattering may be due to static disorder or some dynamical effects. In this paper the authors have examined the possible dynamical origin by recourse to lattice dynamical studies. Dispersion relation of phonons along the three symmetry directionsa*,b* andc* is evaluated based on a lattice dynamical model incorporating Coulomb, covalent and a Born-Mayer-like short range interactions. Group theoretical analysis based on the group of neutral elements of crystal sites (GNES) was essential in order to examine and aid in the numerical computations. The group theoretical technique involving GNES extended to ‘pseudo-molecular’ systems is also discussed in this context. The phonon dispersion relation shows that there are rather flat TA-TO branches of very low frequency in thea andc directions which may give rise to diffuse scattering. The branches along theb-axis are quite dissimilar to those alonga andc axes because of anisotropy. Variation of the potential parameters leads to instability of the lowest TA-TO branch. This is suggestive of a temperatures or pressure-dependent phase transition. However since these modes are optically ‘silent’ one needs to carry out either high resolution neutron scattering or ultrasonic studies to confirm various aspects of the theoretical studies.     

Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in the presence of a hard core potential: A stable ferromagnetic state

We use different determinantal Hartree-Fock (HF) wave functions to calculate true variational upper bounds for the ground state energy of N spin-half fermions in volume V ₀, with mass m, electric charge zero, and magnetic moment μ, interacting through magnetic dipole-dipole interaction. We find that at high densities when the average interparticle distance r ₀ becomes small compared to the magnetic length r _m ≡ 2mμ²/ħ², a ferromagnetic state with spheroidal occupation function n _↑(), involving quadrupolar deformation, gives a lower upper bound compared to the variational energy for the uniform paramagnetic state or for the state with dipolar deformation. This system is unstable towards infinite density collapse, but we show explicitly that a suitable short-range repulsive (hard core) interaction of strength U ₀ and range a can stop this collapse. The existence of a stable equilibrium high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of coupling constants Γ_cm ≡ (U ₀ a ³/μ²) is not very small compared to 1.      

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

Electrons with correlated hopping interaction in one dimension

The 1D system of correlated electrons characterized in addition to the usual on-site (U) and nearest-neighbour (V) repulsion by a correlated-hopping term (t*) is considered. The ground state phase diagram is studied within the framework of the weak-coupling continuum-limit approach. At filling v the effective interaction originating from the correlated-hopping term which appears in the continuum-limit theory is given by t* cos (πv). Being repulsive for v < 1/2 and attractive for v > 1/2, this interaction leads to a characteristic band-filling dependence of the phase diagram of the system. For v ≠ 1/2, depending on the relation between the bare values of the coupling constants (U, V, t* cos (π v)) and, hence, on the band-filling, the system shows three different phases in the infrared limit: a Luttinger metal, a nonmagnetic metal and a singlet superconducting phase. For v = 1/2, the correlated-hopping interaction is dynamically trivial, leading only to a renormalization of the oneelectron hopping amplitude and the phase diagram of the model coincides with that of the extended Hubbard model.     

Global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on bipartite lattices

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U ≠ 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with N_a^D sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N_aa for which D = 1, 2, 3,... in the number N_a^D of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4^N_aD energy eigenstates refer to representations of the new found global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) × SO(3) × U(1) equals the Hilbert-space dimension 4^N_aD. It is confirmed elsewhere that the new found symmetry has important physical consequences.     

Coherent inelastic processes on nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a → b, which may take place in the interaction of hadrons and γ quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. For taking into account the influence of the nucleus matter, the optical model, based on the conception of the refraction index, is used. Analytical formulas for the effective cross section σ _coh (a → b) are obtained, taking into account that, at ultrarelativistic energies, the main contribution into σ _coh (a → b) is provided by very small transferred momenta in the vicinity of the minimal longitudinal momentum transferred to the nucleus. It is shown that the cross section σ _coh (a → b) may be expressed through the “forward” amplitudes of inelastic scattering f _a+N+b+N (0) and elastic scattering f _a+N+a+N(0), f _b+N+b+N(0) on a separate nucleon, and it depends on the ratios L _a /R and L _b /R (L _a and L _b are the mean lengths of the free path in the nucleus matter for the particles a and b, respectively, and R is the nucleus radius). In particular, when L _a /R ≫ 1, but L _b /R ≪ 1 (or L _a /R ≪ 1, but L _b /R ≫ 1), σ _coh (a → b) is equal to the ratio of the “forward” cross sections of inelastic scattering a + N → b + N and elastic scattering of the particle b (or a) on a nucleon, multiplied by the cross section of scattering on the “black” nucleus πR ². When both conditions L _a /R ≫ 1 and L _b /R ≫ 1 are satisfied, σ _coh (a → b) is proportional to the factor R ⁴/k ², where k is the initial energy of particle a in the laboratory frame. The text was submitted by the authors in English.     

The Geometry of¶(Super) Conformal Quantum Mechanics

N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D ^a δ _a whose associated one-form D _a dX ^a is closed. Further, the SL(2,ℝ) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry D ^a I _a ^b δ _b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given. Received: 3 September 1999 / Accepted: 30 January 2000     

Isotope effects on vibronic coupling of pyrazine

The vibronic couplings of pyrazine-d₀ and pyrazine-d₄ between the lowest electronic excited states ¹B_3u(n, π^*) and ¹B_2u(π, π^*) through the out-of-plane CH bending vibration ν_10a(b_1g) have been studied from the Raman, electronic absorption and fluorescence spectra. The isotope effects on the scattering cross section of the ν_10a Raman line, the vibrational potential in the ¹B_3u(n, π^*) state and on the frequency change of the ν_10a vibration between the ground and the lowest electronic excited states are well explained by conventional Herzberg-Teller coupling mechanism. However, the intensities of the vibronic bands in the electronic absorption and fluorescence spectra are hardly explained with this coupling mechanism.     

Probing the sign-changeable interaction between dark energy and dark matter with current observations

We consider the models of vacuum energy interacting with cold dark matter in this study, in which the coupling can change sigh during the cosmological evolution. We parameterize the running coupling b by the form b(a) = b_0 a + b_e(1-a), where at the earlytime the coupling is given by a constant b_e and today the coupling is described by another constant b_0. We explore six specific models with(i) Q = b(a)H_0ρ_0,(ii) Q = b(a)H_0ρ_(de),(iii) Q = b(a)H_0ρ_c,(iv) Q = b(a)Hρ_0,(v) Q = b(a)Hρ_(de), and(vi) Q = b(a)Hρ_c.The current observational data sets we use to constrain the models include the JLA compilation of type Ia supernova data, the Planck 2015 distance priors data of cosmic microwave background observation, the baryon acoustic oscillations measurements,and the Hubble constant direct measurement. We find that, for all the models, we have b_0 0 and b_e 0 at around the 1σ level,and b_0 and b_e are in extremely strong anti-correlation. Our results show that the coupling changes sign during the evolution at about the 1σ level, i.e., the energy transfer is from dark matter to dark energy when dark matter dominates the universe and the energy transfer is from dark energy to dark matter when dark energy dominates the universe.     

Critical behaviour near the metal-insulator transition of a doped Mott insulator

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for U larger than a critical value U _c, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping. Received 15 March 2001 and Received in final form 22 May 2001     

A Study of Resonances in a One-Dimensional Model with Singular Hamiltonian and Mass Jumps

We study the resonances produced in a one dimensional quantum system with an infinite potential on the negative real line plus two Dirac delta barriers centered at the points a,b>0. The system mass is not constant but undergoes jumps at the singular points a and b of the potential. We study the behavior of the resonances under the change of parameters such that the weight of the deltas or the heights of mass jumps. Possible degeneration of these resonances is also considered.     

极化激元系统时间演化的量子涨落特性和非经典统计行为

将极化激元系统约化成模型单模光子-TO声子有效相互作用系统， 在此基础上以解析形式讨论了系统的力学量、压缩态、量子涨落特性以及亚泊松分布等非经典效应的动力学演化行为.结果表明，光子场与极化波量子场彼此交换能量过程随时间演化呈振荡性质，光子场和声子场都可以演化成压缩态，其二阶压缩度随时间演化成复杂周期振荡特性，这种非经典特性是非线性相互作用的结果并且以k₁项和k₂项同时存在并相互关联为前提.而此时光子和声子统计分布随时间演化呈现介于超Poison分布和亚Poison分布之间复杂周期振荡的新结果，非线性作用k₁项和k₂项对这种非经典统计行为都有贡献. 关键词： 极化激元系统动力学演化 单模光场-TO声子有效模型哈密顿量 量子涨落与压缩态 亚泊松分布     

Translational and rotational motions of a diatomic molecule enclosed in a solid matrix

The hamiltonian for a molecule enclosed in a cavity may be written H = H ^R(θ) + H ^T(r) + U ^RT(θ, r), where θ and r denote the molecular orientation and the displacement of the centre of mass. The crystalline potential seen by the guest molecule can be explicitly calculated on the basis of atom-atom and electrostatic multipolar interactions, by using an nth-order gradient formula in the spherical representation. We take a N ₂ molecule encaged in β-quinol clathrate as our model system, and solve variationally the Schrödinger equation for H to clarify the translation-rotation coupling. Energy levels of H are obtained as a function of the height of the hindering potential for rotation, by modifying the strength of the electrostatic multipolar interaction. Three limiting cases of H ^R are important: (a) libration around the Z-axis, (b) free rotation, and (c) an oscillational rotation whose equilibrium orientation is perpendicular to the Z-axis. The constrained translation under consideration is an anharmonic and almost spherically symmetric oscillation. The Pauli principle must be applied to the eigenstate of H. Excepting the case (a), translational states of H are different for different nuclear spin species, and higher-order effects of U ^RT on these states are significant. For p-N₂, some modes of motion interchange if the rotational motion changes from case (a) to case (c). If the constraining potential for translation is steeper, the effect of U ^RT will become smaller. The anharmonicity involved in H ^T is not negligible in discussing this effect.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002