Formulation of unrestricted and restricted Hartree–Fock–Bogoliubov equations

Yamaki, Daisuke; Ohsaku, Tadafumi; Nagao, Hidemi; Yamaguchi, Kizashi

doi:10.1002/qua.10788

Cited by 8 publications

(9 citation statements)

References 15 publications

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“…We will obtain rational explanation of our phenomenological JP and PJ models in terms of such microscopic theories. It is noteworthy that microscopic conditions for cooperation of J and P, and other combinations have been elucidated on the basis of two and MB Hamiltonians 11–21. The present BF model is rationalized in terms of t–J–P and the MB Hamiltonians.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 76%

“…The BCS Hamiltonian in Eq. (6) can be diagonalized by the Bogoliubov transformation 15. The transition temperature ( T BCS ) is determined by solving the so‐called gap (Δ SC ) equation 7: where ε c denotes the cut‐off energy and N (0) is the electronic density of states at the Fermi surface.…”

Section: Theoretical Backgroundsmentioning

confidence: 99%

“…(4), together with the cooperative (mix) mechanisms such as the JP model. Both the low‐ and high‐concentration regimes of hole in cupurates are investigated on the basis of Hartree–Fock–Bogoliubov (HFB) and Bogoliubov–de Gennes equations 14, 15. The Gorkov's approach 16 by the use of the Green function techniques has been also applied to elucidate contributions of the EP, SF, and CF interactions from the metallic (overdoping) side 17–19.…”

Section: Introductionmentioning

confidence: 99%

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N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐T_c superconductivity

Yamaguchi

Nakano

Nagao

et al. 2005

Int J of Quantum Chemistry

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ABSTRACT:In this series of articles (I, II), N-band Hubbard models have been considered for strongly correlated electron systems, which are realized in d-p, -d, -R, and -R conjugated systems. The magnetism and superconductivity of these systems have been elucidated in terms of effective exchange integrals (J), which are calculated by first-principle methods. In part III of this series, the BCS-BEC crossover theory, has been introduced to elucidate the physical foundation of our J and JP model for the high-T c superconductivity (HTSC). The boson-fermion (BF) model for this theory is found useful for a reasonable explanation of the experimental phase diagrams of HTSC. The underlying physics of the BF model is different from that of the slave boson fieldtheoretical model assuming spinon-holon condensations in the low dimension. The interaction boson model (IBM) for nuclear matter is also employed to describe the cooperative mechanisms of electron-phonon (EP), spin fluctuation (SF), charge fluctuation (CF), and many-bands (MB) effects. This phenomenological model is useful for pictorial understanding and for the theoretical explanation of the cooperative mechanisms: (EP ϩ SF), (SF ϩ CF), (EP ϩ SF ϩ MB), etc. These are also investigated in analogy to BF model of fermionic gases, where the Feshbach resonance between boson and fermion is responsible for their coupling. The implications of these theoretical results are discussed in relation to recent ALPES and STM experiments for HTSC, which suggest the contributions of SF (J) and EP (P) interactions. The recently discovered superconductivity of boron-doped diamond is examined as an example of two-band sigma-radical (-R) conjugated systems. Finally, the bipolaron model is briefly discussed in relation to boson-fermion model via EP interaction to superconductivity.

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Section: Discussion and Concluding Remarksmentioning

confidence: 76%

Section: Theoretical Backgroundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐T_c superconductivity

Yamaguchi

Nakano

Nagao

et al. 2005

Int J of Quantum Chemistry

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“…From calculations on larger L, we find that the finite lattice error associated with this choice is negligible, on the scale of the significant digits reported. The BCS bulk state is obtained by solving the lattice spin-unrestricted Bogoliubov-deGennes equation 100,101 with the correlation potential u. The impurity and bath problem is solved in the BCS quasiparticle basis, with general onebody and two-body interactions that do not conserve particle number or locality.…”

Section: G Density Matrix Embedding Theory (Dmet)mentioning

confidence: 99%

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

et al. 2015

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Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods. arXiv:1505.02290v2 [cond-mat.str-el] 15

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“…h can be rewritten in the form of a spin-unrestricted Bogoliubov-de Gennes (BdG) [102,103] equation,…”

Section: Dmet Lattice Hamiltonianmentioning

confidence: 99%

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

2016

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We compute the ground-state phase diagram of the Hubbard and frustrated Hubbard models on the square lattice with density matrix embedding theory using clusters of up to 16 sites. We provide an error model to estimate the reliability of the computations and complexity of the physics at different points in the diagram. We find superconductivity in the ground state as well as competition between inhomogeneous charge, spin, and pairing states at low doping. The estimated errors in the study are below T c in the cuprates and on the scale of contributions in real materials that are neglected in the Hubbard model. DOI: 10.1103/PhysRevB.93.035126 The Hubbard model [1][2][3] is one of the simplest quantum lattice models of correlated electron materials. Its one-band realization on the square lattice plays a central role in understanding the essential physics of high-temperature superconductivity [4,5]. Rigorous, near-exact results are available in certain limits [6]: at high temperatures from series expansions [7][8][9][10], in infinite dimensions from converged dynamical mean-field theory [11][12][13][14], and at weak coupling from perturbation theory [15] and renormalization group analysis [16,17]. Further, at half filling, the model has no fermion sign problem, and unbiased determinantal quantum Monte Carlo simulations can be converged [18]. Away from these limits, however, approximations are necessary. Many numerical methods have been applied to the model at both finite and zero temperatures, including fixed-node, constrained path, determinantal, and variational quantum Monte Carlo (QMC) [19][20][21][22][23][24][25][26][27][28][29], density matrix renormalization group (DMRG) [30][31][32], dynamical cluster (DCA) [33,34], (cluster) dynamical mean-field theories (CDMFT) [35,36], and variational cluster approximations (VCA) [37,38]. (We refer to DCA/CDMFT/VCA collectively as Green's function cluster theories.) These pioneering works have suggested rich phenomenology in the phase diagram including metallic, antiferromagnetic, and d-wave (and other kinds of) superconducting phases, a pseudogap regime, inhomogeneous orders such as stripes, and charge, spin, and pairdensity waves, as well as phase separation [6,19,20,24,25,[27][28][29]32,35,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. However, as different numerical methods have yielded different pictures of the ground-state phase diagram, a precise quantitative picture of the ground-state phase diagram has yet to emerge.It is the goal of this paper to produce such a quantitative picture as best as possible across the full Hubbard model phase diagram below U = 8. Our method of choice is density matrix embedding theory (DMET), which is very accurate in this regime [59][60][61][62][63][64][65][66], employed together with clusters of up to 16 sites and thermodynamic extrapolation. We carefully calibrate errors in our calculations, giving error bars to quantify the remaining uncertainty in our phase diagram. These error bars also serve,...

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Formulation of unrestricted and restricted Hartree–Fock–Bogoliubov equations

Cited by 8 publications

References 15 publications

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐T_c superconductivity

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐T_c superconductivity

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

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Formulation of unrestricted and restricted Hartree–Fock–Bogoliubov equations

Cited by 8 publications

References 15 publications

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐Tc superconductivity

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐Tc superconductivity

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

Contact Info

Product

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N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐T_c superconductivity

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐T_c superconductivity