We propose a general mechanism of disorder-induced order by studying a particular case of classical ferromagnetic XY model in a random uniaxial field which breaks the continuous symmetry of the model. We prove rigorously that the system has spontaneous magnetization at temperature T=0, and we present strong evidence that this is also the case for small T>0. We discuss generalizations of this mechanism to various classical spin models and quantum systems. We propose a realization of this phenomenon with ultracold atoms in an optical lattice.
We propose a general mechanism of disorder-induced order by studying a particular case of classical ferromagnetic XY model in a random uniaxial field which breaks the continuous symmetry of the model. We prove rigorously that the system has spontaneous magnetization at temperature T=0, and we present strong evidence that this is also the case for small T>0. We discuss generalizations of this mechanism to various classical spin models and quantum systems. We propose a realization of this phenomenon with ultracold atoms in an optical lattice.
We propose a general mechanism of random-field-induced order (RFIO), in which long-range order is induced by a random field that breaks the continuous symmetry of the model. We particularly focus on the case of the classical ferromagnetic XY model on a two-dimensional lattice, in a uniaxial random field. We prove rigorously that the system has spontaneous magnetization at temperature T=0, and we present strong evidence that this is also the case for small T>0. We discuss generalizations of this mechanism to various classical and quantum systems. In addition, we propose possible realizations of the RFIO mechanism, using ultracold atoms in an optical lattice. Our results shed new light on controversies in existing literature, and open a way to realize RFIO with ultracold atomic systems.
Ultra-cold atomic gases by themselves and in combination with disorder are a highly active and innovative field of research. Since the first expenmental realization of Bose.-Elnstein condensation in 1995, ultra-cold quantum gases have become a powerful tool to study condensed matter, quantum optics, and quantum Infonnation problems. Disordered systems are been extremely difficult to study, but recent advances of ultra-cold experiments have brought about new tools and approaches to tackle these problems as well. In particular, urtra-cold quantum gases can be subject to controlled spatially disordered potentials. Breakthroughts like the seminal observation of Anderson localization in 2008 illustrate the powerful experimental control of quantum systems. There are currently two main approaches to realizing controlled disordered potentials for ultra-cold atomi gases: incommensurate '!lulti-chromatic lattices and speckle radiation. Altematlve approaches using holographic masks, rapidly oscillating laser beams and secondary lattices xJng scatterers in space are currently being studied by several groups. The sum of these innovative techniques that aim at realizing controlled disorder l'uels studies on disordered ultra-cold systems - In particular, the between interactions and disorder in non-interacting Bose- and Fenni systems, and the creation of glass states together with associated quantum phase transitions are currently attracting a lot of attention this thesis reports on the applicability and robustness of a related phenomenon called disorder-induced order. In essence, it is the process by which certain systems order when a specific type of controlled disorder is applied. In absence of disorder, the systems we consider present a contlnuous vvymmetry, e.g. a rotational U(1) symmetry as In the ferromagnetic XV model. If we apply a homogenous magnetic field along a given direction of the X I lane, all spins will align roughly in this direction. If we replace this homogenous field by a spatially randomly oscillating field in the same direction at low temperature, the system tends to avoid this external field and orders in a direction orthogonal to the field, inside the XV plane. The effect turns out to be robust enough to occur with regularly oscillating fields (e.g. staggered fields, sinuSOlda1ty oscillating fields), pseudo-random fields (realizable by uperposlng optical lattices), and random fields (as created by speckle plates), However, we stress that these disordered fields must not be dlstnbuted according to the continuous symmetry of the system but restricted to a subspace e.g. in the XV model, the spins can orient in any direction of the XV plane - and, if the disordered field is oriented WIth random angles, the system WIll not magnetize. The effect only occurs if the disorder is always along a given direction with random orientation. We study several configurations of disorder-induced order numerically and analytically, and present possible expenmental realizations for the classical XY system as an illustration of the basic Intuition of the effect IPRB 74 224448 (2006)], a system of two Raman-coupled Bose-Elnstein condensates, where disorder allows to control the relative phase of the two condensates IPRl 10030403 (2008)) superfluid BCS pairs in presence of a diatomic reservoir, where disorder fixes the complex phase of the painng function IEPl 86 26004 (2009)], and the quantum XY spin chain, where disorder leads to spontaneous magnetization in the direction orthogonat to the disordered fietd [PRA, accepted] Other systems in which we expect disorder-induced order to occur, not discussed in thiS thesis, are spinor condensates and possibly systems with synthetic gauge fields. Finally, there are reports of randomness-induced XV Ofdering in a graphene quantum Hall ferromagnet (PRl 98 156801 (2007) as well as disorder-induced ordering of superfluid 3HE-A in aerogel [JETPl84 455 (2006), Jl TP 150453 (2008).
We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field regime. We show by perturbative calculations and numerical simulations that although the continuous symmetry of the magnetization is lost due to disorder, the system still magnetizes in specific directions, albeit with a lower value as compared to the case without disorder. The critical temperature at which the system starts magnetizing and the magnetization at low- and high-temperature limits in the presence of disorder are estimated. Moreover, we treat the SO(n)n-component spin model to obtain the generalized expressions for the near-critical scalings, which suggest that the effect of disorder in magnetization increases with increasing dimension. We also study the behavior of magnetization of the classical XY spin model in the presence of a constant magnetic field, in addition to the quenched disorder. We find that in the presence of the uniform magnetic field, disorder may enhance the component of magnetization in the direction that is transverse to the disordered field.
We investigate the effect of a unidirectional quenched random field on the anisotropic quantum spin-1/2 XY model, which magnetizes spontaneously in the absence of the random field. We adopt a mean-field approach for this analysis. In general, the models considered have Ising symmetry, and as such they exhibit ferromagnetic order in two and three dimensions in the presence of not too large disorder. Even in the special case when the model without disorder has U(1) symmetry, a small U(1)-symmetry-breaking random field induces ferromagnetic long-range order in two dimensions. The mean-field approach, consequently, provides a rather good qualitative and even quantitative description when applied not too close to the criticality. We show that spontaneous magnetization persists even in the presence of the random field, but the magnitude of magnetization gets suppressed due to disorder, and the system magnetizes in the directions parallel and transverse to the random field. Our results are obtained via analytical calculations within a perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of magnetization in the presence of the disorder field provided that we apply an additional constant field in the XY plane. Moreover, we derive generalized expressions for the critical temperature and the scalings of the magnetization near the critical point for the XY spin system with arbitrary fixed quantum spin angular momentum.
We observe signatures of disorder-induced order in one-dimensional XY spin chains with an external site-dependent uniaxial random field within the XY plane. We numerically investigate signatures of a quantum phase transition at T=0, in particular, an upsurge of the magnetization in the direction orthogonal to the external magnetic field and the scaling of the block entropy with the amplitude of this field. Also, we discuss possible realizations of this effect in ultracold atomic experiments.
This chapter starts with an introduction to disordered systems, with an emphasis on disorder in condensed matter, and discusses such phenomena as the Anderson localization, and quantum phases such as with Bose glass. It then turns to various experimental realizations of disorder in ultracold atomic gases. The chapter focuses on disordered Bose-Einstein condensates and the phenomenon of Anderson localization in speckle or quasi-periodic, quasi-random potential. It moves on to disordered ultracold fermionic systems, and disordered ultracold Bose–Fermi (B–F) and Bose–Bose (B–B) mixtures. Finally, the chapter examines spin glasses (providing a brief presentation of the mean field theory of Parisi, and the droplet model) and disorder induced order.