We study the interaction effects on the ground state of nanographite ribbons with zigzag edges. Within the mean-field approximation, we found that there are two possible phases: the superconducting (SC) phase and the excitonic insulator (EI). The two phases are separated by a first-order transition point. After taking into account the low-lying fluctuations around the mean-field solutions, the SC phase becomes a spin liquid phase with one gapless charge mode. On the other hand, all excitations in the EI phase, especially the spin excitations, are gapped.Comment: 6 pages, 3 figure

We study the quantum point contact between the topological superconductor and the helical Luttinger liquid. The effects of the electron-electron interactions in the helical Luttinger liquid on the low-energy physics of this system are analyzed by the renormalization group. Among the various couplings at the point contact which arise from the tunneling via the Majorana edge channel, the induced backscattering in the helical Luttinger liquid is the most relevant for repulsive interactions. Hence, at low temperatures, the helical Luttinger liquid is effectively cut into two separated half wires. As a result, the low-temperature physics is described by a fixed point consisting of two leads coupled to the topological superconductor, and the electrical transport properties through the point contact at low temperature and low bias are dominated by the tunneling via the Majorana edge channel. We compute the temperature dependence of the zero-bias tunneling conductance and study the full counting statistics for the tunneling current at zero temperature.Comment: 7 pages, 2 figur

We study the effects of a uniform magnetic field on the one-dimensional spin-orbital model in terms of effective field theories. Two regions are examined: one around the SU(4) point (J=K/4) and the other with K<K/4, the excitation spectrum has a gap. When the magnetic field is beyond some critical value, a quantum phase transition occurs. However, the correlation functions around the SU(4) point and the region with K<

We study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero density fixed point. Moreover, we find that the T = 0 thermodynamics of this system in the unitary limit is exactly identical to the one for an ideal Fermi gas.

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type-I) or Fermi lines (type-II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work, we study the effects of Coulomb interactions, following the spirit of Shankar 1 , by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions. arXiv:1710.09240v1 [cond-mat.str-el]