14085517
Twisted Gauge Theory Model of Topological Phases in Three Dimensions
We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the $3$-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the $SL(3,\mathbb{Z})$ generators as the modular $S$ and $T$ matrices of the ground states, which yield a set of topological quantum numbers classified by $\omega$ and quantities derived from $\omega$. Our model fulfills a Hamiltonian extension of the $3+1$-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group $G$. This work is presented to be accessible for a wide range of physicists and mathematicians.
55429933
Symmetry-protected many-body Aharonov-Bohm effect
It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path\char22{}the Aharonov-Bohm effect. Here we examine an Aharonov-Bohm effect on a many-body wave function. Specifically, we study this many-body effect on the gapless edge states of a bulk gapped phase protected by a global symmetry (such as ${\mathbb{Z}}_{N}$)\char22{}the symmetry-protected topological (SPT) states. The many-body analog of spectral shifts, the twisted wave function, and the twisted boundary realization are identified in this SPT state. An explicit lattice construction of SPT edge states is derived, and a challenge of gauging its non-onsite symmetry is overcome. Agreement is found in the twisted spectrum between a numerical lattice calculation and a conformal field theory prediction.
53622530
Towards a non-relativistic holographic superfluid
We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we found a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system re-enters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.
17803056
Boundary degeneracy of topological order
We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the $Z_2$ toric code and $Z_2$ double-semion model (more generally, the $Z_k$ gauge theory and the $U(1)_k \times U(1)_{-k}$ non-chiral fractional quantum Hall state at even integer $k$) can be numerically and experimentally distinguished, by measuring their boundary degeneracy on an annulus or a cylinder.
56145316
Schrödinger Fermi liquids
A class of strongly interacting many-body fermionic systems in 2+1D non-relativistic conformal field theory is examined via the gauge-gravity duality correspondence. The 5D charged black hole with asymptotic Schrodinger isometry in the bulk gravity side introduces parameters of background density and finite particle number into the boundary field theory. We propose the holographic dictionary, and realize a quantum phase transition of this fermionic liquid with fixed particle number by tuning the background density $\beta$ at zero temperature. On the larger $\beta$ side, we find the signal of a sharp quasiparticle pole on the spectral function A(k,w), indicating a well-defined Fermi surface. On the smaller $\beta$ side, we find only a hump with no sharp peak for A(k,w), indicating the disappearance of Fermi surface. The dynamical exponent $z$ of quasiparticle dispersion goes from being Fermi-liquid-like $z\simeq1$ scaling at larger $\beta$ to a non-Fermi-liquid scaling $z\simeq 3/2$ at smaller $\beta$. By comparing the structure of Green's function with Landau Fermi liquid theory and Senthil's scaling ansatz, we further investigate the behavior of this quantum phase transition.
54687140
Bosonic anomalies, induced fractional quantum numbers, and degenerate zero modes: The anomalous edge physics of symmetry-protected topological states
The boundary of symmetry-protected topological states (SPTs) can harbor new quantum anomaly phenomena. In this work, we characterize the bosonic anomalies introduced by the 1+1D non-onsite-symmetric gapless edge modes of 2+1D bulk bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to $G=\prod_i Z_{N_i}=Z_{N_1} \times Z_{N_2} \times Z_{N_3} \times ...$). We demonstrate that some classes of SPTs (termed "Type II") trap fractional quantum numbers (such as fractional $Z_N$ charges) at the 0D kink of the symmetry-breaking domain walls; while some classes of SPTs (termed "Type III") have degenerate zero energy modes (carrying the projective representation protected by the unbroken part of the symmetry), either near the 0D kink of a symmetry-breaking domain wall, or on a symmetry-preserving 1D system dimensionally reduced from a thin 2D tube with a monodromy defect 1D line embedded. More generally, the energy spectrum and conformal dimensions of gapless edge modes under an external gauge flux insertion (or twisted by a branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish many SPT classes. We provide a manifest correspondence from the physical phenomena, the induced fractional quantum number and the zero energy mode degeneracy, to the mathematical concept of cocycles that appears in the group cohomology classification of SPTs, thus achieving a concrete physical materialization of the cocycles. The aforementioned edge properties are formulated in terms of a long wavelength continuum field theory involving scalar chiral bosons, as well as in terms of Matrix Product Operators and discrete quantum lattice models. Our lattice approach yields a regularization with anomalous non-onsite symmetry for the field theory description. We also formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.
118428312
Energy conditions and stability in generalized f(R) gravity with arbitrary coupling between matter and geometry
Abstract The energy conditions and the Dolgov–Kawasaki criterion in generalized f ( R ) gravity with arbitrary coupling between matter and geometry are derived in this Letter, which are quite general and can degenerate to the well-known energy conditions in GR and f ( R ) gravity with non-minimal coupling and non-coupling as special cases. In order to get some insight on the meaning of these energy conditions and the Dolgov–Kawasaki criterion, we apply them to a class of models in the FRW cosmology and give some corresponding results.
10011957
The Standard model in the latticized bulk
We construct the manifestly gauge invariant effective Lagrangian in 3+1 dimensions describing the Standard Model in 4+1 dimensions, following the transverse lattice technique. We incorporate split generation fermions and we explore naturalness for two Higgs configurations: a universal Higgs VEV, common to each transverse brane, and a local Higgs VEV centered on a single brane with discrete exponential attenuation to other branes, emulating the split-generation model. Extra dimensions, with explicit Higgs, do not ameliorate the naturalness problem.
7377062
Gauge invariant effective Lagrangian for Kaluza-Klein modes
We construct a manifestly gauge invariant Lagrangian in $3+1$ dimensions for N Kaluza-Klein modes of an $\mathrm{SU}(m)$ gauge theory in the bulk. For example, if the bulk is $4+1,$ the effective theory is ${\ensuremath{\Pi}}_{i=1}^{N+1}{\mathrm{SU}(m)}_{i}$ with N chiral $(\overline{m},m)$ fields connecting the groups sequentially. This can be viewed as a Wilson action for a transverse lattice in ${x}^{5},$ and is shown explicitly to match the continuum $4+1$ compactified Lagrangian truncated in momentum space. Scale dependence of the gauge couplings is described by the standard renormalization group technique with threshold matching, leading to effective power law running. We also discuss the unitarity constraints, and chiral fermions.
109333657
RF Design of X-Band RF Deflector for Femtosecond Diagnostics of LCLS Electron Beam
We designed a successful constant impedance traveling wave X-band rf deflector for electron beam diagnostics at the 14 GeV SLAC Linac Coherent Light Source (LCLS). This is the first practical deflector built with a waveguide coupler. The 1-meter rf deflector produces 24 MeV peak transverse kick when powered with 20 MW of 11.424 GHz rf. The design is based on our experience with high gradient X-band accelerating structures. Several deflectors of this design have been built at SLAC and are currently in use. Here we describe the design and distinguishing features of this device.
37988677
Development of Measurement and Transverse Feedback System at HLS
In order to cure and damp coupled bunch (CB) instabilities caused by the high order modes (HOMs) of the RF cavity and the resistive wall impedance of the Ring vacuum chamber. HOMs are ineluctable during the operation of the accelerator. An observer system characterized by bunch by bunch measurement of transverse β oscillation and longitudinal synchrotron phase oscillation has been constructed and commissioned at Hefei Light Source (HLS) [1, 2]. A transverse bunch-by-bunch feedback system is under construction. The design and development of the observe systems, as well as diagnostics results of machine instabilities are presented in this paper.