Detecting crystal symmetry fractionalization from the ground state: Application to Z2\mathbb Z_2 spin liquids on the kagome lattice

In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected $\mathbb Z_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can be used to distinguish several proposed candidates of $\mathbb Z_2$ spin liquid states on the kagome lattice.Comment: main text: 6 pages, 1 figure. supplemental material: 8 pages, 2 figures. Added a few references and the journal referenc

Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators

The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface topological order, in which the anyon excitations carry anomalous symmetry fractionalization that cannot be realized in a genuine two-dimensional system. We show that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern number $n=4$, its surface can be gapped out by an anomalous $\mathbb Z_2$ topological order, where all anyons carry mirror-symmetry fractionalization $M^2=-1$. The identification of such anomalous crystalline symmetry fractionalization implies that in a two-dimensional $\mathbb Z_2$ spin liquid the vison excitation cannot carry $M^2=-1$ if the spinon carries $M^2=-1$ or a half-integer spin.Comment: 6+8 pages, 2 figures. v2: added a new section in the supplemental material, the journal reference and some other change

Excitation function of initial temperature of heavy flavor quarkonium emission source in high energy collisions

The transverse momentum spectra of $J/\psi$, $\psi(2S)$, and $\Upsilon(nS, n=1,2,3)$ produced in proton-proton ($p$+$p$), proton-antiproton ($p$+$\bar{p}$), proton-lead ($p$+Pb), gold-gold (Au+Au), and lead-lead (Pb+Pb) collisions over a wide energy range are analyzed by the (two-component) Erlang distribution, the Hagedorn function (the inverse power-law), and the Tsallis-Levy function. The initial temperature is obtained from the color string percolation model due to the fit by the (two-component) Erlang distribution in the framework of multisource thermal model. The excitation functions of some parameters such as the mean transverse momentum and initial temperature increase from dozens of GeV to above 10 TeV. The mean transverse momentum and initial temperature decrease (increase slightly or do not change obviously) with the increase of rapidity (centrality). Meanwhile, the mean transverse momentum of $\Upsilon(nS, n=1,2,3)$ is larger than that of $J/\psi$ and $\psi(2S)$, and the initial temperature for $\Upsilon(nS, n=1,2,3)$ emission is higher than that for $J/\psi$ and $\psi(2S)$ emission, which shows a mass-dependent behavior.Comment: 26 pages, 12 figures. Advances in High Energy Physics, accepte

Loops, sign structures and emergent Fermi statistics in three-dimensional quantum dimer models

We introduce and study three-dimensional quantum dimer models with positive resonance terms. We demonstrate that their ground state wave functions exhibit a nonlocal sign structure that can be exactly formulated in terms of loops, and as a direct consequence, monomer excitations obey Fermi statistics. The sign structure and Fermi statistics in these "signful" quantum dimer models can be naturally described by a parton construction, which becomes exact at the solvable point.Comment: 9 pages, 12 figure

Causal holographic information does not satisfy the linearized quantum focusing condition

The Hubeny-Rangamani causal holographic information (CHI) defined by a region $R$ of a holographic quantum field theory (QFT) is a modern version of the idea that the area of event horizons might be related to an entropy. Here the event horizon lives in a dual gravitational bulk theory with Newton's constant $G_{\rm bulk}$, and the relation involves a factor of $4G_{\rm bulk}$. The fact that CHI is bounded below by the von Neumann entropy $S$ suggests that CHI is coarse-grained. Its properties could thus differ markedly from those of $S$. In particular, recent results imply that when $d\le 4$ holographic QFTs are perturbatively coupled to $d$-dimensional gravity, the combined system satisfies the so-called quantum focusing condition (QFC) at leading order in the new gravitational coupling $G_d$ when the QFT entropy is taken to be that of von Neumann. However, by studying states dual to spherical bulk (anti--de Sitter) Schwarschild black holes in the conformal frame for which the boundary is a $(2+1)$-dimensional de Sitter space, we find the QFC defined by CHI is violated even when perturbing about a Killing horizon and using a single null congruence. Since it is known that a generalized second law (GSL) holds in this context, our work demonstrates that the QFC is not required in order for an entropy, or an entropy-like quantity, to satisfy such a GSL.Comment: 12 pages, 3 figures; v2: modifications to address referee comment

Comparing a few distributions of transverse momenta in high energy collisions

Transverse momentum spectra of particles produced in high energy collisions are very important due to their relations to the excitation degree of interacting system. To describe the transverse momentum spectra, one can use more than one probability density functions of transverse momenta, which are simply called the functions or distributions of transverse momenta in some cases. In this paper, a few distributions of transverse momenta in high energy collisions are compared with each other in terms of plots to show some quantitative differences. Meanwhile, in the framework of Tsallis statistics, the distributions of momentum components, transverse momenta, rapidities, and pasudorapidities are obtained according to the analytical and Monte Carlo methods. These analyses are useful to understand carefully different distributions in high energy collisions.Comment: 11 pages, 7 figures. Results in Physics, Accepte

An Internal Observability Estimate for Stochastic Hyperbolic Equations

This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the $L^2$-space. Different from the deterministic case, a delicate analysis of the adaptedness for some stochastic processes is required in the stochastic setting