Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of \emph{gapped quantum liquid} as a special kind of gapped quantum states that can "dissolve" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant -- topological entanglement entropy -- to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by \emph{stochastic local (SL) transformations} (i.e.\ \emph{local invertible transformations}): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a new definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.Comment: Revised version. Figures and references adde

The production and decay of the top partner TT in the left-right twin higgs model at the ILC and CLIC

The left-right twin Higgs model (LRTHM) predicts the existence of the top partner $T$. In this work, we make a systematic investigation for the single and pair production of this top partner $T$ through the processes: e^{+}e^{-}\to t\ov{T} + T\bar{t} and T\ov{T}, the neutral scalar (the SM-like Higgs boson $h$ or neutral pseudoscalar boson $\phi^{0}$) associate productions e^{+}e^{-}\to t\ov{T}h +T\bar{t}h, T\ov{T}h, t\ov{T}\phi^{0}+T\bar{t}\phi^{0} and T\ov{T}\phi^{0}. From the numerical evaluations for the production cross sections and relevant phenomenological analysis we find that (a) the production rates of these processes, in the reasonable parameter space, can reach the level of several or tens of fb; (b) for some cases, the peak value of the resonance production cross section can be enhanced significantly and reaches to the level of pb; (c) the subsequent decay of $T\to \phi^{+}b \to t\bar{b}b$ may generate typical phenomenological features rather different from the signals from other new physics models beyond the standard model(SM); and (d) since the relevant SM background is generally not large, some signals of the top partner $T$ predicted by the LRTHM may be detectable in the future ILC and CLIC experiments.Comment: 20pages, 15 figures and 6 Tables. Minor corrections on text. new references adde