A model of chiral spin liquids with Abelian and non-Abelian topological phases

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a Random Phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.Comment: 31 pages, 9 figure

Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace

We study why in quantum many-body systems the adiabatic fidelity and the overlap between the initial state and instantaneous ground states have nearly the same values in many cases. We elaborate on how the problem may be explained by an interplay between the two intrinsic limits of many-body systems: the limit of small values of evolution parameter and the limit of large system size. In the former case, conventional perturbation theory provides a natural explanation. In the latter case, a crucial observation is that pairs of vectors lying in the complementary Hilbert space of the initial state are almost orthogonal. Our general findings are illustrated with a driven Rice-Mele model, a paradigmatic model of driven many-body systems.Comment: 10+6 pages, 7 figure

Effect on Higgs Boson Decays from Large Light-Heavy Neutrino Mixing in Seesaw Models

In seesaw models with more than one generation of light and heavy neutrinos, nu and N, respectively, it is possible to have sizable mixing between them for heavy-neutrino masses of order 100 GeV or less. We explore this possibility further, taking into account current experimental constraints, and study its effect on Higgs-boson decays in the contexts of seesaw models of types I and III. We find that in the type-I case the Higgs decay into a pair of light and heavy neutrinos, h -> nu N, could increase the total Higgs width in the standard model by up to almost 30% for a relatively light Higgs-boson, which would significantly affect Higgs searches at the LHC. The subsequent prompt decay of N into three light fermions makes this Higgs decay effectively a four-body decay. We further find that, in the presence of the large light-heavy mixing, these four-body Higgs decays can have rates a few times larger than their standard-model counterparts and therefore could provide a potentially important window to reveal the underlying seesaw mechanism.Comment: 16 pages, 3 figures, with more discussion on experimental constraints and references, main conclusions unchanged, to match journal versio

Effect on Higgs Boson Decays from Large Light-Heavy Neutrino Mixing in Seesaw Models

在多於一個微中子世代的蹺蹺板模型內，如果重微中子( N )的質量在100 GeV 左右，輕微中子(ν)和重微中子可以有相當大程度的混合。我們更進一步的探究了這種大程度混合的可能，同時考慮了目前實驗數據的限制，在此論文裡我們研究了I型和III型蹺蹺板模型內這種輕、重微中子大程度混合的情況對於希格斯玻色子(h)衰變的影響。在I型蹺蹺板模型內，我們發現希格斯玻色子可以衰變成一對輕、重微中子(h → ν N )，對於質量相對輕的希格斯玻色子而言，這個新的衰變模式與標準模型的貢獻相比有機會增加高達近30％的希格斯玻色子總衰變寬度，這會大大影響在大強子對撞機(LHC)裡尋找希格斯玻色子的工作。重微中子隨後迅速衰變為三個輕的費米子，使得整個 h → ν N 衰變模式可以有效地被看成是一個希格斯玻色子的四體衰變模式。我們進一步的發現，對於存在輕、重微中子大程度混合的情況，這個新的希格斯玻色子四體衰變模式之衰變率可以數倍的大於標準模型裡相應的希格斯玻色子四體衰變模式之衰變率。因此，這個新的希格斯玻色子四體衰變模式在實驗上可以提供一個潛在的重要窗口以揭示潛藏的微中子蹺蹺板機制。 然而，在III型蹺蹺板模型內，因為實驗數據給了輕、重微中子的混合矩陣元較強的限制，同時因為實驗數據加諸較高的質量下限於重微中子的質量上，這些因素使得大程度輕、重微中子混合的存在只會微小程度(大約5%)的修改希格斯玻色子的總衰變寬度，遠小於I型蹺蹺板模型裡的情況。因此，比起I型蹺蹺板模型，在III型蹺蹺板模型內之希格斯玻色子衰變為四個輕的費米子的模式較無法提供人們資訊以探究潛藏的微中子蹺蹺板機制。In seesaw models with more than one generation of light and heavy neutrinos, ν and N, respectively, it is possible to have sizable mixing between them for heavy neutrino masses of order 100 GeV or less. We explore this possibility further, taking into account current experimental constraints, and study its effect on Higgs boson decays in the contexts of seesaw models of types I and III. We find that in the type-I case the Higgs decay into a pair of light and heavy neutrinos, h → νN, could increase the total Higgs width in the standard model by up to almost 30% for a relatively light Higgs boson, which would significantly affect Higgs searches at the LHC. The subsequent prompt decay of N into three light fermions makes this Higgs decay effectively a four body decay. We further find that, in the presence of the large light-heavy mixing, these four body Higgs decays can have rates a few times larger than their standard model counterparts and therefore could provide a potentially important window to reveal the underlying seesaw mechanism. However, in type-III seesaw model, due to the stronger experimental constraints on the elements of the mixing matrix U_{νN} and also to the lower limit on the heavy lepton masses, the large light-heavy mixing gives rise to modifications of the SM Higgs total width that are modest, roughly only 5%, much smaller than those in the type-I case. As a consequence, the Higgs decays into four light fermions in this case would be less sensitive for probing the underlying seesaw mechanism than their type-I counterparts

Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries

We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in two-dimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of Majorana edge modes can be gapped out by an appropriate interaction without spontaneously breaking any one of the protecting symmetries. Hence, the noninteracting classification Z reduces to Z(8) when these interactions are present. It is also known that the stability when there are less than eight modes can be understood in terms of the presence of topological obstructions in the low-energy bosonic effective theories, which prevent opening of a gap. Here, we investigate the stability of the edge theories with four, two, and one edge modes, respectively. We give an analytical derivation of the topological term for the first case, because of which the edge theory remains gapless. For two edge modes, we employ bosonization methods to derive an effective bosonic action. When gapped, this bosonic theory is necessarily associated to the spontaneous symmetry breaking of either one of time-reversal or reflection symmetry whenever translation symmetry remains on the boundary. For one edge mode, stability is explicitly established in the Majorana representation of the edge theory