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 $\bf{j}$. A recent proposal for a conserved spin current $\bf{J}$ [J. Shi {\it et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in equilibrium. We suggest another conserved spin current $\bar{\bf{J}}$ that may flow persistently in equilibrium. We give two arguments for the instability of persistent current of the form $\bf{J}$: 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