An efficient and stable numerical scheme based on Hill's determinant is proposed for computing the whole spectrum of the single-mode spin-boson model. Its shown that for the low-lying levels a simple version of Hill's determinant method works well, while for high levels a normalization of the determinant is necessary and this normalization results in an entire function whose zeros correspond to the energy levels. It is very convenient to use this entire function to compute all the energy levels numerically. Some high levels of the model are computed and compared with Irish's general rotating-wave approximation. A scaling law in the large photon number limit is numerically tested and several statistical properties of the spectrum are investigated.

We theoretically study the coexistence of spin density wave (SDW) and superconductivity (SC) in ironpnictide superconductors based on a three-orbital model, focusing on the momentum-space and real-space distributions of SDW and SC order parameters in the coexistence region. We show that a SDW-SC coexisting state lies in the T-n phase diagram, in qualitative agreement with those of NaFe 1−x Co x As and Ba(Fe 1−x Co x) 2 As 2. In the SC state the pairing wavefunction has s ± symmetry with s x 2 y 2 and s x 2 +y 2 components. In the coexisting state, the SDW and SC order parameters display strong orbital-selective competitions in momentum space, which also result in real-space modulation and spin singlet-triplet mixing in the Cooper pairing amplitude. We expect that the obtained features may be observed in future experiments.

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The dynamical correlations of nonlocal operators in general quadratic open fermion systems is still a challenging problem. Here we tackle this problem by developing a new formulation of open fermion many-body systems, namely, the characteristic function approach. Illustrating the technique, we analyze a finite Kitaev chain with boundary dissipation and consider anyon-type nonlocal excitations. We give explicit formula for the Green's functions, demonstrating an asymmetric light cone induced by the anyon statistical parameter and an increasing relaxation rate with this parameter. We also analyze some other types of nonlocal operator correlations such as the full counting statistics of the charge number and the Loschmidt echo in a quench from the vacuum state. The former shows clear signature of a nonequilibrium quantum phase transition, while the later exhibits cusps at some critical times and hence demonstrates dynamical quantum phase transitions.