Related papers: Linear phase space deformations with angular momen…
The geometry of the $q$-deformed line is studied. A real differential calculus is introduced and the associated algebra of forms represented on a Hilbert space. It is found that there is a natural metric with an associated linear connection…
Motivated by the absence of cooperative Jahn-Teller effect and of magnetic ordering in LiNiO$_2$, a layered oxide with triangular planes, we study a general spin-orbital model on the triangular lattice. A mean-field approach reveals the…
We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the…
It is shown that the physical phase space of $\g$-deformed Hamiltonian lattice Yang-Mills theory, which was recently proposed in refs.[1,2], coincides as a Poisson manifold with the moduli space of flat connections on a Riemann surface with…
The Grassmannian, which is the manifold of all $k$-dimensional subspaces in the Euclidean space $\mathbb{R}^n$, was decomposed through three equivalent methods connecting combinatorial geometries, Schubert cells and convex polyhedra by…
We study the low-temperature phase diagram of quantum Kitaev-Heisenberg spin-orbital models with XXZ anisotropy on the honeycomb lattice. Within a parton mean-field theory, we identify three different quantum phases, distinguished by their…
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
We discuss the static and kinetic properties of a Ginzburg-Landau spherically symmetric $O(N)$ model recently introduced (Phys. Rev. Lett. {\bf 75}, 2176, (1995)) in order to generalize the so called Phase field model of Langer. The…
The subject of the article is linear systems of wave equations on cosmological backgrounds with convergent asymptotics. The condition of convergence corresponds to the requirement that the second fundamental form, when suitably normalised,…
We give a classification of gapped quantum phases of one-dimensional systems in the framework of Matrix Product States (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states, and both in…
The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is…
The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order.…
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations:…
Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…
Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…
Symmetries are important guiding principle for phase transitions. We systematically construct field theory models with local quantum fields that exhibit the following phase transitions: (1) different symmetry protected topological (SPT)…
We study the geometry of an important class of generic curves in the Grassmannian manifolds of $n$-dimensional subspaces and Lagrangian subspaces of $R^{2n}$ under the action of the linear and linear symplectic group.
Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not…
We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d polarised (split type) symplectic manifolds…
In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$,…