arXiv subjects

Yong-Shi Wu

Publications and source records attributed to Yong-Shi Wu.

At least 37 records · Page 2Linked to original sources

arXiv2016

Noncommutative Chern-Simons theory and exotic geometry emerging from the lowest Landau level

We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $ν=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in two-dimensional guiding center space emerges from these internal geometric modes. Using the Dirac bracket method, we find that this quantum geometric field theory is a topological non-commutative Chern-Simons theory.Topological indices, such as the guiding center angular momentum (also called the shift) and the guiding center spin, which characterize the fractional quantum Hall (FQH) states besides the filling factor, are naturally defined. A noncommutative K-matrix Chern-Simons theory is proposed as a generalization to a large class of Abelian FQH topological orders.

cond-mat.str-el↗

arXiv2016

CHY formula and MHV amplitudes

In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.

hep-th↗

arXiv2014

Exotic electronic states in the world of flat bands: from theory to material

It has long been noticed that special lattices contain single-electron flat bands (FB) without any dispersion. Since the kinetic energy of electrons is quenched in the FB, this highly degenerate energy level becomes an ideal platform to achieve strongly correlated electronic states, such as magnetism, superconductivity and Wigner crystal. Recently, the FB has attracted increasing interests, because of the possibility to go beyond the conventional symmetry-breaking phases, towards topologically ordered phases, such as lattice versions of fractional quantum Hall states. This article reviews different aspects of FBs in a nutshell. Starting from the standard band theory, we aim to bridge the frontier of FBs with the textbook solid-state physics. Then, based on concrete examples, we show the common origin of FBs in terms of destructive interference, and discuss various many-body phases associated with such a singular band structure. In the end, we demonstrate real FBs in quantum frustrated materials and organometallic frameworks.

cond-mat.str-el↗

arXiv2014

Exotic Fractional Topological States in Two-Dimensional Organometallic Material

Fractional Chern insulators (FCIs), having properties similar to those of the fractional quantum Hall effect, have been established numerically in various toy models. To fully explore their fundamental physics and to develop practical applications, material realization is indispensable. Here we theoretically predict a realization of FCI in a two-dimensional organometallic material, which is known to have the prerequisite topological at bands. Using numerical exact diagonalization we demonstrate that the presence of strong electronic correlations and fractional filling of such a system could lead to a rich phase diagram, including Abelian fractional quantum Hall (FQH), Fermi-liquid, and Wigner crystal states. In particular, the FQH state has been confirmed systematically by calculating the topological ground-state degeneracies, topological Chern number, and the quasihole excitation spectrum as well as the particle entanglement spectrum. Future experimental realization of the FQH state in such material may provide a route for developing practical applications of FCI with no need of the extreme conditions.

cond-mat.str-el↗

arXiv2014

Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases

We demonstrate how the generalized Pauli exclusion principle emerges for quasiparticle excitations in 2d topological phases. As an example, we examine the Levin-Wen model with the Fibonacci data (specified in the text), and construct the number operator for fluxons living on plaquettes. By numerically counting the many-body states with fluxon number fixed, the matrix of exclusion statistics parameters is identified and is shown to depend on the spatial topology (sphere or torus) of the system. Our work reveals the structure of the (many-body) Hilbert space and some general features of thermodynamics for quasiparticle excitations in topological matter.

cond-mat.str-el↗

arXiv2013

Twisted Quantum Double Model of Topological Phases in Two--Dimension

We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $α$ over $G$. The detailed properties of the ground states are studied, and we find that the ground--state subspace can be characterized in terms of the twisted quantum double $D^α(G)$ of $G$. When $α$ is the trivial 3-cocycle, the model becomes Kitaev's quantum double model based on the finite group $G$, in which the elementary excitations are known to be classified by the quantum double $D(G)$ of $G$. Our model can be viewed as a Hamiltonian extension of the Dijkgraaf--Witten topological gauge theories to the discrete graph case with gauge group being a finite group. We also demonstrate a duality between a large class of Levin-Wen string-net models and certain twisted quantum double models, by mapping the string--net 6j symbols to the corresponding 3-cocycles. The paper is presented in a way such that it is accessible to a wide range of physicists.

cond-mat.str-el↗

arXiv2013

Construction of New D=3, N=4 Quiver Gauge Theories

In this paper we propose a special class of 3-algebras, called double-symplectic 3-algebras. We further show that a consistent contraction of the double-symplectic 3-algebra gives a new 3-algebra, called an N=4 three-algebra, which is then identified as the exact gauged three-algebra in the N=4 quiver gauge theories. A systematic construction is proposed for the 3-brackets and fundamental identities used in building up the N=4 theories, by starting with two superalgebras whose bosonic parts share at least one simple factor or U(1) factor. This leads to a systematic way of constructing D=3, N=4 quiver theories, of which several examples with new gauge groups are presented in detail. The general N=4 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be also re-derived in our new 3-algebra approach.

hep-th↗

arXiv2012

Fusion of Superalgebras and D=3, N=4 Quiver Gauge Theories

For further investigating the underlying structures of the D=3, N=4 Chern-Simons-matter (CSM) theories, we suggest a new concept and procedure for "fusing" two superalgebras into a single new superalgebra. The starting superalgebras may be those used in the previous construction of the double-symplectic 3-algebras in the N=4 CSM theories: The bosonic parts of these two superalgebras share at least one simple factor or U(1) factor. We are able to provide two different methods to do the "fusion". Several explicit examples are presented to demonstrate the "fusion" procedure. We also generalize the "fusion" procedure so that more than two superaglebras can be fused into a single one, provided some conditions are satisfied. It is shown that two or more N=4 theories with different gauge groups may be associated with the same "fused" superalgebra.

hep-th↗

arXiv2012

Flat Chern Band in a Two-Dimensional Organometallic Framework

By combining exotic band dispersion with nontrivial band topology, an interesting type of band structure, namely the flat chern band (FCB), has recently been proposed to spawn high-temperature fractional quantum hall states. Despite the proposal of several theoretical lattice models, however, it remains a doubt whether such a "romance of flatland" could exist in a real material. Here, we present a first-principles design of a two-dimensional (2D) Indium-Phenylene Organometallic Framework (IPOF) that realizes a nearly FCB right around the Fermi level by combining lattice geometry, spin-orbit coupling and ferromagnetism. An effective four-band model is constructed to reproduce the first-principles results. Our design in addition provides a general strategy to synthesize topologically nontrivial materials in virtue of organic chemistry and nanotechnology.

cond-mat.mtrl-sci↗

arXiv2012

Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories

We present a superspace formulation of the D=3, N=4,5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action, and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new super-potential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4,5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be rederived in our 3-algebra approach. All known N=4,5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie-algebra realization of symplectic 3-algebras.

hep-th↗

arXiv2012

Ground State Degeneracy in the Levin-Wen Model for Topological Phases

We study properties of topological phases by calculating the ground state degeneracy (GSD) of the 2d Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always non-degenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.

cond-mat.str-el↗

arXiv2011

Renormalization Group Flow for Noncommutative Fermi Liquids

Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding B-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau's Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in two spatial dimensions. Channels ZS, ZS' and BCS are discussed in detail. It is shown that while the Gaussian fixed point remains unchanged, the BCS instability is modified due to the space non-commutativity.

hep-th↗

arXiv2011

Stable nontrivial Z2 topology in ultrathin Bi (111) films: a first-principles study

Recently, there have been intense efforts in searching for new topological insulator (TI) materials. Based on first-principles calculations, we find that all the ultrathin Bi (111) films are characterized by a nontrivial Z2 number independent of the film thickness, without the odd-even oscillation of topological triviality as commonly perceived. The stable nontrivial Z2 topology is retained by the concurrent band gap inversions at multiple time-reversal-invariant k-points and associated with the intermediate inter-bilayer coupling of the multi-bilayer Bi film. Our calculations further indicate that the presence of metallic surface states in thick Bi(111) films can be effectively removed by surface adsorption.

cond-mat.mtrl-sci↗

arXiv2010

Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates

In this paper we describe connections among extraspecial 2-groups, unitary representations of the braid group and multi-qubit braiding quantum gates. We first construct new representations of extraspecial 2-groups. Extending the latter by the symmetric group, we construct new unitary braid representations, which are solutions to generalized Yang-Baxter equations and use them to realize new braiding quantum gates. These gates generate the GHZ (Greenberger-Horne-Zeilinger) states, for an arbitrary (particularly an \emph{odd}) number of qubits, from the product basis. We also discuss the Yang-Baxterization of the new braid group representations, which describes unitary evolution of the GHZ states. Our study suggests that through their connection with braiding gates, extraspecial 2-groups and the GHZ states may play an important role in quantum error correction and topological quantum computing.

quant-ph↗

arXiv2010

Symplectic Three-Algebra and N=6, Sp(2N) X U(1) Superconformal Chern-Simons-Matter Theory

We introduce an anti-symmetric metric into a 3-algebra and call it a symplectic 3-algebra. The N=6, Sp(2N) X U(1) superconformal Chern-Simons-matter theory with SU(4) R-symmetry in three dimensions is constructed by specifying the 3-brackets in a symplectic 3-algebra. We also demonstrate that the N=6, U(M) X U(N) theory can be recast into this symplectic 3-algebraic framework.

hep-th↗

arXiv2009

Braided Categorical Quantum Mechanics I

This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet emerged. The picture is complicated by a diversity of examples that lacks a unifying framework for proving theorems and discovering new protocols. We use category theory to construct a high-level language that abstracts the quantum mechanical properties of braided systems. We exploit this framework to propose an axiomatic description of braided quantum information intended for topological quantum computation. In this installment we first generalize the primordial Abramsky-Coecke "quantum information flow" paradigm from compact closed categories to right-rigid strict monoidal categories. We then study dagger structures for rigid and/or braided categories and formulate a graphical dagger calculus. We then propose two generalizations of strongly compact closed categories. Finally we study partial traces in the context of dagger categories.

quant-ph↗

arXiv2009

Stochastic Quantization of the Hořava Gravity

The stochastic quantization method is applied to the recent proposal by Hořava for gravity. We show that in contrast to General Relativity, the Hořava's action, satisfying the detailed balance condition, has a stable, non-perturbative quantum vacuum when the DeWitt parameter $λ$ is not greater than 1/3, providing a possible candidate for consistent quantum gravity.

hep-th↗

arXiv2008

Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice

We propose a twisted SUSY invariant formulation of Chern-Simons theory on a Euclidean three dimensional lattice. The SUSY algebra to be realized on the lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et al.. In order to keep the manifest anti-hermiticity of the action, we introduce oppositely oriented supercharges. Accordingly, the naive continuum limit of the action formally corresponds to the Landau gauge fixed version of Chern-Simons theory with complex gauge group which was originally proposed by Witten. We also show that the resulting action consists of parity even and odd parts with different coefficients.

hep-lat↗