2,476 research outputs found
Highest Weight Modules and Invariant Integrable n-State Models with Periodic Boundary Conditions"
The weights are computed for the Bethe vectors of an RSOS type model with
periodic boundary conditions obeying ()
invariance. They are shown to be highest weight vectors. The q-dimensions of
the corresponding irreducible representations are obtained.Comment: 5 pages, LaTeX, SFB 288 preprin
Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces
We show how to design a universal shape replicator in a self- assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown holefree polyomino shape, produces an unbounded number of copies of that shape (plus constant-size garbage objects). The constant-size objects can be easily constructed from a constant number of individual tile types using a constant number of preprocessing self-assembly steps. Our construction uses the well-studied 2-Handed Assembly Model (2HAM) of tile self-assembly, in the simple model where glues interact only with identical glues, allowing glue strengths that are either positive (attractive) or negative (repulsive), and constant temperature (required glue strength for parts to hold together). We also require that the given shape has specified glue types on its surface, and that the feature size (smallest distance between nonincident edges) is bounded below by a constant. Shape replication necessarily requires a self-assembly model where parts can both attach and detach, and this construction is the first to do so using the natural model of negative/repulsive glues (also studied before for other problems such as fuel-efficient computation); previous replication constructions require more powerful global operations such as an “enzyme” that destroys a subset of the tile types.National Science Foundation (U.S.) (Grant EFRI1240383)National Science Foundation (U.S.) (Grant CCF-1138967
Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces
We show how to design a universal shape replicator in a self- assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown holefree polyomino shape, produces an unbounded number of copies of that shape (plus constant-size garbage objects). The constant-size objects can be easily constructed from a constant number of individual tile types using a constant number of preprocessing self-assembly steps. Our construction uses the well-studied 2-Handed Assembly Model (2HAM) of tile self-assembly, in the simple model where glues interact only with identical glues, allowing glue strengths that are either positive (attractive) or negative (repulsive), and constant temperature (required glue strength for parts to hold together). We also require that the given shape has specified glue types on its surface, and that the feature size (smallest distance between nonincident edges) is bounded below by a constant. Shape replication necessarily requires a self-assembly model where parts can both attach and detach, and this construction is the first to do so using the natural model of negative/repulsive glues (also studied before for other problems such as fuel-efficient computation); previous replication constructions require more powerful global operations such as an “enzyme” that destroys a subset of the tile types.National Science Foundation (U.S.) (Grant EFRI1240383)National Science Foundation (U.S.) (Grant CCF-1138967
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
Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces
We show how to design a universal shape replicator in a self- assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown holefree polyomino shape, produces an unbounded number of copies of that shape (plus constant-size garbage objects). The constant-size objects can be easily constructed from a constant number of individual tile types using a constant number of preprocessing self-assembly steps. Our construction uses the well-studied 2-Handed Assembly Model (2HAM) of tile self-assembly, in the simple model where glues interact only with identical glues, allowing glue strengths that are either positive (attractive) or negative (repulsive), and constant temperature (required glue strength for parts to hold together). We also require that the given shape has specified glue types on its surface, and that the feature size (smallest distance between nonincident edges) is bounded below by a constant. Shape replication necessarily requires a self-assembly model where parts can both attach and detach, and this construction is the first to do so using the natural model of negative/repulsive glues (also studied before for other problems such as fuel-efficient computation); previous replication constructions require more powerful global operations such as an “enzyme” that destroys a subset of the tile types
Quantum dynamics in photonic crystals
Employing a recently developed method that is numerically accurate within a
model space simulating the real-time dynamics of few-body systems interacting
with macroscopic environmental quantum fields, we analyze the full dynamics of
an atomic system coupled to a continuum light-field with a gapped spectral
density. This is a situation encountered, for example, in the radiation field
in a photonic crystal, whose analysis has been so far been confined to limiting
cases due to the lack of suitable numerical techniques. We show that both
atomic population and coherence dynamics can drastically deviate from the
results predicted when using the rotating wave approximation, particularly in
the strong coupling regime. Experimental conditions required to observe these
corrections are also discussed.Comment: 5 pages, 2 figures Updated with published versio
New reflection matrices for the U_q(gl(m|n)) case
We examine super symmetric representations of the B-type Hecke algebra. We
exploit such representations to obtain new non-diagonal solutions of the
reflection equation associated to the super algebra U_q(gl(m|n)). The boundary
super algebra is briefly discussed and it is shown to be central to the super
symmetric realization of the B-type Hecke algebraComment: 13 pages, Latex. A few alterations regarding the representations. A
reference adde
On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
Motivated by a study of the crossing symmetry of the `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 representation
of the Temperley--Lieb algebra appears in this construction, and in particular
that this construction builds new representations. We extend these to new
representations of the blob algebra, which build new solutions to the Boundary
Yang--Baxter equation (i.e. open spin chains with integrable boundary
conditions).
We prove that the open spin chain Hamiltonian derived from Sklyanin's
commuting transfer matrix using such a solution can always be expressed as the
representation of an element of the blob algebra, and determine this element.
We determine the representation theory (irreducible content) of the new
representations and hence show that all such Hamiltonians have the same
spectrum up to multiplicity, for any given value of the algebraic boundary
parameter. (A corollary is that our models have the same spectrum as the open
XXZ chain with nondiagonal boundary -- despite differing from this model in
having reference states.) Using this multiplicity data, and other ideas, we
investigate the underlying quantum group symmetry of the new Hamiltonians. We
derive the form of the spectrum and the Bethe ansatz equations.Comment: 43 pages, multiple figure
Structure of the two-boundary XXZ model with non-diagonal boundary terms
We study the integrable XXZ model with general non-diagonal boundary terms at
both ends. The Hamiltonian is considered in terms of a two boundary extension
of the Temperley-Lieb algebra.
We use a basis that diagonalizes a conserved charge in the one-boundary case.
The action of the second boundary generator on this space is computed. For the
L-site chain and generic values of the parameters we have an irreducible space
of dimension 2^L. However at certain critical points there exists a smaller
irreducible subspace that is invariant under the action of all the bulk and
boundary generators. These are precisely the points at which Bethe Ansatz
equations have been formulated. We compute the dimension of the invariant
subspace at each critical point and show that it agrees with the splitting of
eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction
The antiferromagnetic transition for the square-lattice Potts model
We solve the antiferromagnetic transition for the Q-state Potts model
(defined geometrically for Q generic) on the square lattice. The solution is
based on a detailed analysis of the Bethe ansatz equations (which involve
staggered source terms) and on extensive numerical diagonalization of transfer
matrices. It involves subtle distinctions between the loop/cluster version of
the model, and the associated RSOS and (twisted) vertex models. The latter's
continuum limit involves two bosons, one which is compact and twisted, and the
other which is not, with a total central charge c=2-6/t, for
sqrt(Q)=2cos(pi/t). The non-compact boson contributes a continuum component to
the spectrum of critical exponents. For Q generic, these properties are shared
by the Potts model. For Q a Beraha number [Q = 4 cos^2(pi/n) with n integer]
the two-boson theory is truncated and becomes essentially Z\_{n-2}
parafermions. Moreover, the vertex model, and, for Q generic, the Potts model,
exhibit a first-order critical point on the transition line, i.e., the critical
point is also the locus of level crossings where the derivatives of the free
energy are discontinuous. In that sense, the thermal exponent of the Potts
model is generically nu=1/2. Things are profoundly different for Q a Beraha
number, where the transition is second order, with nu=(t-2)/2 determined by the
psi\_1 parafermion. As one enters the adjacant Berker-Kadanoff phase, the model
flows, for t odd, to a minimal model of CFT with c=1-6/t(t-1), while for t even
it becomes massive. This provides a physical realization of a flow conjectured
by Fateev and Zamolodchikov in the context of Z\_N integrable perturbations.
Finally, we argue that the antiferromagnetic transition occurs as well on other
two-dimensional lattices
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