Pairing in 4-component fermion systems: The bulk limit of SU(4)-symmetric Hamiltonians

Fermion systems with more than two components can exhibit pairing condensates of a much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin (RG) model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground-state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.     

Ground-state properties of Fermi gases in the strongly interacting regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.     

Local energy density functional and density-dependent pairing in nuclear systems

An approach based on the local energy density functional method for describing the ground-state properties of superfluid nuclei is presented. A generalized variational principle is formulated which corresponds, in the weak pairing approximation, to a full treatment of the Hartree-Fock-Bogoliubov problem with an effective contact pairing interaction. The Gor’kov equations for generalized Green’s functions are treated exactly in the coordinate-space representation. The method is used to calculate the differential observables including odd-even mass differences and odd-even effects in charge radii which turn out to be very sensitive to the density dependence of the effective pairing force. A better knowledge of this density dependence allows one to make predictions for the pairing gap at the Fermi surface as a function of nuclear matter density. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 260–265 (25 August 1998)     

二电子系列关联能的并行计算

用组态相互作用方法计算了二电子体系电子关联能,为了获得高精度的结果往往需要巨大的计算量,以往单个处理器上的串行计算通常存在着机时长,内存不够的严重困难,为此采用并行分块消去迭地,同时在多个处理器上并行计算,得到了了基态关联能。     

The skyrme-plus-pairing effective interaction and the global neutron-excess dependence of the pairing gap

The neutron and proton pairing gaps were recently found to have a global dependence on neutron excess. We investigate whether the couplings necessary to obtain this behaviour can be provided by a mean field associated with a Skyrme-type plus usual pairing effective interaction. The parameters of this effective interaction are constrained by nuclear-matter properties, such as binding energy, saturation density, effective mass and values of the second derivatives of the energy with respect to the four densities (neutron and proton with spin-up and spin-down), together with the surface energy. The pairing gaps are then calculated as a function of neutron excess for various parameter sets for very large systems and for finite nuclei in the local-density approximation. We find that the empirical results cannot be reproduced by this procedure. We put forward therefore the hypothesis that, to account for this failure, the usual phenomenology of effective interactions in nuclei ought to be modified; we propose a simple residual neutron-proton interaction that can do that, yet maintains all the previous successes.     

Density matrix renormalization group study of incompressible fractional quantum Hall states

We develop the density-matrix renormalization group (DMRG) technique for numerically studying incompressible fractional quantum Hall (FQH) states on the sphere. We calculate accurate estimates for ground-state energies and excitation gaps at FQH filling fractions nu=1/3 and nu=5/2 for systems that are considerably larger than the largest ever studied by exact diagonalization. We establish, by carefully comparing with existing numerical results on smaller systems, that DMRG is a highly effective numerical tool for studying incompressible FQH states.     

A generation-based particle–hole density-matrix renormalization group study of interacting quantum dots

The particle–hole version of the density-matrix renormalization-group method (PH-DMRG) is utilized to calculate the ground-state energy of an interacting two-dimensional quantum dot. We show that a modification of the method, termed generation-based PH-DMRG, leads to significant improvement of the results, and discuss its feasibility for the treatment of large systems. As another application we calculate the addition spectrum.     

Testing the sign-changing superconducting gap in iron-based superconductors with quasiparticle interference and neutron scattering

We present a phenomenological calculation of the quasiparticle interference (QPI) pattern and inelastic neutron scattering (INS) spectra in iron-pnictide and layered iron-selenide compounds by using material specific band structure and superconducting (SC) gap properties. As both the QPI and the INS spectra arise due to scattering of the Bogolyubov quasiparticles, they exhibit a one-to-one correspondence of the scattering vectors and the energy scales. We show that these two spectroscopies complement each other in such a way that a comparative study allows one to extract quantitative and unambiguous information about the underlying pairing structure and the phase of the SC gap. Due to the nodeless and isotropic nature of the SC gaps, both the QPI and INS maps are concentrated at only two energies in pnictide (two SC gaps) and one energy in iron-selenide, while the associated scattering vectors q for scattering of sign-changing and same sign of the SC gaps change between these spectroscopies. The results presented, particularly for the newly discovered iron-selenide compounds, can be used to test the nodeless d-wave pairing in this class of high temperature superconductor.     

Multi-band pairing of ultrarelativistic electrons and holes in graphene bilayer

Multi-band pairing of effectively ultrarelativistic electrons and holes in asymmetrically biased graphene bilayer in strong coupling regime is considered. In this regime, the pairing affects both conduction and valence bands of the both graphene layers, and the order parameter is a matrix, which indices correspond to the bands. For band-diagonal s-wave pairing, we derive the system of multi-band gap equations for the gaps in the valence and conduction bands and solve it in the approximation of constant gaps and in the approximation of separable pairing potential. For a characteristic width of the pairing region of order of magnitude of the chemical potential, the gap values are not much different from single-band BCS estimations. However, if the pairing region is wider, then the gaps can be much larger and depend exponentially on its energy width. We also predict gapped and soliton-like oscillations of a relative phase of the gaps and unpairing of quarter-vortices at Kosterlitz-Thouless transition.     

New effective interaction for the trapped fermi gas

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of energies at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. We estimate the ground-state energy of the four-particle system to be (5.045 +/- 0.003) variant Planck's constant over 2 pi omega.     

Pairing correlations in finite nuclear systems

We discuss an approach for the treatment of correlations in finite nuclear systems. The approach is based on a boson formalism, the basic boson operators representing elementary particle-hole excitations. We show an application of the method within an exactly solvable multilevel pairing model. We calculate the correlation energy of the system and compare it with the exact results as well as with results obtained within other approaches.     

Ground state of Fermi systems with strong short-range order

A new variational method is developed to calculate the ground-state energy of a fermion system with strong short-range order. As well as intrasite correlations, the Gutzwiller trial wave function explicitly contains nearest-neighbor correlations. The Kikuchi pseudo-ensemble method was used to calculate the total energy of the fermion system. The calculations were made for the paramagnetic and antiferromagnetic phases of the half-filled Hubbard model. It is shown that for two-and three-dimensional lattices the short-range order in the paramagnetic phase strongly influences the ground-state energy whereas in the antiferromagnetic phase it is insignificant.     

Frozen glass phase in the multi-index matching problem

The multi-index matching is an NP-hard combinatorial optimization problem; for two indices it reduces to the well understood bipartite matching problem that belongs to the polynomial complexity class. We use the cavity method to solve the thermodynamics of the multi-index system with random costs. The phase diagram is much richer than for the case of the bipartite matching problem: it shows a finite temperature phase transition to a completely frozen glass phase, similar to what happens in the random energy model. We derive the critical temperature, the ground-state energy density, and properties of the energy landscape and compare the results to numerics based on exact analysis of small systems.     

Two energy scales in the magnetic resonance spectrum of electron and hole doped pnictide superconductors

We argue that a multiband superconductor with sign-changing gaps may have multiple spin resonances. We calculate the RPA-based spin resonance spectra of a pnictide superconductor by using the five-band tight-binding model or angle-resolved photoemission spectroscopy Fermi surface (FS) and experimental values of superconducting gaps. The resonance spectra split in both energy and momenta due to the effects of multiband and multiple gaps in s(±) pairing; the higher energy peak appears around the commensurate momenta due to scattering between α-FS to γ/δ-FS pockets. The second resonance is incommensurate, coming from β-FS to γ/δ-FS scatterings, and its q vector is doping-dependent and, hence, on the FS topology. Energies of both resonances ω(res)(1,2) are strongly doping-dependent and are proportional to the gap amplitudes at the contributing FSs.     

能量密度泛函中不同对关联处理方式对原子核形变描述影响的探讨

在Skyrme能量密度泛函理论的框架下,研究了不同对关联处理近似,如Hartree-Fock-Bogoliubov(HFB)、Hartree-Fock-Bogoliubov Lipkin-Nogami (HFBLN)及在HFBLN基础上考虑粒子数投影,对于原子核势能曲面计算及基态结合能的影响。同时,也研究了不同对力,如体积对力、表面对力及混合对力对结果的影响。研究的对象为典型的双幻核16O,40Ca,100Sn和208Pb,它们的基态为球形;还有典型的形变核48Cr,也研究了相应的Cr和Fe同位素链的结合能,最后讨论了对超重核298Fl的势能面计算。研究发现,对关联基本不改变形变极小点,但是由于对关联能的引入,对结合能会带来几个MeV的修正能量,HFB、HFBLN及投影计算的修正能量逐渐递增。对关联可以改变位能面最小点附近曲线的软度,使得形变较小点变浅,而在HFBLN基础上考虑粒子数投影,又可以让形变极小点变得更加明显。对关联也降低了位垒高度。在相同对关联处理近似下,混合对力与体积对力计算的势能面结果相接近,表面对力带来了更多的对关联能,对关联的效果更加显著。     

Diffusion Monte Carlo analysis of the crossover from three to two dimensions for trapped Bose gases

We investigate the crossover from three to two dimensions for harmonically trapped hard-sphere Bose gases by varying the aspect ratio of the trapping potential. The diffusion Monte Carlo method is used to calculate both the ground-state energy and structural properties. The effect of trap anisotropy, interparticle interaction, and number of particles on the ground-state properties is discussed. Our results show that the minimum value of the aspect ratio at which the system reaches an asymptotic equilibrium distribution in the weakly confined direction decreases with increasing scattering length, while the minimum value of the aspect ratio at which the system enters the quasi-two-dimensional (2D) regime increases as both the scattering length and the number of particles increase. Additionally, the role played by particle correlations is proved to be more pronounced in the quasi-2D system than in the three-dimensional (3D) system by directly comparing the ground-state properties for the two cases.     

Magnetic phase transitions in one-dimensional strongly attractive three-component ultracold fermions

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.     

Lieb's Spin-Reflection-Positivity Method and Its Applications to Strongly Correlated Electron Systems

In this paper, we discuss the spin-reflection-positivity method introduced by Lieb [E. H. Lieb, Phys. Rev. Lett. 62:1201 (1989)] and its applications to strongly correlated electron systems in a pedagogical manner. We emphasize the important role played by the sign rule of the ground-state wave function in studying a many-body system. To make our explanation more readable, we shall first review some well-known one-dimensional examples and recall the Lieb–Mattis theorem on the Heisenberg localized spin models. Then, after introducing the general theory of spin-reflection positivity, we show in detail how to use it to overcome the sign problem caused by the fermion characteristics of itinerant electrons in strongly correlated models. Finally, we establish several rigorous results on the Hubbard model, the periodic Anderson model and the Kondo lattice model.