Related papers: Smectics: Symmetry Breaking, Singularities, and Su…

Though symmetry-based indicators formulae are powerful in diagnosing topological states with a gapped band structure at/between any high-symmetry points, it fails in diagnosing topological degeneracies when the compatibility condition is…

Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is…

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

We study the Z2 topologically ordered surface state of three-dimensional bosonic SPT phases with the discrete symmetries G1 x G2. It has been argued that the topologically ordered surface state cannot be realized on a purely two-dimensional…

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local…

We show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces.…

We study the realization of the (super) conformal topological symmetry in two-dimensional field theories. The mirror automorphism of the topological algebra is represented as a reflection in the space of fields. As a consequence, a double…

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…

First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime.…

Structural imperfections such as grain boundaries (GBs) and dislocations are ubiquitous in solids and have been of central importance in understanding nature of polycrystals. In addition to their classical roles, advent of topological…

Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is…

Fractons are particles with restricted mobility. We give a symmetry-based derivation of effective field theories of gapless phases with fractonic topological defects, such as solids and supersolids, using a coset construction. The resulting…

We study topological holography for 2+1-D gapped and gapless phases with generalized symmetries using tools from higher linear algebra and higher condensation theory. We focus on bosonic fusion 2-category symmetries, where the Symmetry…

We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…

Topological defects in elastic media may be described by a geometric field akin to three-dimensional gravity. From this point of view, disclinations are line defects of zero width corresponding to a singularity of the curvature in an…

In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…

A general concept for the derivation of symmetry-based pseudo spin Hamiltonians is described. It systematically bridges the gap between the atomistic basis and various pseudo spin models presented in literature. It thus allows the…