This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

China

Yanyan Chen

Siyuan Wang

Yu Zhao

Yuting Hu

Yidun Wan

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.

United States

Jessica Christian

David Green

Peter Huston

David Penneys

A lattice model for condensation in Levin-Wen systems

A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.

Hongyu Wang

Extend the Levin-Wen model to two-dimensional topological orders with gapped boundary junctions

Relativistic millicharged particles (<math><msub><mi>χ</mi><mi>q</mi></msub></math>) have been proposed in various extensions to the standard model of particle physics. We consider the scenarios where they are produced at nuclear reactor core and via interactions of cosmic rays with the Earth’s atmosphere. Millicharged particles could also be candidates for dark matter and become relativistic through acceleration by supernova explosion shock waves. The atomic ionization cross section of <math><msub><mi>χ</mi><mi>q</mi></msub></math> with matter are derived with the equivalent photon approximation. Smoking-gun signatures with significant enhancement in the differential cross section are identified. New limits on the mass and charge of <math><msub><mi>χ</mi><mi>q</mi></msub></math> are derived, using data taken with a point-contact germanium detector with 500 g mass functioning at an energy threshold of 300 eV at the Kuo-Sheng Reactor Neutrino Laboratory.

Taiwan

India

L. Singh

J. W. Chen

H. C. Chi

C.P. Liu

M. K. Pandey

H. T. Wong

C. P. Wu

Türkiye

M. Agartioglu

M. Deniz

H. B. Li

S. T. Lin

V. Sharma

M. K. Singh

V. Singh

Q. Yue

Constraints on millicharged particles with low-threshold germanium detectors at Kuo-Sheng Reactor Neutrino Laboratory

The honeycomb lattice Kitaev model <math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub></math> with two kinds of Wen–Toric-code four-body interactions <math><msub><mrow><mi>H</mi></mrow><mrow><mi>W</mi><mi>T</mi></mrow></msub></math> is investigated exactly using a new fermionization method, and the ground state phase diagram is obtained. Six kinds of three-body interactions are also considered. A Hamiltonian equivalent to the honeycomb lattice Kitaev model is also introduced. The fermionization method is generalized to two-dimensional systems, and the two-dimensional Jordan–Wigner transformation is obtained as a special case of this formula. The model <math><msub><mrow><mi>H</mi></mrow><mrow><mi>K</mi></mrow></msub><mo>+</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>W</mi><mi>T</mi></mrow></msub></math> is symmetric in four-dimensional space of coupling constants, and the anyon type excitations appear in each phase.

Japan

Kazuhiko Minami

Honeycomb lattice Kitaev model with Wen–Toric-code interactions, and anyon excitations

With a combined analysis of data on Î¥(5S)âhb(1P,2P)Ï+Ï- and Î¥(5S)âB(â)BÂ¯(â)Ï in an effective field theory approach, we determine resonance parameters of Zb states in two scenarios. In one scenario we assume that Zb states are pure molecular states, while in the other one we assume that Zb states contain compact components. We find that the present data favor that there should be some compact components inside Zb(â²) associated with the molecular components. By fitting the invariant mass spectra of Î¥(5S)âhb(1P,2P)Ï+Ï- and Î¥(5S)âB(â)BÂ¯âÏ , we determine that the probability of finding the compact components in Zb states may be as large as about 40Â %.

Wen-Sheng Huo

Guo-Ying Chen

The nature of Zb states from a combined analysis of Υ(5S)→hb(mP)π+π- and Υ(5S)→B(∗)B¯(∗)π

We revisit the compositeness theorem proposed by Weinberg in an effective field theory (EFT) and explore criteria which are sensitive to the structure of S-wave threshold states. On a general basis, we show that the wave function renormalization constant Z, which is the probability of finding an elementary component in the wave function of a threshold state, can be explicitly introduced in the description of the threshold state. As an application of this EFT method, we describe the near-threshold line shape of the D*0DÌ 0 invariant mass spectrum in BâD*0DÌ 0K and determine a nonvanishing value of Z. It suggests that the X(3872) as a candidate of the D*0DÌ 0 molecule may still contain a small ccÌ core. This elementary component, on the one hand, explains its production in the B meson decay via a short-distance mechanism, and on the other hand, is correlated with the D*0DÌ 0 threshold enhancement observed in the D*0DÌ 0 invariant mass distributions. Meanwhile, we also show that if Z is non-zero, the near-threshold enhancement of the D*0DÌ 0 mass spectrum in the B decay will be driven by the short-distance production mechanism.

Qiang Zhao

Identifying the structure of near-threshold states from the line shapeSupported by National Natural Science Foundation of China (11147022, 11035006, 11305137), Chinese Academy of Sciences (KJCX2-EW-N01), Ministry of Science and Technology of China (2009CB825200), DFG and NSFC (11261130311) through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD”, and Doctor Foundation of Xinjiang University (BS110104)