Variational study of the Holstein polaron

The paper deals with the ground and the first excited state of the polaron in the one dimensional Holstein model. Various variational methods are used to investigate both the weak coupling and strong coupling case, as well as the crossover regime between them. Two of the methods, which are presented here for the first time, introduce interesting elements to the understanding of the nature of the polaron. Reliable numerical evidence is found that, in the strong coupling regime, the ground and the first excited state of the self-trapped polaron are well described within the adiabatic limit. The lattice vibration modes associated with the self-trapped polarons are analyzed in detail, and the frequency softening of the vibration mode at the central site of the small polaron is estimated. It is shown that the first excited state of the system in the strong coupling regime corresponds to the excitation of the soft phonon mode within the polaron. In the crossover regime, the ground and the first excited state of the system can be approximated by the anticrossing of the self-trapped and the delocalized polaron state. In this way, the connection between the behavior of the ground and the first excited state is qualitatively explained.Comment: 11 pages, 4 figures, PRB 65, 14430

Ground state of spin-1 Bose-Einstein condensates with spin-orbit coupling in a Zeeman field

We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing wave phase or plane wave phase when the strength of Zeeman field is below a critical value related to the strength of spin-orbit coupling. Zeeman field can induce the phase transition between standing wave and plane wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner, the linear Zeeman effect magnetizes the standing wave phase along the direction of the magnetic field, but the quadratic one demagnetizes the plane wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum

Transfer-matrix renormalization group study of the spin ladders with cyclic four-spin interactions

The temperature dependence of the specific heat and spin susceptibility of the spin ladders with cyclic four-spin interactions in the rung-singlet phase is explored by making use of the transfer-matrix renormalization group method. The values of spin gap are extracted from the specific heat and susceptibility, respectively. It is found that for different relative strength between interchain and intrachain interactions, the spin gap is approximately linear with the cyclic four-spin interaction in the region far away from the critical point. Furthermore, we show that the dispersion for the one-triplet magnon branch can be obtained by numerically fitting on the partition function.Comment: 7 pages, 7 figures, 1 tabl

Conductance plateau in quantum spin transport through an interacting quantum dot

Quantum spin transport is studied in an interacting quantum dot. It is found that a conductance "plateau" emerges in the non-linear charge conductance by a spin bias in the Kondo regime. The conductance plateau, as a complementary to the Kondo peak, originates from the strong electron correlation and exchange processes in the quantum dot, and can be regarded as one of the characteristics in quantum spin transport.Comment: 5 pages, 5 figure

Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit

We analyze the optical selection rules of the microwave-assisted transitions in a flux qubit superconducting quantum circuit (SQC). We show that the parities of the states relevant to the superconducting phase in the SQC are well-defined when the external magnetic flux $\Phi_{e}=\Phi_{0}/2$, then the selection rules are same as the ones for the electric-dipole transitions in usual atoms. When $\Phi_{e}\neq \Phi_{0}/2$, the symmetry of the potential of the artificial "atom'' is broken, a so-called $\Delta$-type "cyclic" three-level atom is formed, where one- and two-photon processes can coexist. We study how the population of these three states can be selectively transferred by adiabatically controlling the electromagnetic field pulses. Different from $\Lambda$-type atoms, the adiabatic population transfer in our three-level $\Delta$-atom can be controlled not only by the amplitudes but also by the phases of the pulses

On the nature of the lightest scalar resonances

We briefly review the recent progresses in the new unitarization approach being developed by us. Especially we discuss the large $N_c$ $\pi\pi$ scatterings by making use of the partial wave $S$ matrix parametrization form. We find that the $\sigma$ pole may move to the negative real axis on the second sheet of the complex $s$ plane, therefore it raises the interesting question that this `$\sigma$' pole may be related to the $\sigma$ in the linear $\sigma$ model.Comment: Talk presented by Zheng at ``Quark Confinement and Hadron Spectroscopy VI'', 21--25 Sept. 2004, Cagliari, Italy. 3 pages with 2 figure