Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries

We propose a general approach to construct symmetry protected topological (SPT) states i.e the short-range entangled states with symmetry) in 2D spin/boson systems on lattice. In our approach, we fractionalize spins/bosons into different fermions, which occupy nontrivial Chern bands. After the Gutzwiller projection of the free fermion state obtained by filling the Chern bands, we can obtain SPT states on lattice. In particular, we constructed a U(1) SPT state of a spin-1 model, a SO(3) SPT state of a boson system with spin-1 bosons and spinless bosons, and a SU(2) SPT state of a spin-1/2 boson system. By applying the "spin gauge field" which directly couples to the spin density and spin current of $S^z$ components, we also calculate the quantum spin Hall conductance in each SPT state. The projective ground states can be further studied numerically in the future by variational Monte Carlo etc.Comment: 7+ pages, accepted by Phys. Rev.

Performance Analysis of a Low-Interference N-Continuous OFDM Scheme

This paper investigates two issues of power spectrum density (PSD) and bit error rate (BER) of an N-continuous orthogonal frequency division multiplexing (NC-OFDM) aided low-interference time-domain scheme, when the smooth signal is designed by the linear combination of basis signals truncated by a window. Based on the relationship between the continuity and sidelobe decaying, the PSD performance is first analyzed and compared, in terms of the highest derivative order (HDO) N and the length of the smooth signal L. Since the high-order derivative of the truncation window has the finite continuity, the N-continuous signal has two finite continuities, which may have different continuous derivative orders. In this case, we develop a close PSD expression by introducing another smooth signal, which is also linearly combined by other basis signals, to explain the sidelobe decaying related to N and L. Then, in the context of BER, considering the multipath Rayleigh fading channel, based on the effect of the delayed tail of the smooth signal to the received signal, we provide a procedure for calculating the BER expressed in the form of an asymptotic summation.Comment: 7 pages, 6 figure

Translation invariant topological superconductors on lattice

In this paper we introduce four Z_2 topological indices zeta_k=0,1 at k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D superconducting states that have translation symmetry but may break any other symmetries. The 16 classes of superconducting states are distinguished by their even/odd numbers of fermions on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices. As a result, the 16 classes topological superconducting states exist even for interacting systems. For non-interacting systems, we find that zeta_k is the number of electrons on k=(0,0), (0,pi), (pi, 0), or (pi,pi) orbitals (mod 2) in the ground state. For 3D superconducting states with only translation symmetry, there are 256 different types of topological superconductors.Comment: 4 pages, RevTeX

Novel Algorithms for LDD Motif Search

Background: Motifs are crucial patterns that have numerous applications including the identification of transcription factors and their binding sites, composite regulatory patterns, similarity between families of proteins, etc. Several motif models have been proposed in the literature. The (l,d)-motif model is one of these that has been studied widely. However, this model will sometimes report too many spurious motifs than expected. We interpret a motif as a biologically significant entity that is evolutionarily preserved within some distance. It may be highly improbable that the motif undergoes the same number of changes in each of the species. To address this issue, in this paper, we introduce a new model which is more general than (l,d)-motif model. This model is called (l,d1,d2)-motif model (LDDMS) and is NP-hard as well. We present three elegant as well as efficient algorithms to solve the LDDMS problem, i.e., LDDMS1, LDDMS2 and LDDMS3. They are all exact algorithms. Results: We did both theoretical analyses and empirical tests on these algorithms. Theoretical analyses demonstrate that our algorithms have less computational cost than the pattern driven approach. Empirical results on both simulated datasets and real datasets show that each of the three algorithms has some advantages on some (l,d1,d2) instances. Conclusions: We proposed LDDMS model which is more practically relevant. We also proposed three exact efficient algorithms to solve the problem. Besides, our algorithms can be nicely parallelized. We believe that the idea in this new model can also be extended to other motif search problems such as Edit-distance-based Motif Search (EMS) and Simple Motif Search (SMS)