23 research outputs found
Partial domain wall partition functions
We consider six-vertex model configurations on an n-by-N lattice, n =< N,
that satisfy a variation on domain wall boundary conditions that we define and
call "partial domain wall boundary conditions". We obtain two expressions for
the corresponding "partial domain wall partition function", as an
(N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first
obtained by I Kostov. We show that the two determinants are equal, as expected
from the fact that they are partition functions of the same object, that each
is a discrete KP tau-function, and, recalling that these determinants represent
tree-level structure constants in N=4 SYM, we show that introducing 1-loop
corrections, as proposed by N Gromov and P Vieira, preserves the determinant
structure.Comment: 30 pages, LaTeX. This version, which appeared in JHEP, has an
abbreviated abstract and some minor stylistic change
Nested Algebraic Bethe Ansatz for Open Spin Chains with Even Twisted Yangian Symmetry
We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible so2n- or sp2n-representations and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian Y±(gl2n). We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so2n- or sp2n-symmetric open spin chain to that of a gln-symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations
Crystallization of strongly interacting photons in a nonlinear optical fiber
Understanding strongly correlated quantum systems is a central problem in
many areas of physics. The collective behavior of interacting particles gives
rise to diverse fundamental phenomena such as confinement in quantum
chromodynamics, phase transitions, and electron fractionalization in the
quantum Hall regime. While such systems typically involve massive particles,
optical photons can also interact with each other in a nonlinear medium. In
practice, however, such interactions are often very weak. Here we describe a
novel technique that allows the creation of a strongly correlated quantum gas
of photons using one-dimensional optical systems with tight field confinement
and coherent photon trapping techniques. The confinement enables the generation
of large, tunable optical nonlinearities via the interaction of photons with a
nearby cold atomic gas. In its extreme, we show that a quantum light field can
undergo fermionization in such one-dimensional media, which can be probed via
standard photon correlation measurements