Classical and quantum depinning of a domain wall with a spin-polarized current

We study in detail the classical and quantum depinning of a domain wall (DW) induced by a fast-varying spin-polarized current. By confirming the adiabatic condition for calculating the spin-torque in fast-varying current case, we show that the time-dependent spin current has two critical values that determine the classical depinning of DW. This discovery successfully explains the recent experiments. Furthermore, a feasible way is proposed to lower the threshold of spin currents and control the direction of DW's motion. Finally, the quantum properties for the depinning of DW are also investigated in this paper.Comment: 8 pages, 3 figure

Amino acid substitution matrices for protein conformation identification

Methods for alignment of protein sequences typically measure similarity by using substitution matrix with scores for all possible exchanges of one amino acid with another. Although widely used, the matrices derived from homologous sequence segments, such as Dayhoff's PAM matrices and Henikoff's BLOSUM matrices, are not specific for protein conformation identification. Using a different approach, we got many amino acid segment blocks. For each of them, the protein secondary structure is identical. Based on these blocks, we have derived new amino acid substitution matrices. The application of these matrices led to marked improvements in conformation segment search and homologues detection in twilight zone.Comment: 13 pages, 1 figur

Symmetry-protected gapless spin liquids on the strained honeycomb lattice

By including a material-relevant off-diagonal interaction called the $\Gamma$ term into the Kitaev model and introducing spatial anisotropy in the interaction strength on the honeycomb lattice, we obtain a series of nodal Z$_2$ quantum spin liquids (QSLs) from parton approach. These QSLs share the same projective symmetry group and are characterized by certain numbers of symmetry-protected Majorana cones in their low-energy excitation spectrum. We illustrate that the physical properties of the QSLs are dependent on the information of the cones. Using the $\pmb k\cdot\pmb p$ method, we analyze the chirality of every cone with respect to mass generating perturbations. Especially, for an applied external magnetic field, we provide the maximum-mass field-orientation for every cone. Thus, for arbitrarily oriented weak magnetic fields, we can immediately read out the Chern number of the system and the properties of the resultant chiral spin liquids. The new gapless QSLs predicted in our phase diagrams are promising to be realized experimentally by exerting uniaxial pressure to tune the anisotropy of the interaction strength. We further show that all these QSLs can be distinguished by measurable quantities. Based on the study of these QSL phases, we conclude that a complete classification of nodal QSLs with certain symmetry should include not only the projective symmetry groups but also the information of the cones, {\it i.e.}, their total number, their chiralities, and the way in which they are symmetry-related.Comment: 19 pages, 13 figures, 5 tabl

Dirac and Chiral Quantum Spin Liquids on the Honeycomb Lattice in a Magnetic Field

Motivated by recent experimental observations in $\alpha$-RuCl$_3$, we study the $K$-$\Gamma$ model on the honeycomb lattice in an external magnetic field. By a slave-particle representation and Variational Monte Carlo calculations, we reproduce the phase transition from zigzag magnetic order to a field-induced disordered phase. The nature of this state depends crucially on the field orientation. For particular field directions in the honeycomb plane, we find a gapless Dirac spin liquid, in agreement with recent experiments on $\alpha$-RuCl$_3$. For a range of out-of-plane fields, we predict the existence of a Kalmeyer-Laughlin-type chiral spin liquid, which would show an integer-quantized thermal Hall effect.Comment: 5+9 pages, 4+6 figure

A protein structural alphabet and its substitution matrix CLESUM

By using a mixture model for the density distribution of the three pseudobond angles formed by $C_\alpha$ atoms of four consecutive residues, the local structural states are discretized as 17 conformational letters of a protein structural alphabet. This coarse-graining procedure converts a 3D structure to a 1D code sequence. A substitution matrix between these letters is constructed based on the structural alignments of the FSSP database.Comment: 10 page

Irreducible Projective Representations and Their Physical Applications

An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur's lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo Simulations.Comment: 41 pages, 1 figur

Fluctuation of Eigenvalues for Random Toeplitz and Related Matrices

Consider random symmetric Toeplitz matrices $T_{n}=(a_{i-j})_{i,j=1}^{n}$ with matrix entries $a_{j}, j=0,1,2,...,$ being independent real random variables such that \be \mathbb{E}[a_{j}]=0, \ \ \mathbb{E}[|a_{j}|^{2}]=1 \ \ \textrm{for}\,\ \ j=0,1,2,...,\ee (homogeneity of 4-th moments) \be{\kappa=\mathbb{E}[|a_{j}|^{4}],}\ee \noindent and further (uniform boundedness)\be\sup\limits_{j\geq 0} \mathbb{E}[|a_{j}|^{k}]=C_{k}<\iy\ \ \ \textrm{for} \ \ \ k\geq 3.\ee Under the assumption of $a_{0}\equiv 0$, we prove a central limit theorem for linear statistics of eigenvalues for a fixed polynomial with degree $\geq 2$. Without the assumption, the CLT can be easily modified to a possibly non-normal limit law. In a special case where $a_{j}$'s are Gaussian, the result has been obtained by Chatterjee for some test functions. Our derivation is based on a simple trace formula for Toeplitz matrices and fine combinatorial analysis. Our method can apply to other related random matrix models, including Hankel matrices and product of several Toeplitz matrices in a flavor of free probability theory etc. Since Toeplitz matrices are quite different from the Wigner and Wishart matrices, our results enrich this topic.Comment: 27 pages, corrected small gap in proof of Theorem 1.1, added remark 1.

Manipulating Topological Edge Spins in One-Dimensional Optical Lattice

We propose to observe and manipulate topological edge spins in 1D optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In free-fermion case the SPT phase is classified by a $Z$ invariant which reduces to $Z_4$ with interactions. The zero edge modes of the SPT phase are spin-polarized, with left and right edge spins polarized to opposite directions and forming a topological spin-qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in optical lattice. The manipulation of TSQs has potential applications to quantum computation.Comment: 4+pages+Supplementary material. Details for the model realization has been added to the supplementary material. Accepted by Phys. Rev. Let

Classification of quantum critical states of integrable antiferromagnetic spin chains and their correspondent two-dimensional topological phases

We examine the effective field theory of the Bethe ansatz integrable Heisenberg antiferromagnetic spin chains. It shows that the quantum critical theories for the integer spin-S chains should be characterized by the SO(3)level-S Wess-Zumino-Witten model, and classified by the third cohomology group $H^{3}(SO(3),Z)=Z$. Depending on the parity of spin S, this integer classification is further divided into two distinct universality classes, which are associated with two completely different conformal field theories: the even-S chains have gapless bosonic excitations and the odd-S chains have both bosonic and fermionic excitations. We further show that these two classes of critical states correspond to the boundary states of two distinct topological phases in two dimension, which can be described by two-dimensional doubled SO(3) topological Chern-Simons theory and topological spin theory, respectively.Comment: 5 pages, 1 tabl

Symmetry protected topological phases in spin-1 ladders and their phase transitions

We study two-legged spin-1 ladder systems with $D_2\times \sigma$ symmetry group, where $D_2$ is discrete spin rotational symmetry and $\sigma$ means interchain reflection symmetry. The system has one trivial phase and seven nontrivial symmetry protected topological (SPT) phases. We construct Hamiltonians to realize all of these SPT phases and study the phase transitions between them. Our numerical results indicate that there is no direct continuous transition between any two SPT phases we studied. We interpret our results via topological nonlinear sigma model effective field theory, and further conjecture that generally there is no direct continuous transition between two SPT phases in one dimension if the symmetry group is discrete at all length scales.Comment: 20 pages, 8 figures, published versio