Continuous topological phase transitions between clean quantum Hall states

Continuous transitions between states with the {\em same} symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral quasiparticles are shown to have such transitions. For clean bilayer (nnm) states, a continous transition to other QH states (including non-Abelian states) can be driven by increasing interlayer repulsion/tunneling. The effective theories describing the critical points at some transitions are derived.Comment: 4 pages, RevTeX, 2 eps figure

Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study

We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the similarities and differences between these two types of stabilizer codes. We compute the error correcting rate $C:=n/d^2$ for surface codes $C_s$ and color codes $C_c$ in several instances. On the torus, typical values are $C_s=2$ and $C_c=3/2$, but we find that the optimal values are $C_s=1$ and $C_c=9/8$. For planar codes, a typical value is $C_s=2$, while we find that the optimal values are $C_s=1$ and $C_c=3/4$. In general, a color code encodes twice as much logical qubits as a surface code does.Comment: revtex, 6 pages, 7 figure

Renormalization Group Study of Magnetic Catalysis in the 3d Gross-Neveu Model

Magnetic catalysis describes the enhancement of symmetry breaking quantum fluctuations in chirally symmetric quantum field theories by the coupling of fermionic degrees of freedom to a magnetic background configuration. We use the functional renormalization group to investigate this phenomenon for interacting Dirac fermions propagating in (2+1)-dimensional spacetime, described by the Gross-Neveu model. We identify pointlike operators up to quartic fermionic terms that can be generated in the renormalization group flow by the presence of an external magnetic field. We employ the beta function for the fermionic coupling to quantitatively analyze the field dependence of the induced spectral gap. Within our pointlike truncation, the renormalization group flow provides a simple picture for magnetic catalysis.Comment: 14 pages, 6 figures, typos correcte

Topological Computation without Braiding

We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net condensates in 3-colexes. The universal set of gates is implemented without selective addressing of physical qubits and, being fully topologically protected, it does not rely on quasiparticle excitations or their braiding.Comment: revtex4, 4 pages, 4 figure

SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms

Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as "SU(3) spin-orbit-coupling," where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically non-trivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an exact equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states -- the hallmark feature of such an SU(3) topological insulator.Comment: 4.2 pages, 1 figur

Competition between the BCS superconductivity and ferromagnetic spin fluctuations in MgCNi3_3

The low temperature specific heat of the superconductor MgCNi$_3$ and a non-superconductor MgC$_{0.85}$Ni$_3$ is investigated in detail. An additional contribution is observed from the data of MgCNi$_3$ but absent in MgC$_{0.85}$Ni$_3$, which is demonstrated to be insensitive to the applied magnetic field even up to 12 Tesla. A detailed discussion on its origin is then presented. By subtracting this additional contribution, the zero field specific heat of MgCNi$_3$ can be well described by the BCS theory with the gap ratio ($\Delta/k_BT_c$) determined by the previous tunneling measurements. The conventional s-wave pairing state is further proved by the magnetic field dependence of the specific heat at low temperatures and the behavior of the upper critical field.Comment: To appear in Physical Review B, 6 pages, 7 figure

Measurement of a Sign-Changing Two-Gap Superconducting Phase in Electron-Doped Ba(Fe_{1-x}Co_x)_2As_2 Single Crystals using Scanning Tunneling Spectroscopy

Scanning tunneling spectroscopic studies of $Ba(Fe_{1-x}Co_x)_2As_2$ (x = 0.06, 0.12) single crystals reveal direct evidence for predominantly two-gap superconductivity. These gaps decrease with increasing temperature and vanish above the superconducting transition $T_c$. The two-gap nature and the slightly doping- and energy-dependent quasiparticle scattering interferences near the wave-vectors $(\pm \pi, 0)$ and $(0, \pm \pi)$ are consistent with sign-changing $s$-wave superconductivity. The excess zero-bias conductance and the large gap-to-$T_c$ ratios suggest dominant unitary impurity scattering.Comment: 4 pages, 4 figures. Paper accepted for publication in Physical Review Letters. Contact author: Nai-Chang Yeh ([email protected]