53 research outputs found
Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space
Solids are distinguished from fluids by their ability to resist shear. In
traditional solids, the resistance to shear is associated with the emergence of
broken translational symmetry as exhibited by a non-uniform density pattern,
which results from either minimizing the energy cost or maximizing the entropy
or both. In this work, we focus on a class of systems, where this paradigm is
challenged. We show that shear-driven jamming in dry granular materials is a
collective process controlled solely by the constraints of mechanical
equilibrium. We argue that these constraints lead to a broken translational
symmetry in a dual space that encodes the statistics of contact forces and the
topology of the contact network. The shear-jamming transition is marked by the
appearance of this broken symmetry. We extend our earlier work, by comparing
and contrasting real space measures of rheology with those obtained from the
dual space. We investigate the structure and behavior of the dual space as the
system evolves through the rigidity transition in two different shear
protocols. We analyze the robustness of the shear-jamming scenario with respect
to protocol and packing fraction, and demonstrate that it is possible to define
a protocol-independent order parameter in this dual space, which signals the
onset of rigidity.Comment: 14 pages, 17 figure
Three-dimensional topological lattice models with surface anyons
We study a class of three dimensional exactly solvable models of topological
matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these
are not models of interacting fermions, they may well capture the topological
behavior of some strongly correlated systems. In this work we give a full
pedagogical treatment of a special simple case of these models, which we call
the 3D semion model: We calculate its ground state degeneracies for a variety
of boundary conditions, and classify its low-lying excitations. While point
defects in the bulk are confined in pairs connected by energetic strings, the
surface excitations are more interesting: the model has deconfined point
defects pinned to the boundary of the lattice, and these exhibit semionic
braiding statistics. The surface physics is reminiscent of a bosonic
fractional quantum Hall effect in its topological limit, and these
considerations help motivate an effective field theoretic description for the
lattice models as variants of theories. Our special example of the 3D
semion model captures much of the behavior of more general `confined
Walker-Wang models'. We contrast the 3D semion model with the closely related
3D version of the toric code (a lattice gauge theory) which has deconfined
point excitations in the bulk and we discuss how more general models may have
some confined and some deconfined excitations. Having seen that there exist
lattice models whose surfaces have the same topological order as a bosonic
fractional quantum Hall effect on a confining bulk, we construct a lattice
model whose surface has similar topological order to a fermionic quantum hall
effect. We find that in these models a fermion is always deconfined in the
three dimensional bulk
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