Inversion symmetry protected topological insulators and superconductors

Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry. In this work we systematically study another class of topological phases of weakly interacting electrons protected by spatial inversion symmetry, which generally don't support stable gapless boundary states. We classify these inversion-symmetric topological insulators and superconductors in the framework of K-theory, and construct their lattice models. We also discuss quantized response functions of these inversion-protected topological phases, which serve as their experimental signatures.Comment: 9.5+2.5 pages, 4 figures, 2 table

Applications of Lerch's theorem and permutations concerning quadratic residues

Let $p$ be an odd prime. For each integer $a$ with $p\nmid a$, the famous Zolotarev's Lemma says that the Legendre symbol $(\frac{a}{p})$ is the sign of the permutation of $\Z/p\Z$ induced by multiplication by $a$. The extension of Zolotarev's result to the case of odd integers was shown by Frobenius. After that, Lerch extended these to all positive integers. In this paper we explore some applications of Lerch's result. For instance, we study permutations involving arbitrary $k$-th power residue modulo $p$ and primitive roots of a power of $p$. Finally, we discuss some permutation problems concerning quadratic residues modulo $p$. In particular, we confirm some conjectures posed by Sun.Comment: 11 page

Generalized Compute-Compress-and-Forward

Compute-and-forward (CF) harnesses interference in wireless communications by exploiting structured coding. The key idea of CF is to compute integer combinations of codewords from multiple source nodes, rather than to decode individual codewords by treating others as noise. Compute-compress-and-forward (CCF) can further enhance the network performance by introducing compression operations at receivers. In this paper, we develop a more general compression framework, termed generalized compute-compress-and-forward (GCCF), where the compression function involves multiple quantization-and-modulo lattice operations. We show that GCCF achieves a broader compression rate region than CCF. We also compare our compression rate region with the fundamental Slepian-Wolf (SW) region. We show that GCCF is optimal in the sense of achieving the minimum total compression rate. We also establish the criteria under which GCCF achieves the SW region. In addition, we consider a two-hop relay network employing the GCCF scheme. We formulate a sum-rate maximization problem and develop an approximate algorithm to solve the problem. Numerical results are presented to demonstrate the performance superiority of GCCF over CCF and other schemes.Comment: 27 pages, 11 figures, submitted to IEEE Transaction on Information Theor

Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent QED3QED_3 and anyon superfluid

Inspired by Chern-Simons effective theory description of symmetry protected topological (SPT) phases in two dimensions, we present a projective construction for many-body wavefunctions of SPT phases. Using this projective construction we can systematically write down trial wavefunctions of SPT phases on a lattice. An explicit example of SPT phase with $U(1)$ symmetry is constructed for two types of bosons with filling $\nu_{b_1}=\nu_{b_2}=\frac12$ per site on square lattice. We study continuous phase transitions between different $U(1)$-SPT phases based on projective construction. The effective theory around the critical point is emergent $QED_3$ with fermion number $N_f=2$. Such a continuous phase transition however needs fine tuning, and in general there are intermediate phases between different $U(1)$-SPT phases. We show that such an intermediate phase has the same response as an anyon superconductor, and hence dub it "anyon superfluid". A schematic phase diagram of interacting bosons with $U(1)$ symmetry is depicted.Comment: 11 pages, 3 figures, published versio

Spin quantum Hall effects in a spin-1 topological paramagnet

AKLT state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets, which hosts symmetry-protected gapless excitations on the boundary. In this work we show how to realize this type of featureless spin-1 states on a generic two-dimensional lattice. These states have a gapped spectrum in the bulk but supports gapless edge states protected by spin rotational symmetry along a certain direction, and are featured by spin quantum Hall effect. Using fermion representation of integer-spins we show a concrete example of such spin-1 topological paramagnets on kagome lattice, and suggest a microscopic spin-1 Hamiltonian which may realize it.Comment: 5 pages, 2 figures, published version, references update

Output Feedback Tracking Control for a Class of Uncertain Systems subject to Unmodeled Dynamics and Delay at Input

Besides parametric uncertainties and disturbances, the unmodeled dynamics and time delay at the input are often present in practical systems, which cannot be ignored in some cases. This paper aims to solve output feedback tracking control problem for a class of nonlinear uncertain systems subject to unmodeled high-frequency gains and time delay at the input. By the additive decomposition, the uncertain system is transformed to an uncertainty-free system, where the uncertainties, disturbance and effect of unmodeled dynamics plus time delay are lumped into a new disturbance at the output. Sequently, additive decomposition is used to decompose the transformed system, which simplifies the tracking controller design. To demonstrate the effectiveness, the proposed control scheme is applied to three benchmark examples.Comment: 22 pages, 7 figure

Can deeply underdoped superconducting cuprates be topological superconductors?

The nodal $d_{x^2-y^2}$ superconducting gap is a hallmark of the cuprate high T$_c$ superconductors. Surprisingly recent angle-resolved photoemission spectroscopy of deeply underdoped cuprates revealed a nodeless energy gap which is adhered to the Fermi surface. Importantly this phenomenon is observed for compounds across several different cuprate families. In this letter we propose an exciting possibility, namely the fully gapped state is a topological superconductor.Comment: 4 pages, 1 table, 3 figures + 4.5 pages supplemental material

An optimal consensus tracking control algorithm for autonomous underwater vehicles with disturbances

The optimal disturbance rejection control problem is considered for consensus tracking systems affected by external persistent disturbances and noise. Optimal estimated values of system states are obtained by recursive filtering for the multiple autonomous underwater vehicles modeled to multi-agent systems with Kalman filter. Then the feedforward-feedback optimal control law is deduced by solving the Riccati equations and matrix equations. The existence and uniqueness condition of feedforward-feedback optimal control law is proposed and the optimal control law algorithm is carried out. Lastly, simulations show the result is effectiveness with respect to external persistent disturbances and noise

An explicit representation and enumeration for self-dual cyclic codes over F2m+uF2m\mathbb{F}_{2^m}+u\mathbb{F}_{2^m} of length 2s2^s

Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$ and $s$ a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over $\mathbb{F}_{2^m}$, an efficient method for the construction of all distinct self-dual cyclic codes with length $2^s$ over the finite chain ring $\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ $(u^2=0)$ is provided. On that basis, an explicit representation for every self-dual cyclic code of length $2^s$ over $\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ and an exact formula to count the number of all these self-dual cyclic codes are given

High TcT_c superconductivity at the FeSe/SrTiO3_3 Interface

In a recent experiment the superconducting gap of a single unit cell thick FeSe film on SrTiO$_3$ substrate is observed by scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy. The value of the superconducting gap is much larger than that of the bulk FeSe under ambient pressure. In this paper we study the effects of screening due to the ferroelectric phonons on Cooper pairing. We conclude it can significantly enhance the energy scale of Cooper pairing and even change the pairing symmetry. Our results also raise some concerns on whether phonons can be completely ignored for bulk iron-based superconductors.Comment: 20 one-column pages with appendix, 9 figure