Magnetic phase diagram of a spin-1 condensate in two dimensions with dipole interaction

Several new features arise in the ground-state phase diagram of a spin-1 condensate trapped in an optical trap when the magnetic dipole interaction between the atoms is taken into account along with confinement and spin precession. The boundaries between the regions of ferromagnetic and polar phases move as the dipole strength is varied and the ferromagnetic phases can be modulated. The magnetization of the ferromagnetic phase perpendicular to the field becomes modulated as a helix winding around the magnetic field direction, with a wavelength inversely proportional to the dipole strength. This modulation should be observable for current experimental parameters in $^{87}$Rb. Hence the much-sought supersolid state, with broken continuous translation invariance in one direction and broken global U(1) invariance, occurs generically as a metastable state in this system as a result of dipole interaction. The ferromagnetic state parallel to the applied magnetic field becomes striped in a finite system at strong dipolar coupling.Comment: 11 pages, 7 figures;published versio

Many-body localization in a disordered quantum Ising chain

Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition a reliable extraction of the critical disorder strength is difficult due to a large drift with system size in the studied quantities. In this work we explore two entanglement properties that are promising for the study of the manybody localization transition: the variance of the half-chain entanglement entropy of exact eigenstates and the long time change in entanglement after a local quench from an exact eigenstate. We investigate these quantities in a disordered quantum Ising chain and use them to estimate the critical disorder strength and its energy dependence. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being a separate transition. We thereby give numerical support for a recently proposed phase diagram of many-body localization with localization protected quantum order [Huse et al. Phys. Rev. B 88, 014206 (2013)].Comment: 4+ pages + 1.5 pages appendix, 5 figure

Bound states and E_8 symmetry effects in perturbed quantum Ising chains

In a recent experiment on CoNb_2O_6, Coldea et al. [Science 327, 177 (2010)] found for the first time experimental evidence of the exceptional Lie algebra E_8. The emergence of this symmetry was theoretically predicted long ago for the transverse quantum Ising chain in the presence of a weak longitudinal field. We consider an accurate microscopic model of CoNb_2O_6 incorporating additional couplings and calculate numerically the dynamical structure function using a recently developed matrix-product-state method. The excitation spectra show bound states characteristic of the weakly broken E_8 symmetry. We compare the observed bound state signatures in this model to those found in the transverse Ising chain in a longitudinal field and to experimental data.Comment: 4 pages, 3 figure

Phase diagram of the anisotropic spin-2 XXZ model: Infinite-system density matrix renormalization group study

We study the ground-state phase diagram of the quantum spin-2 XXZ chain in the presence of on-site anisotropy using a matrix-product state based infinite-system density matrix renormalization group (iDMRG) algorithm. One of the interests in this system is in connecting the highly quantum-mechanical spin-1 phase diagram with the classical S=∞ phase diagram. Several of the recent advances within DMRG make it possible to perform a detailed analysis of the whole phase diagram. We consider different types of on-site anisotropies, which allows us to establish the validity of the following statements: (1) the spin-2 model can be tuned into a phase, which is equivalent to the “topologically nontrivial” spin-1 Haldane phase, and (2) the spin-2 Haldane phase at the isotropic Heisenberg point is adiabatically connected to the “trivial” large-D phase, with a continuous change of the Hamiltonian parameters. Furthermore, we study the spin-3 XXZ chain to help explain the development of the classical phase diagram. We present details on how to use the iDMRG method to map out the phase diagram and include an extensive discussion of the numerical methods

Signatures of many-body localisation in a system without disorder and the relation to a glass transition

We study a quantum spin system—adapted from a facilitated spin model for classical glasses—with local bilinear interactions and without quenched disorder which seems to display characteristic signatures of a many-body localisation (MBL) transition. From direct diagonalisation of small systems, we find a change in certain dynamical and spectral properties at a critical value of a coupling, from those characteristic of a thermalising phase to those characteristic of a MBL phase. The system we consider is known to have a quantum phase transition in its ground-state in the limit of large size, related to a first-order active-to-inactive phase transition in the stochastic trajectories of an associated classical model of glasses. Our results here suggest that this first-order transition in the low-lying spectrum may influence the rest of the spectrum of the system in the large size limit. These findings may help understand the connection between MBL and structural glass transitions

Spinor Bose-Einstein condensates

An overview on the physics of spinor and dipolar Bose-Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor-dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed.Comment: To appear in Physics Reports. The PDF file with high resolution figures is available from the following website: http://cat.phys.s.u-tokyo.ac.jp/publication/review_of_spinorBEC.pd