5 research outputs found
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
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
Dualities and the phase diagram of the -clock model
A new "bond-algebraic" approach to duality transformations provides a very
powerful technique to analyze elementary excitations in the classical
two-dimensional XY and -clock models. By combining duality and Peierls
arguments, we establish the existence of non-Abelian symmetries, the phase
structure, and transitions of these models, unveil the nature of their
topological excitations, and explicitly show that a continuous U(1) symmetry
emerges when . This latter symmetry is associated with the appearance
of discrete vortices and Berezinskii-Kosterlitz-Thouless-type transitions. We
derive a correlation inequality to prove that the intermediate phase, appearing
for , is critical (massless) with decaying power-law correlations.Comment: 48 pages, 5 figures. Submitted to Nuclear Physics
Breakdown of a perturbed Z_N topological phase
We study the robustness of a generalized Kitaev's toric code with Z_N degrees
of freedom in the presence of local perturbations. For N=2, this model reduces
to the conventional toric code in a uniform magnetic field. A quantitative
analysis is performed for the perturbed Z_3 toric code by applying a
combination of high-order series expansions and variational techniques. We
provide strong evidences for first- and second-order phase transitions between
topologically-ordered and polarized phases. Most interestingly, our results
also indicate the existence of topological multi-critical points in the phase
diagram.Comment: 27 pages, 10 figure
Generalized Toric Codes Coupled to Thermal Baths
We have studied the dynamics of a generalized toric code based on qudits at
finite temperature by finding the master equation coupling the code's degrees
of freedom to a thermal bath. As a consequence, we find that for qutrits new
types of anyons and thermal processes appear that are forbidden for qubits.
These include creation, annihilation and diffusion throughout the system code.
It is possible to solve the master equation in a short-time regime and find
expressions for the decay rates as a function of the dimension of the
qudits. Although we provide an explicit proof that the system relax to the
Gibbs state for arbitrary qudits, we also prove that above a certain crossing
temperature, qutrits initial decay rate is smaller than the original case for
qubits. Surprisingly this behavior only happens with qutrits and not with other
qudits with .Comment: Revtex4 file, color figures. New Journal of Physics' versio