scholarly journals Synthesis and observation of non-Abelian gauge fields in real space

Science ◽  
2019 ◽  
Vol 365 (6457) ◽  
pp. 1021-1025 ◽  
Author(s):  
Yi Yang ◽  
Chao Peng ◽  
Di Zhu ◽  
Hrvoje Buljan ◽  
John D. Joannopoulos ◽  
...  
Keyword(s):  
Gauge Field ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Final States ◽  
Abelian Gauge ◽  
Classical Waves ◽  
Break Time ◽  
Bohm Effect ◽  
Aharonov Bohm

Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

Observation of non-Abelian Aharonov-Bohm Effect with synthetic gauge fields

2020 ◽  
Author(s):  
Yi Yang ◽  
Chao Peng ◽  
Di Zhu ◽  
Hrvoje Buljan ◽  
John D. Joannopoulos ◽  
...  
Keyword(s):  
Gauge Fields ◽  
Bohm Effect ◽  
Synthetic Gauge Fields ◽  
Aharonov Bohm

BLOCKSPIN AND MULTIGRID FOR STAGGERED FERMIONS IN NON-ABELIAN GAUGE FIELDS

1992 ◽  
Vol 03 (01) ◽  
pp. 121-147 ◽  
Author(s):  
T. KALKREUTER ◽  
G. MACK ◽  
M. SPEH
Keyword(s):  
Gauge Theories ◽  
Free Action ◽  
Real Space ◽  
Gauge Fields ◽  
Group Approach ◽  
Abelian Gauge ◽  
Staggered Fermions ◽  
Real Space Renormalization Group ◽  
Renormalization Group Approach ◽  
Definition Of

We discuss blockspins for staggered fermions, i. e. averaging and interpolation procedures which are needed in a real space renormalization group approach to gauge theories with staggered fermions and in a multigrid approach to the computation of gauge covariant propagators. The discussion starts from the requirement that the symmetries of the free action should be preserved by the blocking procedure in the limit of a pure gauge. A definition of an averaging kernel as a solution of a gauge covariant eigenvalue equation is proposed, and the properties of a corresponding interpolation kernel are examined in the light of general criteria for good choices of blockspins. Some results of multigrid computations of bosonic propagators in an SU(2) gauge field in 4 dimensions are also presented.

scholarly journals PARTICLE SPECTRUM OF NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (14) ◽  
pp. 1137-1161 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Field ◽  
Free Field ◽  
Gauge Fields ◽  
Particle Spectrum ◽  
Field Equations ◽  
Abelian Gauge ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Extended Field ◽  
Rank 2

We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

CHIRAL SPIN LIQUID STATES IN 3-SPACE DIMENSIONS AND TOPOLOGICAL ASPECTS OF MONOPOLE SUPERCONDUCTIVITY

1993 ◽  
Vol 07 (13n14) ◽  
pp. 913-919
Author(s):  
B. BASU ◽  
P. BANDYOPADHYAY
Keyword(s):  
Magnetic Flux ◽  
Gauge Field ◽  
Spin System ◽  
Berry Phase ◽  
Gauge Fields ◽  
Spin Liquid ◽  
Abelian Gauge ◽  
Heisenberg Spin ◽  
Pair Condensation ◽  
Liquid States

We have studied here the topological aspects of monopole superconductivity in 3+1 dimensions. It is pointed out that Heisenberg spin system may be associated with non-Abelian gauge fields. When the spin and charge become separated, spinons and holons emerge and holons interacting with such a gauge field associate a magnetic flux giving rise to nonzero Berry phase and causes the existence of chiral spin liquid. This also suggests that these holons are much heavier than their free counterpart and the pair of such holons forms a bosonic state respecting rotational invariance. Superconductivity arises out of this pair condensation.

scholarly journals Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Seiji Sugawa ◽  
Francisco Salces-Carcoba ◽  
Yuchen Yue ◽  
Andika Putra ◽  
I. B. Spielman
Keyword(s):  
Gauge Field ◽  
Wilson Loop ◽  
Berry Phase ◽  
Einstein Condensate ◽  
Gauge Potential ◽  
Abelian Gauge ◽  
Dimensional Parameter ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Aharonov Bohm

AbstractQuantum states can acquire a geometric phase called the Berry phase after adiabatically traversing a closed loop, which depends on the path not the rate of motion. The Berry phase is analogous to the Aharonov–Bohm phase derived from the electromagnetic vector potential, and can be expressed in terms of an Abelian gauge potential called the Berry connection. Wilczek and Zee extended this concept to include non-Abelian phases—characterized by the gauge-independent Wilson loop—resulting from non-Abelian gauge potentials. Using an atomic Bose–Einstein condensate, we quantum-engineered a non-Abelian SU(2) gauge field, generated by a Yang monopole located at the origin of a 5-dimensional parameter space. By slowly encircling the monopole, we characterized the Wilczek–Zee phase in terms of the Wilson loop, that depended on the solid-angle subtended by the encircling path: a generalization of Stokes’ theorem. This observation marks the observation of the Wilson loop resulting from a non-Abelian point source.

scholarly journals Experimental realization of non-Abelian gauge field in circuit system

2020 ◽  
Author(s):  
Rui Yu ◽  
Ziyin Song ◽  
Tianyu Wu ◽  
Wenquan Wu
Keyword(s):  
Gauge Field ◽  
Building Blocks ◽  
The Novel ◽  
Spin Orbit ◽  
Edge States ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Wide Range ◽  
Exotic Physics ◽  
Spin Texture

Abstract Synthetic gauge field, especially the non-Abelian gauge field, has emerged as a new way to explore exotic physics in a wide range of materials and platforms. Here we present the building blocks, consisting of capacitors and inductors, to implement the non-Abelian tunneling matrices and show that circuit system is an appropriate choice to realize the non-Abelian gauge field. To demonstrate the novel physics enabled by the non-Abelian gauge field, we provide a simple and modular scheme to design the Rashba-Dresselhaus spin-orbit interaction and topological Chern state in circuits. By measuring the spin texture and chiral edge states of the resonant frequency band structures, we confirm the spin-orbit effect and topological Chern state in circuits. Our schemes open a broad avenue to study non-Abelian gauge field and related physics in circuit platform.

scholarly journals Gauge fields in real and momentum spaces in magnets: monopoles and skyrmions

2012 ◽  
Vol 370 (1981) ◽  
pp. 5806-5819 ◽  
Author(s):  
N. Nagaosa ◽  
X. Z. Yu ◽  
Y. Tokura
Keyword(s):  
Hall Effect ◽  
Gauge Field ◽  
Berry Phase ◽  
Solid Angle ◽  
Spontaneous Magnetization ◽  
Anomalous Hall Effect ◽  
Magnetic Monopoles ◽  
Real Space ◽  
Gauge Fields ◽  
Quantum Mechanical

Electronic states in magnets are characterized by the quantum mechanical Berry phase defined in both the real and momentum spaces. This Berry phase constitutes the gauge fields, i.e. the emergent electromagnetic fields in solids, and affects the motion of the electrons. In momentum space, the band crossings act as the magnetic monopoles, i.e. the sources or sinks of the gauge flux. In real space, the spin textures with non-coplanar spin configurations produce the gauge field by the solid angle leading to the spin chirality. Skyrmion is the representative structure supporting this gauge field. A typical phenomenon reflecting this gauge field is the anomalous Hall effect, i.e. the Hall effect produced by the spontaneous magnetization combined with the relativistic spin–orbit interaction. We discuss a few examples recently studied related to these issues with some new results on skyrmion formation.

scholarly journals ABOUT SOME EXACT SOLUTIONS FOR 2 + 1 GRAVITY COUPLED TO GAUGE FIELDS

1992 ◽  
Vol 07 (25) ◽  
pp. 2341-2350 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Black Holes ◽  
Exact Solutions ◽  
Gauge Field ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Planck Mass ◽  
Static Solutions

Some exact static solutions for Einstein gravity in 2 + 1 dimensions coupled to Abelian gauge field are discussed, where the invariant interval is of the form: ds2 = N2 (r) dt2 − dr2 − C2 (r) dθ2. Some of these solutions are three-dimensional analogs of the Schwarzschild black holes. The metrics in the regions inside and outside the horizon are connected by the changing of the Planck mass sign.

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