Related papers: A degeneracy bound for homogeneous topological ord…
Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family…
Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practise this degeneracy is never exact, and the magnitude of the ground-state…
We investigate the zero-temperature behavior of the classical Heisenberg model on the triangular lattice in which the competition between exchange interactions of different orders favors a relative angle between neighboring spins in the…
Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between…
We argue that a general system of scalar fields and gauge fields manifesting vacuum degeneracy induces a principal groupoid bundle over spacetime and that the pattern of spontaneous symmetry breaking and the Higgs mechanism are encoded by…
We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of sets under perturbations with balls. More precisely, we…
This paper aims at investigating necessary (and sufficient) conditions for quasilinear systems of first order PDEs to be Hamiltonian, with non-homogeneous operators of order 1 + 0, also with degenerate leading coefficient. As a byproduct,…
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses…
Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which…
We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph, agnostic to any particular model, that possesses a nontrivial automorphism group. We show that…
Suppose that $L(\partial_t,\partial_x)$ is a homogeneous constant coefficient strongly hyperbolic partial differential operator on ${\mathbb R}^{1+d}$ and $H$ is a characteristic hyperplane. Suppose that in a conic neighborhood of the…
We introduce the concept of a homogeneity supermanifold, which is, roughly speaking, a supermanifold equipped with a privileged atlas whose coordinates carry prescribed (real) homogeneity degrees. This structure defines a sheaf of graded…
We investigate the topological properties of the bond order wave phase arising in the extended Fermi-Hubbard model. In particular, we uncover a topological sector, which remained elusive in previous finite-size numerical studies due to…
While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a…
By definition, the physics of the $d-$dimensional (dim) boundary of a $(d+1)-$dim symmetry protected topological (SPT) state cannot be realized as itself on a $d-$dim lattice. If the symmetry of the system is unitary, then a formal way to…
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and…
The emergence of order and geometric limit shapes in a three-dimensional (3D) Coulomb phase subject to domain wall boundary conditions (DWBC) is investigated. While the arctic circle phenomenon -- the spatial segregation of frozen and…
We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order…