To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high $T_c$ cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature $T_c$ and the pseudogap (spin gap) temperature $T^*$ tangential to $T_c$ in the overdoped region in the observed phase diagram of high $T_c$ cuprates. A universal parabolic scaling behavior of $T^*/T_c$ (or $T_c/T^*$ ) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of $T_c$ but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physical implications and predicted various physical properties of high $T_c$ cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature $T_c$ and the pseudogap (spin gap) temperature $T^*$ tangential to $T_c$ in the overdoped region in the observed phase diagram of high $T_c$ cuprates. A universal parabolic scaling behavior of $T^*/T_c$ (or $T_c/T^*$) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of $T_c$ but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.

arXiv:cond-mat/0304293Apr 12, 20030 citations

The Spectrum of the Spin-Boson Model

Matthias Hübner, Herbert E. Spohn

NATO ASI series. Series B : PhysicsJan 1, 19941 citation

Spectra and Eigenstates of Spin Chain Hamiltonians

Jonathan P. Keating, Noah Linden, H. J. Wells

arXiv:1403.1121Communications in Mathematical PhysicsApr 30, 201581 citations

Unitary transformation with double polaronic generator for spin-boson model: Ground state, thermodynamics and dynamical evolution

Hang Zheng, Zhiguo Lü

Unitary transformation with a double polaronic generator is proposed for the unbiased spin-boson Hamiltonian, which leads to a new ground state with lower ground state energy, as well as an effective Hamiltonian without the counter-rotating coupling. The infrared divergence associated with the nonadiabatic modes in Ohmic bath plays an important role in determining the quantum critical point αc of the ground state, which separates the non-degenerate ground state for α<αc from the degenerate one for α>αc and leads to logarithmic divergence of the bosonic numbers. The thermodynamic properties, the dynamical evolution, and time correlation of the SBM model are studied by the effective Hamiltonian obtained from the unitary transformation, which can be solved easily and transparently by the perturbation theory. As a check of our theoretical treatment and numerical results, we have calculated the Wilson ratio and shown that the spectral sum rule and Shiba's relation are exactly fulfilled.Unitary transformation with a double polaronic generator is proposed for the unbiased spin-boson Hamiltonian, which leads to a new ground state with lower ground state energy, as well as an effective Hamiltonian without the counter-rotating coupling. The infrared divergence associated with the nonadiabatic modes in Ohmic bath plays an important role in determining the quantum critical point αc of the ground state, which separates the non-degenerate ground state for α<αc from the degenerate one for α>αc and leads to logarithmic divergence of the bosonic numbers. The thermodynamic properties, the dynamical evolution, and time correlation of the SBM model are studied by the effective Hamiltonian obtained from the unitary transformation, which can be solved easily and transparently by the perturbation theory. As a check of our theoretical treatment and numerical results, we have calculated the Wilson ratio and shown that the spectral sum rule and Shiba's relation are exactly fulfilled.

The Journal of Chemical PhysicsJan 22, 20261 citation

Ground state(s) of the spin-boson hamiltonian

Herbert E. Spohn

Communications in Mathematical PhysicsJun 1, 1989142 citations

Rigorous Boson Formulation for Calculating Time-Dependent Thermal Properties of Localized Spin Systems

John F. Cooke, H. H. Hahn

We outline a method for rigorously calculating the time-dependent as well as the static thermal properties of localized spin systems from those of an ordinary many-boson system. Our method retains the advantages of both the Holstein-Primakoff and the Dyson-Maleev transformations without having their main disadvantages. The spin operators and the boson Hamiltonian are all finite series in the boson creation and annihilation operators. Our boson Hamiltonian is Hermitian. This method establishes a rigorous correspondence between the thermal properties of the spin-\textonehalf{} isotropic Heisenberg model and those of a hardcore boson system with only two-body interactions.We outline a method for rigorously calculating the time-dependent as well as the static thermal properties of localized spin systems from those of an ordinary many-boson system. Our method retains the advantages of both the Holstein-Primakoff and the Dyson-Maleev transformations without having their main disadvantages. The spin operators and the boson Hamiltonian are all finite series in the boson creation and annihilation operators. Our boson Hamiltonian is Hermitian. This method establishes a rigorous correspondence between the thermal properties of the spin-\textonehalf{} isotropic Heisenberg model and those of a hardcore boson system with only two-body interactions.

Physical ReviewAug 10, 196910 citations

T_c

cuprates. We discuss the significance of coupling (interplay) between the spin and charge degrees of freedom in the Heisenberg interaction term of the t-J Hamiltonian. We discuss its importance in causing the arch-shaped superconducting transition temperature

T_c

and the pseudogap (spin gap) temperature

T^*

tangential to

T_c

in the overdoped region in the observed phase diagram of high

T_c

cuprates. A universal parabolic scaling behavior of

T^*/T_c

(or

T_c/T^*

) with hole doping concentration is predicted in agreement with observations, indicating that there exists correlation between the pseudogap (spin gap) phase and the superconducting phase through antiferromagnetic fluctuations. Our proposed holon-pair boson theory is shown to be self-consistent in that it not only yields the arch (dome) shape structure of

T_c

but also reproduces various other physical properties such as superfluid weight, bose condensation energy, spectral function, optical conductivity and spin susceptibility, including their temperature and doping dependence.