Tensor network implementation of bulk entanglement spectrum

Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs, and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing such topological phase transitions in terms of the boundary degrees of freedom which mediate it. To do so, we make use of a correspondence between a topologically nontrivial ground state and its phase transition to a trivial phase established in T. Hsieh and L. Fu (arXiv:1305.1949). This involved computing the bulk entanglement spectrum (BES) of the ground state upon tracing out an extensive subsystem. This work implements BES via tensor network representations of ground states. In this framework, the universality class of the quantum critical entanglement Hamiltonian in d spatial dimensions is either derived analytically or mapped to a classical statistical model in d + 1 dimensions, which can be studied using Monte Carlo or tensor renormalization-group methods. As an example, we analytically derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase and demonstrate that the Affleck-Kennedy-Lieb-Tasaki (AKLT) wave function (and its generalizations) remarkably contains critical six-vertex (and, in general, eight-vertex) models within it.National Science Foundation (U.S.). Graduate Research Fellowship (0645960)United States. Dept. of Energy. Division of Materials Sciences and Engineering (Award DE-SC0010526

Orthogonal magnetization and symmetry breaking in pyrochlore iridate Eu2Ir2O7

Electrons in the pyrochlore iridates experience a large interaction energy in addition to a strong spin-orbit interaction. Both features make the iridates promising for realizing novel states such as the topological Mott insulator.The pyrochlore iridate Eu₂Ir₂O₇ shows a metal-insulator transition at T[subscript N] 1/4 120 K below which a magnetically ordered state develops. Using torque magnetometry, we uncover an unusual magnetic response. A magnetic field H applied in its a-b plane produces a nonlinear magnetization M⊥ orthogonal to the plane. M⊥ displays a d-wave field-angle pattern consistent with octupolar order, with a handedness dictated by field cooling, leading to symmetry breaking of the chirality. A surprise is that the lobe orientation of the d-wave pattern is sensitive to the direction of the field when the sample is field-cooled below T[subscript N], suggestive of an additional order parameter already present at 300 K.National Science Foundation (U.S.) (Grant DMR 1420541)Gordon and Betty Moore Foundation (Grant GBMF4539)United States. Department of Energy (Grant DE-SC0010526

Topological materials and quantum entanglement

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.Cataloged from PDF version of thesis.Includes bibliographical references (pages 83-91).As the title implies, this thesis consists of two main topics: materials which realize topological phases of matter and applications of the concept of entanglement in understanding topological phases and their transitions. The first part will focus on a particular class of materials called topological crystalline insulators (TCI), which are bulk insulators with metallic boundary states protected by crystal mirror symmetries. The realization of TCIs in the SnTe class of materials and the anti-perovskite family will be described. The second part will focus on using entanglement notions to probe a topological phase transition, based on a single topological wavefunction. This is achieved by performing extensive partitions of the wavefunction, such as a checkerboard partition. Implementing this technique in one dimension naturally involves the use of tensor networks, which will be reviewed and then utilized.by Timothy H. Hsieh.Ph. D

High Statistics Measurement of the Positron Fraction in Primary Cosmic Rays of 0.5–500 GeV with the Alpha Magnetic Spectrometer on the International Space Station

A precision measurement by AMS of the positron fraction in primary cosmic rays in the energy range from 0.5 to 500 GeV based on 10.9 million positron and electron events is presented. This measurement extends the energy range of our previous observation and increases its precision. The new results show, for the first time, that above ∼200  GeV the positron fraction no longer exhibits an increase with energy

Properties of Cosmic Helium Isotopes Measured by the Alpha Magnetic Spectrometer

© 2019 authors. Published by the American Physical Society. Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of He3 and He4 fluxes are presented. The measurements are based on 100 million He4 nuclei in the rigidity range from 2.1 to 21 GV and 18 million He3 from 1.9 to 15 GV collected from May 2011 to November 2017. We observed that the He3 and He4 fluxes exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity. The rigidity dependence of the He3/He4 flux ratio is measured for the first time. Below 4 GV, the He3/He4 flux ratio was found to have a significant long-term time dependence. Above 4 GV, the He3/He4 flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law ∈RΔ with Δ=-0.294±0.004. Unexpectedly, this value is in agreement with the B/O and B/C spectral indices at high energies

Precision Measurement of Cosmic-Ray Nitrogen and its Primary and Secondary Components with the Alpha Magnetic Spectrometer on the International Space Station

A precision measurement of the nitrogen flux with rigidity (momentum per unit charge) from 2.2 GV to 3.3 TV based on 2.2×10[superscript 6] events is presented. The detailed rigidity dependence of the nitrogen flux spectral index is presented for the first time. The spectral index rapidly hardens at high rigidities and becomes identical to the spectral indices of primary He, C, and O cosmic rays above ∼700  GV. We observed that the nitrogen flux Φ[subscript N] can be presented as the sum of its primary component Φ[subscript N][superscript P] and secondary component Φ[subscript N][superscript S], Φ[subscript N] = Φ[subscript N][superscript P]+ Φ[subscript N][superscript S], and we found Φ[subscript N] is well described by the weighted sum of the oxygen flux Φ[subscript O] (primary cosmic rays) and the boron flux Φ[subscript B] (secondary cosmic rays), with Φ[subscript N][superscript P] = (0.090±0.002) × Φ[subscript O] and Φ[subscript N][superscript S] = (0.62±0.02) × Φ[subscript B] over the entire rigidity range. This corresponds to a change of the contribution of the secondary cosmic ray component in the nitrogen flux from 70% at a few GV to <30% above 1 TV

Towards Understanding the Origin of Cosmic-Ray Electrons

Precision results on cosmic-ray electrons are presented in the energy range from 0.5 GeV to 1.4 TeV based on 28.1 x 10(6) electrons collected by the Alpha Magnetic Spectrometer on the International Space Station. In the entire energy range the electron and positron spectra have distinctly different magnitudes and energy dependences. The electron flux exhibits a significant excess starting from 42.1(-5.2)(+5.4) GeV compared to the lower energy trends, but the nature of this excess is different from the positron flux excess above 25.2 +/- 1.8 GeV. Contrary to the positron flux, which has an exponential energy cutoff of 810(-180)(+310) GeV, at the 5 sigma level the electron flux does not have an energy cutoff below 1.9 TeV. In the entire energy range the electron flux is well described by the sum of two power law components. The different behavior of the cosmic-ray electrons and positrons measured by the Alpha Magnetic Spectrometer is clear evidence that most high energy electrons originate from different sources than high energy positrons

Observation of the Identical Rigidity Dependence of He, C, and O Cosmic Rays at High Rigidities by the Alpha Magnetic Spectrometer on the International Space Station

We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with 90×106 helium, 8.4×106 carbon, and 7.0×106 oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way

Precision Measurement of the Proton Flux in Primary Cosmic Rays from Rigidity 1 GV to 1.8 TV with the Alpha Magnetic Spectrometer on the International Space Station

International audienc

Precision Measurement of the (e++e−)\left({e}^{+}+{e}^{-}\right) Flux in Primary Cosmic Rays from 0.5 GeV to 1 TeV with the Alpha Magnetic Spectrometer on the International Space Station

We present a measurement of the cosmic ray (e+ + e−) flux in the range 0.5 GeV to 1 TeV based on the analysis of 10.6 million (e+ + e−) events collected by AMS. The statistics and the resolution of AMS provide a precision measurement of the flux. The flux is smooth and reveals new and distinct information. Above 30.2 GeV, the flux can be described by a single power law with a spectral index γ=−3.170±0.008(stat+syst)±0.008(energy scale)