5,661 research outputs found
Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
Using the Lindblad master equation approach, we investigate the structure of
steady-state solutions of open integrable quantum lattice models, driven far
from equilibrium by incoherent particle reservoirs attached at the boundaries.
We identify a class of boundary dissipation processes which permits to derive
exact steady-state density matrices in the form of graded matrix-product
operators. All the solutions factorize in terms of vacuum analogues of Baxter's
Q-operators which are realized in terms of non-unitary representations of
certain finite dimensional subalgebras of graded Yangians. We present a
unifying framework which allows to solve fermionic models and naturally
incorporates higher-rank symmetries. This enables to explain underlying
algebraic content behind most of the previously-found solutions.Comment: 28 pages, 5 figures + appendice
Conformal Boundary Conditions and what they teach us
The question of boundary conditions in conformal field theories is discussed,
in the light of recent progress. Two kinds of boundary conditions are examined,
along open boundaries of the system, or along closed curves or ``seams''.
Solving consistency conditions known as Cardy equation is shown to amount to
the algebraic problem of finding integer valued representations of (one or two
copies of) the fusion algebra. Graphs encode these boundary conditions in a
natural way, but are also relevant in several aspects of physics ``in the
bulk''. Quantum algebras attached to these graphs contain information on
structure constants of the operator algebra, on the Boltzmann weights of the
corresponding integrable lattice models etc. Thus the study of boundary
conditions in Conformal Field Theory offers a new perspective on several old
physical problems and offers an explicit realisation of recent mathematical
concepts.Comment: Expanded version of lectures given at the Summer School and
Conference Nonperturbative Quantum Field Theoretic Methods and their
Applications, August 2000, Budapest, Hungary. 35 page
Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
The nested off-diagonal Bethe ansatz method is proposed to diagonalize
multi-component integrable models with generic integrable boundaries. As an
example, the exact solutions of the su(n)-invariant spin chain model with both
periodic and non-diagonal boundaries are derived by constructing the nested T-Q
relations based on the operator product identities among the fused transfer
matrices and the asymptotic behavior of the transfer matrices.Comment: Published versio
Line defect Schur indices, Verlinde algebras and fixed points
Given an superconformal field theory, we reconsider the Schur
index in the presence of a half line defect . Recently
Cordova-Gaiotto-Shao found that admits an expansion in terms
of characters of the chiral algebra introduced by Beem et al.,
with simple coefficients . We report a puzzling new feature of
this expansion: the limit of the coefficients is
linearly related to the vacuum expectation values in
-invariant vacua of the theory compactified on . This relation can
be expressed algebraically as a commutative diagram involving three algebras:
the algebra generated by line defects, the algebra of functions on
-invariant vacua, and a Verlinde-like algebra associated to
. Our evidence is experimental, by direct computation in the
Argyres-Douglas theories of type , , , and . In the latter two theories, which have flavor
symmetries, the Verlinde-like algebra which appears is a new deformation of
algebras previously considered.Comment: 64 pages, 21 figures. v2 published version, references update
From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
We start from known solutions of the Yang-Baxter equation with a spectral
parameter defined on the tensor product of two infinite-dimensional principal
series representations of the group or Faddeev's
modular double. Then we describe its restriction to an irreducible
finite-dimensional representation in one or both spaces. In this way we obtain
very simple explicit formulas embracing rational and trigonometric
finite-dimensional solutions of the Yang-Baxter equation. Finally, we construct
these finite-dimensional solutions by means of the fusion procedure and find a
nice agreement between two approaches
Generalised twisted partition functions
We consider the set of partition functions that result from the insertion of
twist operators compatible with conformal invariance in a given 2D Conformal
Field Theory (CFT). A consistency equation, which gives a classification of
twists, is written and solved in particular cases. This generalises old results
on twisted torus boundary conditions, gives a physical interpretation of
Ocneanu's algebraic construction, and might offer a new route to the study of
properties of CFT.Comment: 12 pages, harvmac, 1 Table, 1 Figure . Minor typos corrected, the
figure which had vanished reappears
A-D-E Classification of Conformal Field Theories
The ADE classification scheme is encountered in many areas of mathematics,
most notably in the study of Lie algebras. Here such a scheme is shown to
describe families of two-dimensional conformal field theories.Comment: 19 pages, 4 figures, 4 tables; review article to appear in
Scholarpedia, http://www.scholarpedia.org
Twisted algebra R-matrices and S-matrices for affine Toda solitons and their bound states
We construct new and invariant
-matrices and comment on the general construction of -matrices for
twisted algebras. We use the former to construct -matrices for
affine Toda solitons and their bound states, identifying the lowest breathers
with the particles.Comment: Latex, 24 pages. Various misprints corrected. New section added
clarifying relationship between R-matrices and S-matrice
- …