420 research outputs found
Stripe fractionalization I: the generation of Ising local symmetry
This is part one in a series of two papers dedicated to the notion that the
destruction of the topological order associated with stripe phases is about the
simplest theory controlled by local symmetry: Ising gauge theory. This first
part is intended to be a tutorial- we will exploit the simple physics of the
stripes to vividly display the mathematical beauty of the gauge theory.
Stripes, as they occur in the cuprates, are clearly `topological' in the sense
that the lines of charges are at the same time domain walls in the
antiferromagnet. Imagine that the stripes quantum melt so that all what seems
to be around is a singlet superconductor. What if this domain wall-ness is
still around in a delocalized form? This turns out to be exactly the kind of
`matter' which is described by the Ising gauge theory. The highlight of the
theory is the confinement phenomenon, meaning that when the domain wall-ness
gives up it will do so in a meat-and-potato phase transition. We suggest that
this transition might be the one responsible for the quantum criticality in the
cuprates. In part two, we will become more practical, arguing that another
phase is possible according to the theory. It might be that this quantum
spin-nematic has already been observed in strongly underdoped LSCO
Conservation and persistence of spin currents and their relation to the Lieb-Schulz-Mattis twist operators
Systems with spin-orbit coupling do not conserve "bare" spin current
. A recent proposal for a conserved spin current [J. Shi {\it
et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in
equilibrium. We suggest another conserved spin current that may
flow persistently in equilibrium. We give two arguments for the instability of
persistent current of the form : one based on the equations of motions
and another based on a variational construction using Lieb-Schulz-Mattis twist
operators. In the absence of spin-orbit coupling, the three forms of spin
current coincide.Comment: 5 pages; added references, simplified notation, clearer introductio
Holographic Symmetries and Generalized Order Parameters for Topological Matter
We introduce a universally applicable method, based on the bond-algebraic
theory of dualities, to search for generalized order parameters in disparate
systems including non-Landau systems with topological order. A key notion that
we advance is that of {\em holographic symmetry}. It reflects situations
wherein global symmetries become, under a duality mapping, symmetries that act
solely on the system's boundary. Holographic symmetries are naturally related
to edge modes and localization. The utility of our approach is illustrated by
systematically deriving generalized order parameters for pure and
matter-coupled Abelian gauge theories, and for some models of topological
matter.Comment: v2, 10 pages, 3 figures. Accepted for publication in Physical Review
B Rapid Communication
Unified approach to Quantum and Classical Dualities
We show how classical and quantum dualities, as well as duality relations
that appear only in a sector of certain theories ("emergent dualities"), can be
unveiled, and systematically established. Our method relies on the use of
morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are
characterized as unitary mappings implementing such morphisms, whose even
powers become symmetries of the quantum problem. Dual variables -which were
guessed in the past- can be derived in our formalism. We obtain new
self-dualities for four-dimensional Abelian gauge field theories.Comment: 4+3 pages, 3 figure
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