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

Macroscopic Quantum Tunneling Effect of Z2 Topological Order

In this paper, macroscopic quantum tunneling (MQT) effect of Z2 topological order in the Wen-Plaquette model is studied. This kind of MQT is characterized by quantum tunneling processes of different virtual quasi-particles moving around a torus. By a high-order degenerate perturbation approach, the effective pseudo-spin models of the degenerate ground states are obtained. From these models, we get the energy splitting of the ground states, of which the results are consistent with those from exact diagonalization methodComment: 25 pages, 14 figures, 4 table

Spin-charge Separation in Nodal Antiferromagnetic Insulator

In this paper, by using two dimensional (2D) Hubbard models with pi-flux phase and that on a hexagonal lattice as examples, we explore spin-charge-separated solitons in nodal antiferromagnetic (AF) insulator - an AF order with massive Dirac fermionic excitations (see detail in the paper). We calculate fermion zero modes and induced quantum numbers on solitons (half skyrmions) in the continuum limit, which are similar to that in the quasi one-dimensional conductor polyacetylene (CH)x and that in topological band insulator. In particular, we find some novel phenomena : thanks to an induced staggered spin moment, a mobile half skyrmion becomes a fermionic particle; when a hole or an electron is added, the half skyrmion turns into a bosonic particle with charge degree of freedom only. Our results imply that nontrivial induced quantum number on solitons may be a universal feature of spin-charge separation in different systems

Contactless heater floating zone refining and crystal growth

Floating zone refining or crystal growth is carried out by providing rapid relative rotation of a feed rod and finish rod while providing heat to the junction between the two rods so that significant forced convection occurs in the melt zone between the two rods. The forced convection distributes heat in the melt zone to allow the rods to be melted through with a much shorter melt zone length than possible utilizing conventional floating zone processes. One of the rods can be rotated with respect to the other, or both rods can be counter-rotated, with typical relative rotational speeds of the rods ranging from 200 revolutions per minute (RPM) to 400 RPM or greater. Zone refining or crystal growth is carried out by traversing the melt zone through the feed rod

Translation-symmetry protected topological orders on lattice

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The spin systems on square lattice are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 sub-classes corresponding to 16 new translation-symmetry protected topological orders. We introduced four $Z_2$ topological indices $\zeta_{\v{k}}=0,1$ at $\v {k}=(0,0)$, $(0,\pi)$, $(\pi, 0)$, $(\pi ,\pi)$ to characterize those 16 new topological orders. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on 3D lattice

COMPUTER VISION TECHNIQUES IN AUGMENTED REALITY SYSTEMS

Master'sMASTER OF ENGINEERIN

Mutual Chern-Simons theory for Z_2 topological order

We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual U(1) x U(1) Chern-Simons theory. However, we find that the different Z_2 topological orders are reflected in different projective realizations of lattice symmetry in the same effective mutual Chern-Simons theory. This result is obtained by comparing the ground-state degeneracy, the ground-state quantum numbers, the gapless edge state, and the projective symmetry group of quasi-particles calculated from the slave-particle theory and from the effective mutual Chern-Simons theories. Our study reveals intricate relations between topological order and symmetry.Comment: 13 pages. RevTeX