266 research outputs found
Nonstandard coproducts and the Izergin-Korepin open spin chain
Corresponding to the Izergin-Korepin (A_2^(2)) R matrix, there are three
diagonal solutions (``K matrices'') of the boundary Yang-Baxter equation. Using
these R and K matrices, one can construct transfer matrices for open integrable
quantum spin chains. The transfer matrix corresponding to the identity matrix
K=1 is known to have U_q(o(3)) symmetry. We argue here that the transfer
matrices corresponding to the other two K matrices also have U_q(o(3))
symmetry, but with a nonstandard coproduct. We briefly explore some of the
consequences of this symmetry.Comment: 7 pages, LaTeX; v2 has one additional sentence on the degeneracy
patter
Analytical Bethe Ansatz for quantum-algebra-invariant open spin chains
We determine the eigenvalues of the transfer matrices for integrable open
quantum spin chains which are associated with the affine Lie algebras
, and which have the
quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$,
respectively.Comment: 14 pages, latex, no figures (a character causing latex problem is
removed
Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
The general solutions for the factorization equations of the reflection
matrices for the eight vertex and six vertex models (XYZ, XXZ
and XXX chains) are found. The associated integrable magnetic Hamiltonians are
explicitly derived, finding families dependig on several continuous as well as
discrete parameters.Comment: 13 page
Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps
Classical nonlinear canonical (Poisson) maps have a distinguished role in
quantum mechanics. They act unitarily on the quantum phase space and generate
-independent quantum canonical maps. It is shown that such maps act in
the noncommutative phase space as dictated by the classical covariance. A
crucial observation made is that under the classical covariance the local
quantum mechanical picture can become nonlocal in the Hilbert space. This
nonlocal picture is made equivalent by the Weyl map to a noncommutative picture
in the phase space formulation of the theory. The connection between the
entanglement and nonlocality of the representation is explored and specific
examples of the generation of entanglement are provided by using such concepts
as the generalized Bell states. That the results have direct application in
generating vacuum soliton configurations in the recently popular scalar field
theories of noncommutative coordinates is also demonstrated.Comment: 14 pages, one figur
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Twistors and the massive spinning particle
Gauge-invariant twistor variables are found for the massive spinning particle with N-extended local worldline supersymmetry, in spacetime dimensions D = 3, 4, 6. The twistor action is manifestly Lorentz invariant but the anticommuting spin variables appear exactly as in the non-relativistic limit. This allows a simple confirmation that the quantum N = 2 spinning particle has either spin one or spin zero, and that N > 2 is quantum inconsistent for D = 4, 6.LM acknowledges partial support from the National Science Foundation Award PHY-1214521. PKT acknowledges support from the UK Science and Technology Facilities Council (grant ST/L000385/1). AJR is supported by a grant from the London Mathematical Society, and he thanks the University of Groningen for hospitality during the writing of this paper. LM and PKT are grateful for the hospitality of the Pedro Pascual Benasque Center for Science, where part of this work was done.This is the final version of the article. It first appeared from IOP via http://dx.doi.org/10.1088/1751-8113/49/2/02540
Quantum 3D Superstrings
The classical Green-Schwarz superstring action, with N=1 or N=2 spacetime
supersymmetry, exists for spacetime dimensions D=3,4,6,10, but quantization in
the light-cone gauge breaks Lorentz invariance unless either D=10, which leads
to critical superstring theory, or D=3. We give details of results presented
previously for the bosonic and N=1 closed 3D (super)strings and extend them to
the N=2 3D superstring. In all cases, the spectrum is parity-invariant and
contains anyons of irrational spin.Comment: 46 pages, v5 corrects more typos and minor error
The XX--model with boundaries. Part I: Diagonalization of the finite chain
This is the first of three papers dealing with the XX finite quantum chain
with arbitrary, not necessarily hermitian, boundary terms. This extends
previous work where the periodic or diagonal boundary terms were considered. In
order to find the spectrum and wave-functions an auxiliary quantum chain is
examined which is quadratic in fermionic creation and annihilation operators
and hence diagonalizable. The secular equation is in general complicated but
several cases were found when it can be solved analytically. For these cases
the ground-state energies are given. The appearance of boundary states is also
discussed and in view to the applications considered in the next papers, the
one and two-point functions are expressed in terms of Pfaffians.Comment: 56 pages, LaTeX, some minor correction
Quantum Group Invariant Supersymmetric t-J Model with periodic boundary conditions
An integrable version of the supersymmetric t-J model which is quantum group
invariant as well as periodic is introduced and analysed in detail. The model
is solved through the algebraic nested Bethe ansatz method.Comment: 11 pages, LaTe
Simplified Calculation of Boundary S Matrices
The antiferromagnetic Heisenberg spin chain with N spins has a sector with
N=odd, in which the number of excitations is odd. In particular, there is a
state with a single one-particle excitation. We exploit this fact to give a
simplified derivation of the boundary S matrix for the open antiferromagnetic
spin-1/2 Heisenberg spin chain with diagonal boundary magnetic fields.Comment: 8 pages, LaTeX, no figure
The Supersymmetric t-J Model with a Boundary
An open supersymmetric t-J chain with boundary fields is studied by means of
the Bethe Ansatz. Ground state properties for the case of an almost half-filled
band and a bulk magnetic field are determined. Boundary susceptibilities are
calculated as functions of the boundary fields. The effects of the boundary on
excitations are investigated by constructing the exact boundary S-matrix. From
the analytic structure of the boundary S-matrices one deduces that holons can
form boundary bound states for sufficiently strong boundary fields.Comment: 23 pages of revtex, discussion on analytic structure of holon
S-matrix change
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