30 research outputs found
Deconfining the rotational Goldstone mode: the superconducting nematic liquid crystal in 2+1D
The Goldstone theorem states that there should be a massless mode for each
spontaneously broken symmetry generator. There is no such rotational mode in
crystals, however superconducting quantum nematics should carry rotational
Goldstone modes. By generalization of thermal 2D defect mediated melting theory
into a 2+1D quantum duality, the emergence of the rotational mode at the
quantum phase transition from the solid to the nematic arises as a
deconfinement phenomenon, with the unusual property that the stiffness of the
rotational mode originates entirely in the dual dislocation condensate.Comment: 5 page
Charged and neutral fixed points in the O ( N ) ⊕ O ( N ) model with Abelian gauge fields
In the Abelian-Higgs model, or Ginzburg-Landau model of superconductivity,
the existence of an infrared stable charged fixed point ensures that there is a
parameter range where the superconducting phase transition is second order, as
opposed to fluctuation-induced first order as one would infer from the
Coleman-Weinberg mechanism. We study the charged and neutral fixed points of a
two-field generalization of the Abelian-Higgs model, where two N-component
fields are coupled to two gauge fields and to each other, using the functional
renormalization group. Focusing mostly on three dimensions, in the neutral
case, this is a model for two-component Bose-Einstein condensation, and we
confirm the fixed-point structure established in earlier works using different
methods. The charged model is a dual theory of two-dimensional
dislocation-mediated quantum melting. We find the existence of three charged
fixed points for all N>2, while there are additional fixed points for N=2.Comment: RevTeX. 14 pages, 4 figures. Matches published versio
Crystal gravity
We address a subject that could have been analyzed century ago: how does the
universe of general relativity look like when it would have been filled with
solid matter? Solids break spontaneously the translations and rotations of
space itself. Only rather recently it was realized in various context that the
order parameter of the solid has a relation to Einsteins dynamical space time
which is similar to the role of a Higgs field in a Yang-Mills gauge theory.
Such a "crystal gravity" is therefore like the Higgs phase of gravity. The
usual Higgs phases are characterized by a special phenomenology. A case in
point is superconductivity exhibiting phenomena like the Type II phase,
characterized by the emergence of an Abrikosov lattice of quantized magnetic
fluxes absorbing the external magnetic field. What to expect in the
gravitational setting? The theory of elasticity is the universal effective
field theory associated with the breaking of space translations and rotations
having a similar status as the phase action describing a neutral superfluid. A
geometrical formulation appeared in its long history, similar in structure to
general relativity, which greatly facilitates the marriage of both theories.
With as main limitation that we focus entirely on stationary circumstances --
the dynamical theory is greatly complicated by the lack of Lorentz invariance
-- we will present a first exploration of a remarkably rich and often simple
physics of "Higgsed gravity".Comment: 64 pages, 22 figures. The introduction has been revised compared to
the first versio
Type-II Bose-Mott insulators
The Mott insulating state formed from bosons is ubiquitous in solid He-4,
cold atom systems, Josephson junction networks and perhaps underdoped high-Tc
superconductors. We predict that close to the quantum phase transition to the
superconducting state the Mott insulator is not at all as featureless as is
commonly believed. In three dimensions there is a phase transition to a low
temperature state where, under influence of an external current, a
superconducting state consisting of a regular array of 'wires' that each carry
a quantized flux of supercurrent is realized. This prediction of the "type-II
Mott insulator" follows from a field theoretical weak-strong duality, showing
that this 'current lattice' is the dual of the famous Abrikosov lattice of
magnetic fluxes in normal superconductors. We argue that this can be exploited
to investigate experimentally whether preformed Cooper pairs exist in high-Tc
superconductors.Comment: RevTeX, 17 pages, 6 figures, published versio
Dual gauge field theory of quantum liquid crystals in two dimensions
We present a self-contained review of the theory of dislocation-mediated
quantum melting at zero temperature in two spatial dimensions. The theory
describes the liquid-crystalline phases with spatial symmetries in between a
quantum crystalline solid and an isotropic superfluid: quantum nematics and
smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto
gauge bosons ("stress photons"), which encode for the capacity of the crystal
to propagate stresses. Dislocations and disclinations, the topological defects
of the crystal, are sources for the gauge fields and the melting of the crystal
can be understood as the proliferation (condensation) of these defects, giving
rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal
phases, the shear sector of the gauge bosons becomes massive signaling that
shear rigidity is lost. Resting on symmetry principles, we derive the
phenomenological imaginary time actions of quantum nematics and smectics and
analyze the full spectrum of collective modes. The quantum nematic is a
superfluid having a true rotational Goldstone mode due to rotational symmetry
breaking, and the origin of this 'deconfined' mode is traced back to the
crystalline phase. The two-dimensional quantum smectic turns out to be a
dizzyingly anisotropic phase with the collective modes interpolating between
the solid and nematic in a non-trivial way. We also consider electrically
charged bosonic crystals and liquid crystals, and carefully analyze the
electromagnetic response of the quantum liquid crystal phases. In particular,
the quantum nematic is a real superconductor and shows the Meissner effect.
Their special properties inherited from spatial symmetry breaking show up
mostly at finite momentum, and should be accessible by momentum-sensitive
spectroscopy.Comment: Review article, 137 pages, 32 figures. Accepted versio
An Introduction to Spontaneous Symmetry Breaking
Perhaps the most important aspect of symmetry in physics is the idea that a
state does not need to have the same symmetries as the theory that describes
it. This phenomenon is known as spontaneous symmetry breaking. In these lecture
notes, starting from a careful definition of symmetry in physics, we introduce
symmetry breaking and its consequences. Emphasis is placed on the physics of
singular limits, showing the reality of symmetry breaking even in small-sized
systems. Topics covered include Nambu-Goldstone modes, quantum corrections,
phase transitions, topological defects and gauge fields. We provide many
examples from both high energy and condensed matter physics. These notes are
suitable for graduate students.Comment: 149 pages; matches published versio