Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.Comment: 17 pages, 9 figure

Transport through a double barrier for interacting quasi one-dimensional electrons in a Quantum Wire in the presence of a transverse magnetic field

We discuss the Luttinger Liquid behaviour of a semiconducting Quantum Wire. We show that the measured value of the bulk critical exponent, $\alpha_{bulk}$, for the tunneling density of states can be easily calculated. Then, the problem of the transport through a Quantum Dot formed by two Quantum Point Contacts along the Quantum Wire, weakly coupled to spinless Tomonaga-Luttinger liquids is studied, including the action of a strong transverse magnetic field $B$. The known magnetic dependent peaks of the conductance, $G(B)$, in the ballistic regime at a very low temperature, $T$, have to be reflected also in the transport at higher $T$ and in different regimes. The temperature dependence of the maximum $G_{max}$ of the conductance peak, according to the Correlated Sequential Tunneling theory, yields the power law $G_{max}\propto T^{2\alpha_{end}-1}$, with the critical exponent, $\alpha_{end}$, strongly reduced by $B$. This behaviour suggests the use of a similar device as a magnetic field modulated transistor.Comment: 6 pages, 4 figure

Boundary contributions to specific heat and susceptibility in the spin-1/2 XXZ chain

Exact low-temperature asymptotic behavior of boundary contribution to specific heat and susceptibility in the one-dimensional spin-1/2 XXZ model with exchange anisotropy 1/2 < \Delta \le 1 is analytically obtained using the Abelian bosonization method. The boundary spin susceptibility is divergent in the low-temperature limit. This singular behavior is caused by the first-order contribution of a bulk leading irrelevant operator to boundary free energy. The result is confirmed by numerical simulations of finite-size systems. The anomalous boundary contributions in the spin isotropic case are universal.Comment: 6 pages, 3 figures; corrected typo

Spectral functions of strongly interacting isospin-1/2 bosons in one dimension

We study a system of one-dimensional (iso)spin-1/2 bosons in the regime of strong repulsive interactions. We argue that the low-energy spectrum of the system consists of acoustic density waves and the spin excitations described by an effective ferromagnetic spin chain with a small exchange constant J. We use this description to compute the dynamic spin structure factor and the spectral functions of the system.Comment: reference adde

Density Matrix Renormalization Group Method for the Random Quantum One-Dimensional Systems - Application to the Random Spin-1/2 Antiferromagnetic Heisenberg Chain -

The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are consistent with the predictions of the renormalization group theory demonstrating the effectiveness of the present method in random systems. The possible application of the present method to other random systems is discussed.Comment: 13 pages, 3 figures upon reques

Low Energy Properties of the Random Spin-1/2 Ferromagnetic-Antiferromagnetic Heisenberg Chain

The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a small fraction of the ferromagnetic bond, the effect of the crossover to the random singlet phase on the low temperature susceptibility and specific heat is discussed. The crossover concentration of the ferromagnetic bond is estimated from the numerical data.Comment: 11 pages, revtex, figures upon reques

Kondo Problems in Tomonaga-Luttinger liquids

Quantum impurity problems in Tomonaga-Luttinger liquids (TLLs) are reviewed with emphasis on their analogy to the Kondo problem in Fermi liquids. First, the problem of a static impurity in a spinless TLL is considered, which is related to the model studied in the context of the macroscopic quantum coherence. In the low-energy limit the TLL is essentially cut into two pieces when interaction is repulsive. The orthogonality catastrophe in a TLL is then discussed. Finally, the Kondo effect of a spin-1/2 impurity in a one-dimensional repulsively interacting electron liquids (a spinful TLL) is reviewed. Regardless of the sign of the exchange coupling, the impury spin is completely screened in the ground state. The leading low-temperature contributions to thermodynamic quantities come from boundary contributions of a bulk leading irrelevant operator.Comment: 7 pages, submitted to a special edition of JPSJ "Kondo Effect -- 40 Years after the Discovery"; corrected typos, added reference