Collective excitations and the nature of Mott transition in undoped gapped graphene

Particle-hole continuum (PHC) for massive Dirac fermions in presence of short range interactions, provides an unprecedented opportunity for formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel in undoped system. Both poles are close in energy and are separated from thec continuum of free particle-hole excitations by an energy scale of the order of gap parameter $\Delta$. They both disperse linearly with two different velocities reminiscent of spin-charge separation in Luttinger liquids. When the strength of Hubbard interactions is stronger than a critical value, the velocity of singlet excitation which we interpret as a charge boson composite becomes zero, and renders the system a Mott insulator. Beyond this critical point, the low-energy sector is left with a linearly dispersing triplet mode -- a characteristic of a Mott insulator. The velocity of triplet mode at the Mott criticality is twice the velocity of underlying Dirac fermions. The phase transition line in the space of $U$ and $\Delta$ is in qualitative agreement with a more involved dynamical mean field theory (DMFT) calculation.Comment: 4 pages, 2 fig

Exact phase diagram and topological phase transitions of the XYZ spin chain

Within the block spin renormalization group we are able to construct the "exact" phase diagram of the XYZ spin chain. First we identify the Ising order along $\hat x$ or $\hat y$ as attractive renormalization group fixed points of the Kitaev chain. Then in a global phase space composed of the anisotropy $\lambda$ of the XY interaction and the coupling $\Delta$ of the $\Delta\sigma^z\sigma^z$ interaction we find that the above fixed points remain attractive in the two dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain which in turn is characterized by winding number $\pm 1$ depending whether the Ising order parameter is along $\hat x$ or $\hat y$ directions; or (2) attracted to the Mott phases of the underlying Jordan-Wigner fermions which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the XYZ model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the XYZ model justifies why our analytical solution of the three-site problem which is at the core of the renormalization group treatment is able to produce the exact phase diagram of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the Mott-Ising phase is entitled to host apprpriate form of zero modes. We further observe that the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.Comment: 6 Fig

Gapless chiral excitons in thin films of topological insulators

In a nanoscopic thin film of a strong topological insulator (TI) the Coulomb interaction in the channel that exchanges the two electrons with the same chirality in two different planes of the slab takes advantage of the minus sign resulting from such "exchange" and gives rise to a bound state between the positive energy states in one surface and the negative energy states in the opposite surfaces. Therefore particle and hole pairs in the {\em undoped} Dirac cone of the TI thin film form an inter-surface spin-singlet state that lies below the continuum of free particle-hole pairs. This mode is similar to the excitons of semiconductors, albeit formed between the electron and hole pairs from two different two-dimensional surfaces. For low-momenta the dispersion relation characterizing this collective mode is linear. Experimental comparison of two slabs with different thicknesses can capture the exponential dependence of the present effect on the slab thickness.Comment: Comments are welcom