The tensor renormalization group study of the general spin-S Blume-Capel model

We focus on the special situation of $D=2J$ of the general spin-S Blume-Capel model on the square lattice. Under the infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are discussed by the newly developed tensor renormalization group method. For the case of the integer spin-S, the system will undergo $S$ first-order phase transitions with the successive symmetry breaking with the magnetization $M=S,S-1,...0$. For the half-integer spin-S, there are similar $S-1/2$ first order phase transition with $M=S,S-1,...1/2$ stepwise structure, in addition, there is a continuous phase transition due to the spin-flip $Z_2$ symmetry breaking. In the low temperature regions, all first-order phase transitions are accompanied by the successive disappearance of the optional spin-component pairs($s,-s$), furthermore, the critical temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of the magnetic field, the visualization parameter characterizing the intrinsic degeneracy of the different phases clearly demonstrates the phase transition process.Comment: 6 pages, 7 figure

Surface transport coefficients for three-dimensional topological superconductors

We argue that surface spin and thermal conductivities of three-dimensional topological superconductors are universal and topologically quantized at low temperature. For a bulk winding number $\nu$, there are $|\nu|$ "colors" of surface Majorana fermions. Localization corrections to surface transport coefficients vanish due to time-reversal symmetry (TRS). We argue that Altshuler-Aronov interaction corrections vanish because TRS forbids color or spin Friedel oscillations. We confirm this within a perturbative expansion in the interactions, and to lowest order in a large-$|\nu|$ expansion. In both cases, we employ an asymptotically exact treatment of quenched disorder effects that exploits the chiral character unique to two-dimensional, time-reversal-invariant Majorana surface states.Comment: 24 pages, 15 figures. v3: published versio

Spin-current Seebeck effect in quantum dot systems

We first bring up the concept of spin-current Seebeck effect based on a recent experiment [Nat. Phys. {\bf 8}, 313 (2012)], and investigate the spin-current Seebeck effect in quantum dot (QD) systems. Our results show that the spin-current Seebeck coefficient $S$ is sensitive to different polarization states of QD, and therefore can be used to detect the polarization state of QD and monitor the transitions between different polarization states of QD. The intradot Coulomb interaction can greatly enhance the $S$ due to the stronger polarization of QD. By using the parameters for a typical QD, we demonstrate that the maximum $S$ can be enhanced by a factor of 80. On the other hand, for a QD whose Coulomb interaction is negligible, we show that one can still obtain a large $S$ by applying an external magnetic field.Comment: 6 pages, 8 figure

Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.Comment: 6+3 pages, 2+1 figure