Motivated by a study of the crossing symmetry of the asymmetric twin or ‘gemini’ representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to the Yang– Baxter equation satisfying the crossing condition (that is, integrable quantum spin chains). We show that every crossing represen...

What is the limit of information storage capacity of discrete spin systems? To answer this question, we study classical error-correcting codes which can be physically realized as the energy ground space of gapped local Hamiltonians. For discrete spin systems on a D-dimensional lattice governed by local frustration-free Hamiltonians, the following bound is known to hold; kd 1/D ≤ O(n) where k is...

2014 An effective Hamiltonian has been proposed for the study of the neutral states of boron clusters, i.e. for a 1/6th filled band. This generalization of Heisenberg Hamiltonians rests upon the definition of a model space spanned by products of ground state 2P(s2p) atomic wave-functions. The resulting effective Hamiltonian involves, besides Heisenberg-type effective spin exchange terms, angula...

We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in [ 11. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamilton...

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is a...

We review problems involving the use of Grassmann techniques in the field of classical spin systems in two dimensions. These techniques are useful to perform exact correspondences between classical spin Hamiltonians and field-theory fermionic actions. This contributes to a better understanding of critical behavior of these models in term of non-quadratic effective actions which can been seen as...

We put forward a broader picture of the effective theory spinning particle within EFT gravitating objects, through which we derive and establish new precision frontier at fifth PN (5PN) order. This includes higher-spin sectors, quadratic quartic in spin, both display novel physical features, due to extension beyond linear order curvature. The quadratic-in-spin sectors give rise tidal effect, qu...