53385594
An intrinsic connection between topological stabilities of Fermi surfaces and topological insulators/superconductors
A topology-intrinsic connection between the stabilities of Fermi surfaces (FSs) and topological insulators/superconductors (TIs/TSCs) is revealed. In particular, a one-to-one relation between the topological types of FSs and TIs/TSCs is rigorously derived; combining it with a well-established topological theory of FSs, we produce a complete table illustrating precisely topological types of all TIs/TSCs, while a valid part of it was postulated before. Moreover, we propose and prove a general index theorem that relates the topological charge of FSs on the natural boundary of a strong TI/TSC to its bulk topological number. Implications of the general index theorem on the boundary quasi-particles are also addressed.
197485150
Searching for New Topological Types of Majorana Fermions from Boundary-bulk Correspondence of Topological Insulators/Superconductors
Majorana fermions (MFs) are particles that are their own anti-particles and may satisfy non-Abelian statistics. For the past ten years, a kind of MFs have been theoretically predicted in one-dimensional superconducting models without the time-reversal symmetry (TRS), which has recently intrigued a huge experimental interest to search for this type of exotic particles. Here we report our theoretical discoveries, including (i) a general and quantitative relation between topological stabilities of Fermi surfaces (FSs) and topological insulators(TIs)/superconductors(TSCs) is rigorously established; (ii) based on (i), we find four topologically distinct types of MFs in fermionic systems that have at least the particle-hole symmetry (PHS); (iii) apart from the existing one type, three new types of topologically nontrivial gapless edge-modes (MFs) are revealed for the first time in one dimensional finite systems with both TP and (iv) all kinds of candidate models that potentially have MFs are presented, opening a wider door for searching MFs experimentally.
117851662
The emergence of Hopf term and the marginality of Dirac model
The subtle relation of the marginality of Dirac model and the emergence of the Hopf term through a Yukawa-type interaction is revealed in this work. We show that the improvement of the marginality of Dirac mode through an infinitesimal non-relativistic term, which is irrelevant for renormalization group, is necessary to emerge the Hopf term. It is found that the appearance of the Hopf term is always accompanied with chiral boundary modes, and the sign of the coupling constant of the infinitesimal non-relativistic term decides their chirality. A lattice Dirac model is also constructed to realize the Hopf term.
119293149
Particle-number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
We propose an experimental scheme to simulate the fractionalization of the particle number by using a one-dimensionalspin-orbit-coupledultracoldfermionicgas.Thedesiredspin-orbitcoupling,akinklikepotential, andaconjugation-symmetry-breakingmasstermareproperlyconstructedbylaser-atominteractions,leadingtoan effectivelow-energyrelativisticDiracHamiltonianwithatopologicallynontrivialbackgroundfield.Thedesigned system supports a localized soliton excitation with a fractional particle number that is generally irrational and experimentally tunable, providing a direct realization of the celebrated generalized Su-Schrieffer-Heeger model. In addition, we elaborate on how to detect the induced soliton mode with the fractional particle number in the system.
126306148
Quantum simulation of DIII class topological superconductors using superconducting quantum circuits
Yong Hu, Y. X. Zhao, Zheng-Yuan Xue, and Z. D. Wang Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China and Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
30708364
Topological classification and stability of Fermi surfaces.
In the framework of the Cartan classification of Hamiltonians, a kind of topological classification of Fermi surfaces is established in terms of topological charges. The topological charge of a Fermi surface depends on its codimension and the class to which its Hamiltonian belongs. It is revealed that six types of topological charges exist, and they form two groups with respect to the chiral symmetry, with each group consisting of one original charge and two descendants. It is these nontrivial topological charges which lead to the robust topological protection of the corresponding Fermi surfaces against perturbations that preserve discrete symmetries.
118588275
Analysis of the $X(1835)$ as a baryonium state with Bethe-Salpeter equation
In this article, we take the X(1835) as a pseudoscalar baryonium state, and calculate the mass spectrum of the baryon-antibaryon bound states pp̄, ΣΣ̄, ΞΞ̄, and ΛΛ̄ in the framework of the Bethe-Salpeter equation with a phenomenological potential. The numerical results indicate the pp̄, ΣΣ̄ and ΞΞ̄ bound states maybe exist, and the X(1835) can be tentatively identified as the pp̄ bound state. PACS number: 12.39.Ki, 12.39.Pn
7625841
Topological Hamiltonian as an exact tool for topological invariants.
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
4372235
A debris disk around an isolated young neutron star
Pulsars are rotating, magnetized neutron stars that are born in supernova explosions following the collapse of the cores of massive stars. If some of the explosion ejecta fails to escape, it may fall back onto the neutron star or it may possess sufficient angular momentum to form a disk. Such ‘fallback’ is both a general prediction of current supernova models and, if the material pushes the neutron star over its stability limit, a possible mode of black hole formation. Fallback disks could dramatically affect the early evolution of pulsars, yet there are few observational constraints on whether significant fallback occurs or even the actual existence of such disks. Here we report the discovery of mid-infrared emission from a cool disk around an isolated young X-ray pulsar. The disk does not power the pulsar's X-ray emission but is passively illuminated by these X-rays. The estimated mass of the disk is of the order of 10 Earth masses, and its lifetime (≥ 106 years) significantly exceeds the spin-down age of the pulsar, supporting a supernova fallback origin. The disk resembles protoplanetary disks seen around ordinary young stars, suggesting the possibility of planet formation around young neutron stars.
122884461
On the composition laws of Beltrami-Liouville theories and 2D quantum gravity☆
Abstract We present the composition laws or cocycle conditions of the Liouville theory and Beltrami-Liouville theory as well as the quantum gravity in two dimensions. We show that for the 2D gravity, their special cases give rise to the composition laws of Polyakov's light-cone action and that of the geometric action of the Virasoro group. By means of the composition laws, we give the gravitational Ward identities and a relation between the actions of the Liouville theory and the topological gravity and find that the principal action of the 2D topological gravity is a coboundary which should obey a cocylce condition in the Liouville complex.
54896614
Galois conjugates of topological phases
Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois-conjugated Hamiltonians are typically non-Hermitian, we find that their ground-state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground-state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such nonunitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this, we rigorously prove that no local change of basis can transform the ground states of the Galois-conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasilocal Hamiltonians. A similar statement holds for many other nonunitary TQFTs. One consequence is that these nonunitary TQFTs do not describe physical realizations of topological phases. In particular, this implies that the ``Gaffnian'' wave function can not be the ground state of a gapped fractional quantum Hall state.