1 Abstract Topological color codes are among the stabilizer codes with remarkable properties from quantum information perspective. In this paper we construct a lattice, the so called ruby lattice, with coordination number four governed by a 2-body Hamiltonian. In a particular regime of coupling constants, in the triangular limit, degenerate perturbation theory implies that the low energy spectr...

We examine the requirements placed upon the Hamiltonian under the demand of gauge invariance. From these requirements we derive the gauge-invariant form of the tight-binding Hamiltonian with electromagnetic coupling. In our derivation we do not make recourse to a Peierls substitution and hence avoid introducing any ambiguities of path. Our expression transparently reduces to the familiar expres...

Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin (BFT), we embed the second-class non-abelian SU(2) Higgs model in the unitary gauge into a gauge invariant theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. Furthermore, comparing these results with those obtained from the gauge...

The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony (phase locking). Here we present a classical Hamiltonian (and thus conservative) system with 2N state variables that in its action-angle representation exactly yields Kuramoto dynamics on N-dimensional invariant manifolds. We...

Abstract It is shown that for a given hermitian Hamiltonian possessing supersymmetry, there is always a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for c...

The relativistic spinning particle model, recently proposed by Staruszkiewicz, is analyzed in a Hamiltonian framework. The model is heavily constrained and constraint analysis, in the Dirac scheme, is both novel and instructive. Our major finding is an associated noncommutative spacetime the structure of which is completely new. We have shown that this non-commutative phase space algebra is ess...

Following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin, we embed the second-class non-abelian self-dual model of P. K. Townsend et al into a gauge theory. The strongly involutive Hamiltonian and constraints are obtained as an infinite power series in the auxiliary fields. By formally summing the series we obtain a simple interpretation for the first-class H...

Multivortex dynamics in Manton's Schrödinger–Chern–Simons variant of the Landau– Ginzburg model of thin superconductors is studied within a moduli space approximation. It is shown that the reduced flow on M N , the N vortex moduli space, is hamiltonian with respect to ω L 2 , the L 2 Kähler form on M N. A purely hamiltonian discussion of the conserved momenta associated with the euclidean symme...

Quantum mechanical Hamiltonian models, which represent an aribtrary but finite number of steps of any Turing machine computation, are constructed here on a finite lattice of spin-1/2 systems. Different regions of the lattice correspond to different components of the Turing machine (plus recording system). Successive states of any machine computation are represented in the model by spin configur...