Translational Symmetry

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Jorn W F Venderbos - One of the best experts on this subject based on the ideXlab platform.

  • Symmetry analysis of Translational Symmetry broken density waves application to hexagonal lattices in two dimensions
    Physical Review B, 2016
    Co-Authors: Jorn W F Venderbos
    Abstract:

    In this work we introduce a Symmetry classification for electronic density waves which break Translational Symmetry due to commensurate wave-vector modulations. The Symmetry classification builds on the concept of extended point groups: Symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become ``nonsymmorphic''-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of Symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional ($\text{2D}$) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate $M$-point ordering vectors are worked out in detail. To show that our results generally apply to $2\text{D}$ hexagonal lattices, we develop a general low-energy $\text{SU}(3)$ theory of (spinless) saddle-point electrons.

  • Symmetry analysis of Translational Symmetry broken density waves application to hexagonal lattices in two dimensions
    Physical Review Letters, 2016
    Co-Authors: Jorn W F Venderbos
    Abstract:

    In this work we introduce a Symmetry classification for electronic density waves which break Translational Symmetry due to commensurate wave-vector modulations. The Symmetry classification builds on the concept of extended point groups: Symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become “nonsymmorphic”-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of Symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple singleand two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M-point ordering vectors are worked out in detail. To show that our results generally apply to 2D hexagonal lattices, we develop a general low-energy SU(3) theory of (spinless) saddle-point electrons.

Tobias Donner - One of the best experts on this subject based on the ideXlab platform.

  • supersolid formation in a quantum gas breaking a continuous Translational Symmetry
    Nature, 2017
    Co-Authors: Julian Léonard, Andrea Morales, Tilman Esslinger, Philip Zupancic, Tobias Donner
    Abstract:

    The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous Translational invariance to form the crystal. Despite having been proposed for helium almost 50 years ago, experimental verification of supersolidity remains elusive. A variant with only discrete Translational Symmetry breaking on a preimposed lattice structure-the 'lattice supersolid'-has been realized, based on self-organization of a Bose-Einstein condensate. However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous Translational Symmetry breaking along one direction in a quantum gas. The continuous Symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose-Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the crystal position over many realizations through the light fields that leak from the cavities. These light fields are also used to monitor the position fluctuations in real time. Our concept provides a route to creating and studying glassy many-body systems with controllably lifted ground-state degeneracies, such as supersolids in the presence of disorder.

  • supersolid formation in a quantum gas breaking a continuous Translational Symmetry
    Nature, 2017
    Co-Authors: Julian Léonard, Andrea Morales, Tilman Esslinger, Philip Zupancic, Tobias Donner
    Abstract:

    A supersolid with continuous Translational Symmetry breaking along one direction is realized by symmetrically coupling a Bose–Einstein condensate to the modes of two optical cavities. Supersolidity is a state of matter that combines the spatial order of a crystal with superfluid properties. Superfluids are phase invariant, and crystals break continuous Translational Symmetry, so a supersolid must break both of these symmetries. Previous studies have predicted that helium is a supersolid at very low temperatures, but unambiguous proof of supersolidity in helium, or in any system, has been missing. Here, Tilman Esslinger and colleagues get a step closer to verifying supersolidity in an ultracold quantum gas system. They observe the breaking of continuous Translational Symmetry along one direction by coupling a Bose–Einstein condensate of atoms to two optical cavities. Using this experimental platform, other exotic states of matter could be created, such as supersolids in the presence of disorder. Elsewhere in this issue, Jun-Ru Li and colleagues create a special stripe phase in a one-dimensional spin–orbit-coupled Bose–Einstein condensate and observe supersolid properties. The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous Translational invariance to form the crystal1,2. Despite having been proposed for helium almost 50 years ago3,4, experimental verification of supersolidity remains elusive5,6. A variant with only discrete Translational Symmetry breaking on a preimposed lattice structure—the ‘lattice supersolid’7—has been realized, based on self-organization of a Bose–Einstein condensate8,9. However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous Translational Symmetry breaking along one direction in a quantum gas. The continuous Symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose–Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the crystal position over many realizations through the light fields that leak from the cavities. These light fields are also used to monitor the position fluctuations in real time. Our concept provides a route to creating and studying glassy many-body systems with controllably lifted ground-state degeneracies, such as supersolids in the presence of disorder.

Matteo Baggioli - One of the best experts on this subject based on the ideXlab platform.

  • a unified description of Translational Symmetry breaking in holography
    Journal of High Energy Physics, 2019
    Co-Authors: Martin Ammon, Matteo Baggioli, Amadeo Jimenez Alba
    Abstract:

    We provide a complete and unified description of Translational Symmetry breaking in a simple holographic model. In particular, we focus on the distinction and the interplay between explicit and spontaneous breaking. We consider a class of holographic massive gravity models which allow to range continuously from one situation to the other. We study the collective degrees of freedom, the electric AC conductivity and the shear correlator in function of the explicit and spontaneous scales. We show the possibility of having a sound-to-diffusion crossover for the transverse phonons. Within our model, we verify the validity of the Gell-Mann-Oakes-Renner relation. Despite of strong evidence for the absence of any standard dislocation induced phase relaxation mechanism, we identify a novel relaxation scale controlled by the ratio between the explicit and spontaneous breaking scales. Finally, in the pseudo-spontaneous limit, we prove analytically the relation, which has been discussed in the literature, between this novel relaxation scale, the mass of the pseudo-phonons and the Goldstone diffusivity. Our numerical data confirms this analytic result.

  • under the dome doped holographic superconductors with broken Translational Symmetry
    Journal of High Energy Physics, 2016
    Co-Authors: Matteo Baggioli, Mikhail Goykhman
    Abstract:

    We comment on a simple way to accommodate Translational Symmetry breaking into the recently proposed holographic model which features a superconducting domeshaped region on the temperature-doping phase diagram.

  • phases of holographic superconductors with broken Translational Symmetry
    Journal of High Energy Physics, 2015
    Co-Authors: Matteo Baggioli, Mikhail Goykhman
    Abstract:

    We consider holographic superconductors in a broad class of massive gravity backgrounds. These theories provide a holographic description of a superconductor with broken Translational Symmetry. Such models exhibit a rich phase structure: depending on the values of the temperature and the disorder strength the boundary system can be in superconducting, normal metallic or normal pseudo-insulating phases. Furthermore the system supports interesting collective excitation of the charge carriers, which appears in the normal phase, persists in the superconducting phase, but eventually gets destroyed by the superconducting condensate. We also show the possibility of building a phase diagram of a system with the superconducting phase occupying a dome-shaped region on the temperature-disorder plane.

Wonho Jhe - One of the best experts on this subject based on the ideXlab platform.

  • dynamic vibration phase reversal transition in discrete time Translational Symmetry broken cold atoms
    Journal of The Optical Society of America B-optical Physics, 2019
    Co-Authors: Jihyoun Kim, Geol Moon, Wonho Jhe
    Abstract:

    We experimentally demonstrate vibration phase reversal transition in a discrete time-Translational Symmetry broken cold atomic system by the application of a pulsed bias-field opposite to the existing phase of the Symmetry broken vibrational state. The reversal transition depends on the strength hp and the duration Δt of the applied pulse. Consequently, we obtain a hp−Δt phase boundary with a divergent relaxation time τ due to the critical slowdown behavior. Interestingly, the dependence of the dynamic phase boundary and relaxation time on the noise-induced switching rate implies that the system is out of equilibrium, though not so in the Ising model of a spin system.

Carles Navau - One of the best experts on this subject based on the ideXlab platform.