The Hall coefficient, RH, of high-Tc cuprates in the normal state shows the striking non-Fermi liquid behavior: RH follows a Curie-Weiss type temperature dependence, and |RH| ≫ 1/|ne| at low temperatures in the under-doped compounds. Moreover, RH is positive for hole-doped compounds and is negative for electron-doped ones, although each of them has a similar hole-like Fermi surface. In this paper, we give the explanation of this long-standing problem from the standpoint of the nearly antiferromagnetic (AF) Fermi liquid. We consider seriously the vertex corrections for the current which are indispensable to satisfy the conservation laws, which are violated within the conventional Boltzmann transport approximation. The obtained total current J k takes an enhanced value and is no more perpendicular to the Fermi surface due to the strong AF fluctuations. By virtue of this mechanism, the anomalous behavior of RH in high-Tc cuprates is neutrally explained. We find that both the temperature and the (electron, or hole) doping dependences of RH in high-Tc cuprates are reproduced well by numerical calculations based on the fluctuation-exchange (FLEX) approximation, applied to the single-band Hubbard model. We also discuss the temperature dependence of RH in other nearly AF metals, e.g., V2O3, κ-BEDT-TTF organic superconductors, and heavy fermion systems close to the AF phase boundary.PACS number(s): 72.10. Bg, 74.25.Fy

In the normal state of high-Tc cuprates, the Hall coefficient shows remarkable temperature dependence, and its absolute value is enhanced in comparison with that value simply estimated on the basis of band structure. It has been recognized that this temperature dependence of the Hall coefficient is due to highly anisotropic quasiparticle damping rate on the Fermi surface. In this paper we further take account of the vertex correction to the current vertex arising from quasiparticle interactions. Then the transport current is transformed to a large extent from the quasiparticle velocity, and is no longer proportional to the latter. As a consequence some pieces of the Fermi surface outside of the antiferromagnetic Brillouin zone make negative contribution to the Hall conductivity, even if the curvature of the Fermi surface is hole-like. The Hall coefficient is much larger at low temperatures than the estimate made without the vertex correction. Temperature dependence of the antiferromagnetic spin correlation length is also crucial to cause remarkable temperature dependence of the Hall coefficient. In our treatment the Hall coefficient of the electron-doped cuprates can be negative despite hole-like curvature of the Fermi surface.

We have theoretically investigated the time-symmetry breaking phase transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue problem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy dependence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry breaking phase transition: as a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.

At the exceptional point where two eigenstates coalesce in open quantum systems, the usual diagonalization scheme breaks down and the Hamiltonian can only be reduced to Jordan block form. Most of the studies on the exceptional point appearing in the literature introduce a phenomenological effective Hamiltonian that essentially reduces the problem to that of a finite non-Hermitian matrix for which it is straightforward to obtain the Jordan form. In this paper, we demonstrate how the microscopic total Hamiltonian of an open quantum system reduces to Jordan block form at an exceptional point in an exact manner that treats the continuum without any approximation by extending the problem to include eigenstates with complex eigenvalues that reside outside the Hilbert space. Our method relies on the Brillouin-Wigner-Feshbach projection method according to which we can obtain a finite dimensional effective Hamiltonian that shares the discrete sector of the spectrum with the total Hamiltonian. Because of the eigenvalue dependence of the effective Hamiltonian due to the dynamical nature of the coupling between the discrete states via the continuum states, a coalescence of eigenvalues results in the coalescence of the corresponding eigenvectors of the total Hamiltonian, which means that the system is at an exceptional point. We also introduce an extended Jordan form basis away from the exceptional point, which provides an alternative way to obtain the Jordan block at an exceptional point. The extended Jordan block connects continuously to the Jordan block exactly at the exceptional point implying that the observable quantities are continuous at the exceptional point.

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