Momentum polarization: an entanglement measure of topological spin and chiral central charge

Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by $2\pi$. For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge $c$. In this paper we propose a new approach to compute the topological spin and chiral central charge in lattice models by defining a new quantity named as the momentum polarization. Momentum polarization is defined on the cylinder geometry as a universal subleading term in the average value of a "partial translation operator". We show that the momentum polarization is a quantum entanglement property which can be computed from the reduced density matrix, and our analytic derivation based on edge conformal field theory shows that the momentum polarization measures the combination $h_a-\frac{c}{24}$ of topological spin and central charge. Numerical results are obtained for two example systems, the non-Abelian phase of the honeycomb lattice Kitaev model, and the $\nu=1/2$ Laughlin state of a fractional Chern insulator described by a variational Monte Carlo wavefunction. The numerical results verifies the analytic formula with high accuracy, and further suggests that this result remains robust even when the edge states cannot be described by a conformal field theory. Our result provides a new efficient approach to characterize and identify topological states of matter from finite size numerics.Comment: 13 pages, 8 figure

Thermodynamics in the universe described by the emergence of the space and the energy balance relation

It has previously been shown that it is more general to describe the evolution of the universe based on the emergence of the space and the energy balance relation. Here we investigate the thermodynamic properties of the universe described by such a model. We show that the first law of thermodynamics and the generalized second law of thermodynamics (GSLT) are both satisfied and the weak energy condition are also fulfilled for two typical examples. Finally we examine the physical consistency for the present model.Comment: 9 pages, 2 figure

Ligand Path: A Software Tool for Mapping Dynamic Ligand Migration Channel Networks

AbstractProteins are essential compositions of the living organisms and involved in the processes of different life events. Basically proteins are like amazing tiny bio-machines performing the functions in a stable and predictable manner and understanding the underline mechanisms can facilitate the pharmaceutical development. However, protein functions are not carried in a static style, so experimental observations of these dynamic movements of the drugs inside the proteins are difficult, so computational methods have an important and irreplaceable role.We developed a software tool called LigandPath for mapping the ligand migration channels in a constantly moving protein and this software can function with CADD (Computer aided drug design) software to map the possible migration pathways of candidate drugs inside a protein. Traditionally, biologists use MD (Molecular Dynamics) simulation to locate the ligand migration channels, but it takes long time for them to observe the complete migration paths. In order to overcome the limitations of the trajectory-based MD simulation, we adopt a computational method inspired from robotic motion planning called DyME (Dynamic Map Ensemble) and we develop the software tool LigandPath based on DyME. The software tool has already been successfully applied to map the potential migration channels of drugs candidates of three proteins, PPAR (peroxisome proliferator-activated receptors), UROD (uroporphyrinogen decarboxylase) and Sirt1 (silent information regulator 1) complexes in three publications

Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains

We study in this paper a series of Gutzwiller Projected wavefunctions for S=1 spin chains obtained from a fermionic mean-field theory for general S>1/2 spin systems [Phys. Rev. B 81, 224417] applied to the bilinear-biquadratic (J-K) model. The free-fermion mean field states before the projection are 1D paring states. By comparing the energies and correlation functions of the projected pairing states with those obtained from known results, we show that the optimized Gutzwiller projected wavefunctions are very good trial ground state wavefunctions for the antiferromagnetic bilinear-biquadratic model in the regime K0). We find that different topological phases of the free-fermion paring states correspond to different spin phases: the weak pairing (topologically non-trivial) state gives rise to the Haldane phase, whereas the strong pairing (topologically trivial) state gives rise to the dimer phase. In particular the mapping between the Haldane phase and Gutwziller wavefunction is exact at the AKLT point K=1/3. The transition point between the two phases determined by the optimized Gutzwiller Projected wavefunction is in good agreement with the known result. The effect of Z2 gauge fluctuations above the mean field theory is analyzed.Comment: 10 pages,7 figure

Non-Abelian Chiral Spin Liquid on the Kagome Lattice

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study we observe a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.Comment: 12 pages, 7 figures, 1 tabl