Benchmarking the simplest slave-particle theory with Hubbard dimer

Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal–insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods:(i) slave-spin method on mean-field level,(ii) slave-spin method with gauge constraint, and(iii) the exact solution as a benchmark. We find that, protected by the particle–hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space.These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.     

Single-particle spectral function of the Hubbard chain: frustration induced

The one-electron spectral function of a frustrated Hubbard chain is computed by making use of the cluster perturbation theory. The spectral weight we found turns out to be strongly dependent on the frustrating next-nearest-neighbor hopping t'. A frustration induced pseudogap arises when the system evolves from a gapful Mott insulator to a gapless conductor for an intermediate value of the frustration parameter |t'|. Furthermore, the opening of a pseudogap in the density of states already in the metallic side leads to a continuous opening of the true gap in the insulator. For the hole-doped case, the pseudogap is pinned at the Fermi energy, while the Mott gap is shifted in energy with increasing Hubbard interaction U. The separation of the pseudogap and Mott gap in the hole-doped system demonstrates the validity of the existence of a pseudogap.     

Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer

Gross–Oliveira–Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excited-state densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [K. Deur et al., Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre–Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.     

Hubbard Hamiltonian in the dimer representation Large‐U case

The nonperturbative approach, presented in this paper, can, in principle, be applied to clusters of any size, as well as, to another type of model Hamiltonians.     

Diagrammatic analysis of the Hubbard model: Stationary property of the thermodynamic potential

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of f — localized electrons as a main parameter of the theory. f-Electrons are strongly correlated and c-conduction electrons are uncorrelated. Correlation function for f- and mass operator for c-electrons are determined. The Dyson equation for c- and Dyson-type equation for f-electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential with respect to, the variation of the mass operator is established. The result is appropriate both for the normal and for the superconducting states of the system.     

Diagram analysis of the Hubbard model: Stationarity property of the thermodynamic potential

The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green’s functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.     

消光式核壳二聚体传感器的设计与光谱特性分析

根据ITO/Au纳米核壳二聚体粒子在生物医学领域的应用合理性,设计了一种实时检测生物液体的核壳二聚体探针消光式传感器;由偶极子理论推导出输出波长与外界环境折射率关系;利用MATLAB设计ITO/Au纳米核壳二聚体粒子结构;采用软件DDSCAT7.3结合离散偶极近似法,利用二聚体有效半径模拟计算了300~950nm可见光到红外光波段不同核壳比、二聚体间距、以及不同介质折射率的消光光谱;根据传感芯片折射率与偶极共振、耦合八级共振的响应关系得出ITO/Au二聚体的折射率灵敏特性。与传统Ag/Au核壳纳米粒子相比,ITO/Au纳米核壳二聚体结构引入了可作为传感芯片灵敏性自参考参数的耦合八级共振峰,同时ITO/Au二聚体结构的折射率灵敏度可达到419nm/RIU。这些工作及其结果对制作消光式传感器具有重要的意义。     

Calculation of the potential energy curves of the HgZn dimer

Potential energies for the ground and several excited states of the HgZn excimer molecule have been calculated in order to assist experimenters in assigning the observed spectral bands. The CI-singles procedure, followed by a second-order Møller-Plesset perturbation theory correction were applied for the valence electrons. The core electrons were replaced by an effective-core potential. The effect of spin-orbit interaction was not investigated. The calculated energy curves are compared with other available theoretical data, as well as with preliminary experimental assignments.     

Electron spectral density of the half-filled Hubbard model in the atomic limit at finite temperature

We have calculated the spectral function and density of states of halffilled two-dimensional Hubbard model in the Hubbard-I approximation assuming an antiferromagnetic long range order at low temperature and compared results to the QMC data. It occurs that calculated functions are in a qualitative agreement with the QMC one. We have also shown that Neel ordered state dispersion has the similar form to the spin density wave one.     

Algebraic Bethe ansatz for the one-dimensional Hubbard model with chemical potential

The integrability and the algebraic Bethe ansatz approach for the one-dimensional (1D) Hubbard model with chemical potential are studied in the framework of the quantum inverse scattering method. We also investigate the hidden local gauge invariance for the model. It is found that the R-matrix only permits Abelian $\text{U(1) ⋇}{}_{\mathrm{s}}\text{U(1)}$ gauge transformations, and it is shown that the energy spectrum is gauge invariant whereas the eigenvectors and the Bethe ansatz equations are explicitly gauge dependent.     

Redistribution of the hole spectral weight due to longrange spin correlations in the three-band Hubbard model

The spectrum of the spin-polaron hole exitation is investigated in the framework of the three-band model for the CuO₂ plane in hightemperature superconductors. The problem is treated taking into account the coupling of a local polaron with the antiferromagnetic spin wave with Q=(≈,≈). This leads to fundamental changes in the lowest polaron band ε₁(k) and to a strong redistribution of the bare electron filling. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 173–177 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A(k, ω) in the Brillouin zone. As a result, the modulation of A(k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A(k, ω) decreases according to the angle-resolved photoemission spectroscopy data.     

Deterministic escape of a dimer over an anharmonic potential barrier

In the present paper we consider the deterministic escape dynamics of a dimer from a metastable state over an anharmonic potential barrier. The underlying dynamics is conservative and noiseless and thus, the allocated energy has to suffice for barrier crossing. The two particles comprising the dimer are coupled through a spring. Their motion takes place in a two-dimensional plane. Each of the two constituents for itself is unable to escape, but as the outcome of strongly chaotic coupled dynamics the two particles exchange energy in such a way that eventually exit from the domain of attraction may be promoted. We calculate the corresponding critical dimer configuration as the transition state and its associated activation energy vital for barrier crossing. It is found that there exists a bounded region in the parameter space where a fast escape entailed by chaotic dynamics is observed. Interestingly, outside this region the system can show Fermi resonance which, however turns out to impede fast escape.     

Quarkonium spectral functions with complex potential

We study quarkonium spectral functions at high temperatures using a potential model with complex potential. The real part of the potential is constrained by the lattice QCD data on static quark anti-quark correlation functions, while the imaginary part of the potential is taken from perturbative calculations. We find that the imaginary part of the potential has significant effect on quarkonium spectral functions, in particular, it leads to the dissolution of the 1S charmonium and excited bottomonium states at temperatures about 250 MeV and melting of the ground state bottomonium at temperatures slightly above 450 MeV.