Related papers: Integrable crosscaps in classical sigma models
The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive…
We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b)…
We construct a new class of integrable $\sigma$-models based on current algebra theories for a general semisimple group $G$ by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two…
We analyze the classical and quantum properties of the integrable dimer problem. The classical version exhibits exactly one bifurcation in phase space, which gives birth to permutational symmetry broken trajectories and a separatrix. The…
We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $\sigma$ of $G$ satisfying the classical reflection…
This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
The entanglement spectra for a subsystem in a spin chain fine-tuned to a quantum-critical point contains signatures of the underlying quantum field theory that governs its low-energy properties. For an open chain with given boundary…
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…
The sigma model on complex projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle \theta. Our main goal is to…
An overview of maximally superintegrable classical Hamitonians on spherically symmetric spaces is presented. It turns out that each of these systems can be considered either as an oscillator or as a Kepler-Coulomb Hamiltonian. We show that…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The…
In this thesis, we present results from the investigation of two problems, one related to the phase transition of long-range Ising models and the other one associated with the characterization of equilibrium states in quantum spin systems.…
The correspondence between classical extra dimensional geometry and quantum behavior, typical of the AdS/CFT, has a heuristic semiclassical interpretation in terms of undulatory mechanics and relativistic geometrodynamics. We note, in fact,…
We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.
An exactly solvable model of a quantum spin interacting with a spin environment is considered. The interaction is chosen to be such that the state of the environment is conserved. The reduced density matrix of the spin is calculated for…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum criticality admit sigma model descriptions in…
We establish the equivalence between the continuum limit of the quantum spherical model with competing interactions, which is relevant to the investigation of Lifshitz points, and the O(N) nonlinear sigma model with the addition of higher…