21,073 research outputs found
The dimer-RVB State of the Four-Leg Heisenberg Ladder: Interference among Resonances
We study the ground state of the 4-leg spin ladder using a dimer-RVB ansatz
and the Lanczos method. Besides the well known resonance mechanism between
valence bond configurations we find novel interference effects among nearby
resonances.Comment: 4 pages, RevTex, 7 eps fig
Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory
We propose a general method for the description of arbitrary single spin-j
states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz
algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for
fermions, and by means of second order Lagrangians. The method allows to avoid
the cumbersome matrix calculus and higher \partial^{2j} order wave equations
inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor
(tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible
sector and design there a representation reduction algorithm based on one of
the Casimir invariants of the Lorentz algebra. This algorithm allows us to
separate neatly the pure spin-j sector of interest from the rest, while
preserving the separate Lorentz- and Dirac indexes. However, the Lorentz
invariants are momentum independent and do not provide wave equations. Genuine
wave equations are obtained by conditioning the Lorentz-tensors under
consideration to satisfy the Klein-Gordon equation. In so doing, one always
ends up with wave equations and associated Lagrangians that are second order in
the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2)
is comfortably described by a second order Lagrangian in the basis of the
totally antisymmetric Lorentz tensor-spinor of second rank, \Psi_[ \mu\nu].
Moreover, the particle is shown to propagate causally within an electromagnetic
background. In our study of (3/2,0)+(0,3/2) as part of \Psi_[\mu\nu] we
reproduce the electromagnetic multipole moments known from the Weinberg-Joos
theory. We also find a Compton differential cross section that satisfies
unitarity in forward direction. The suggested tensor calculus presents itself
very computer friendly with respect to the symbolic software FeynCalc.Comment: LaTex 34 pages, 1 table, 8 figures. arXiv admin note: text overlap
with arXiv:1312.581
Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
We determine the existence of critical lines in dimerized quantum spin
ladders in their phase diagram of coupling constants using the finite-size DMRG
algorithm. We consider both staggered and columnar dimerization patterns, and
antiferromagnetic and ferromagnetic inter-leg couplings. The existence of
critical phases depends on the precise combination of these patterns. The
nature of the massive phases separating the critical lines are characterized
with generalized string order parameters that determine their valence bond
solid (VBS) content.Comment: 9 pages 10 figure
Antisymmetric multi-partite quantum states and their applications
Entanglement is a powerful resource for processing quantum information. In
this context pure, maximally entangled states have received considerable
attention. In the case of bipartite qubit-systems the four orthonormal
Bell-states are of this type. One of these Bell states, the singlet Bell-state,
has the additional property of being antisymmetric with respect to particle
exchange. In this contribution we discuss possible generalizations of this
antisymmetric Bell-state to cases with more than two particles and with
single-particle Hilbert spaces involving more than two dimensions. We review
basic properties of these totally antisymmetric states. Among possible
applications of this class of states we analyze a new quantum key sharing
protocol and methods for comparing quantum states
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