A Detailed Model Grid for Solid Planets from 0.1 through 100 Earth Masses

This paper describes a new grid for the mass-radius relation of 3-layer exoplanets within the mass range of 0.1 through 100 Earth Masses. The 3 layers are: Fe (epsilon iron), MgSiO3 (including both the perovskite phase, post-perovskite phase, and its dissociation at ultra-high pressures), and H2O (including Ices Ih, III, V, VI, VII, X, and the superionic phase along the melting curve). We discuss the current state of knowledge about the equations of state (EOS) that influence these calculations and the improvements used in the new grid. For the 2-layer model, we demonstrate the utility of contours on the mass-radius diagrams. Given the mass and radius input, these contours can be used to quickly determine the important physical properties of a planet including its p0 (central pressure), p1/p0 (core-mantle boundary pressure over central pressure), CMF (core mass fraction) or CRF (core radius fraction). For the 3-layer model, a curve segment on the ternary diagram represents all possible relative mass proportions of the 3 layers for a given mass-radius input. These ternary diagrams are tabulated into Table3 with the intent to make comparison to observations easier. How the presence of Fe in the mantle affects the mass-radius relations is also discussed in a separate section. A dynamic and interactive tool to characterize and illustrate the interior structure of exoplanets built upon models in this paper is available on the website: http://www.cfa.harvard.edu/~lzengComment: submitted to PASP, including 29 pages, 5 figures, 3 tables. For associated files and interactive tool, see http://www.cfa.harvard.edu/~lzeng

Prethermal time crystals in a one-dimensional periodically driven Floquet system

Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the interplay between interaction and the microwave driving. For intermediate interactions and high drivings, from the time evolution of both stroboscopic spin polarization and mutual information between two ends, we show that Floquet DTCs can exist in a prethermal time regime without the tuning of strong disorder. For much weak interactions the system is a symmetry-unbroken phase, while for strong interactions it gives its way to a thermal phase. Through analyzing the entanglement dynamics, we show that large driving fields protect the prethermal DTCs from many-body localization and thermalization. Our results suggest that by increasing the spin interaction, one can drive the experimental system into optimal regime for observing a robust prethermal DTC phase.Comment: 8 pages, 9 figures; published versio

SU(N) fractional quantum Hall effects in topological flat bands

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $\nu=N/(N+1)$ for bosons ($\nu=N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the $\mathbf{K}$ matrix, and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number $N$.Comment: 9 pages, 12 figure

Orbital Magnetism Induced by Heat Currents in Mott insulators

We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality $\hat{\chi}_{jkl}= \mathbf{S}_l\cdot\left(\mathbf{S}_j\times \mathbf{S}_k\right)$. This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. The relative orientation of the orbital moments depends on the particular lattice of magnetic ions. This subtle effect arises from the symmetries that the heat and electric currents have in common.Comment: 4.3 pages and 3 figure

Face centered cubic and hexagonal close packed skyrmion crystals in centro-symmetric magnets

Skyrmions are disk-like objects that typically form triangular crystals in two dimensional systems. This situation is analogous to the so-called "pancake vortices" of quasi-two dimensional superconductors. The way in which skyrmion disks or pancake skyrmions pile up in layered centro-symmetric materials is dictated by the inter-layer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed skyrmion crystals for different choices of the inter-layer exchange, in addition to the conventional triangular crystal of skyrmion lines. Moreover, an inhomogeneous current induces sliding motion of pancake skyrmions, indicating that they behave as effective mesoscale particles.Comment: 9 pages and 8 figure

Operator representations for a class of quantum entanglement measures and criterions

We find that a class of entanglement measures for bipartite pure state can be expressed by the average values of quantum operators, which are related to any complete basis of one partite operator space. Two specific examples are given based on two different ways to generalize Pauli matrices to $d$ dimensional Hilbert space and the case for identical particle system is also considered. In addition, applying our measure to mixed state case will give a sufficient condition for entanglement.Comment: 9 pages, no figure

Irreducible many-body correlations in topologically ordered systems

Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation, the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits irreducible many-body correlation which becomes reducible when the holes are removed. The appearance of these irreducible correlations then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in an external magnetic field, and show that the topological phase transition is signaled by the irreducible many-body correlations

Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy

We study the equilibrium phase diagram of ultrathin chiral magnets with easy-plane anisotropy $A$. The vast triangular skyrmion lattice phase that is stabilized by an external magnetic field evolves continuously as a function of increasing $A$ into a regime in which nearest-neighbor skyrmions start overlapping with each other. This overlap leads to a continuous reduction of the skyrmion number from its quantized value $Q=1$ and to the emergence of antivortices at the center of the triangles formed by nearest-neighbor skyrmions. The antivortices also carry a small "skyrmion number" $Q_A \ll 1$ that grows as a function of increasing $A$. The system undergoes a first order phase transition into a square vortex-antivortex lattice at a critical value of $A$. Finally, a canted ferromagnetic state becomes stable through another first order transition for a large enough anisotropy $A$. Interestingly enough, this first order transition is accompanied by {\it metastable} meron solutions.Comment: 7.1 pages, 7 figure

Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU(NN) symmetry

We study the many-body ground states of SU($N$) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and intercomponent interactions, we demonstrate that a hierarchy of bosonic SU($N$) fractional quantum Hall (FQH) states emerges at fractional filling factors $\nu=N/(MN+1)$ (odd $M=3$). In order to characterize this series of FQH states, we figure the effective $\mathbf{K}$ matrix from the inverse of the Chern number matrix. The topological characterization of the $\mathbf{K}$ matrix also reveals quantized drag Hall responses and fractional charge pumping that could be detected in future experiments. In addition, we address the general one-to-one correspondence to the spinless FQH states in topological flat bands with Chern number $C=N$ at fillings $\widetilde{\nu}=1/(MC+1)$.Comment: 7 pages, 6 figures. revised versio

Exoplanet Radius Gap Dependence on Host Star Type

Exoplanets smaller than Neptune are numerous, but the nature of the planet populations in the 1-4 Earth radii range remains a mystery. The complete Kepler sample of Q1-Q17 exoplanet candidates shows a radius gap at ~ 2 Earth radii, as reported by us in January 2017 in LPSC conference abstract #1576 (Zeng et al. 2017). A careful analysis of Kepler host stars spectroscopy by the CKS survey allowed Fulton et al. (2017) in March 2017 to unambiguously show this radius gap. The cause of this gap is still under discussion (Ginzburg et al. 2017; Lehmer & Catling 2017; Owen & Wu 2017). Here we add to our original analysis the dependence of the radius gap on host star type.Comment: 2pages, 1 figure, RNAAS 201