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We report on a highly selective experimental setup for particle-$\gamma$ coincidence experiments at the Super-Enge Split-Pole Spectrograph (SE-SPS) of the John D. Fox Superconducting Linear Accelerator Laboratory at Florida State University (FSU) using fast CeBr$_3$ scintillators for $\gamma$-ray detection. Specifically, we report on the results of characterization tests for the first five CeBr$_3$ scintillation detectors of the CeBr$_3$ Array (CeBrA) with respect to energy resolution and timing characteristics. We also present results from the first particle-$\gamma$ coincidence experiments successfully performed with the CeBrA demonstrator and the FSU SE-SPS. We show that with the new setup, $\gamma$-decay branching ratios and particle-$\gamma$ angular correlations can be measured very selectively using narrow excitation energy gates, which are possible thanks to the excellent particle energy resolution of the SE-SPS. In addition, we highlight that nuclear level lifetimes in the nanoseconds regime can be determined by measuring the time difference between particle detection with the SE-SPS focal-plane scintillator and $\gamma$-ray detection with the fast CeBrA detectors. Selective excitation energy gates with the SE-SPS exclude any feeding contributions to these lifetimes.

We study the relaxation dynamics of quantum turbulence in a two-component Bose-Einstein condensate containing half-quantum vortices. We find a temporal scaling regime for the number of vortices and the correlation lengths that at early times is strongly dependent on the relative strength of the inter-species interaction. At later times we find that the scaling becomes universal, independent of the inter-species interaction, and approaches that numerically observed in a scalar Bose-Einstein condensate., Comment: 7 pages, 7 figures

We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition functions associated with symmetry classes of alternating sign matrices. These identities generalize those already found in our earlier paper, via the introduction of additional parameters. The left hand side of each of our identities is a simple refinement of a relevant Cauchy or Littlewood identity. The right hand side of each identity is (one of the two factors present in) the partition function of the six-vertex model on a relevant domain., Comment: 34 pages, 14 figures

We study the scalar product S_{l,m} between an on-shell and an off-shell Bethe state in models with SU(3)-invariance, where l and m denote the cardinalities of the two sets of Bethe roots. We construct recursion relations relating S_{l,m} to scalar products of smaller dimension, namely S_{l-1,m} and S_{l,m-1}. Solving these recursion relations we obtain new multiple integral expressions for S_{l,m}, whose integrands are (l+m) \times (l+m) determinants, and closely related to the Slavnov determinant expression for the SU(2) scalar product., Comment: 19 pages, 5 figures, a reference added in v2

We consider non-local currents in the context of quantized affine algebras, following the construction introduced by Bernard and Felder. In the case of $U_q(A_1^{(1)})$ and $U_q(A_2^{(2)})$, these currents can be identified with configurations in the six-vertex and Izergin--Korepin nineteen-vertex models. Mapping these to their corresponding Temperley--Lieb loop models, we directly identify non-local currents with discretely holomorphic loop observables. In particular, we show that the bulk discrete holomorphicity relation and its recently derived boundary analogue are equivalent to conservation laws for non-local currents.

We study lattice configurations related to S_n, the scalar product of an off-shell state and an on-shell state in rational A_n integrable vertex models, n = {1, 2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A_n models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S_2 [1, 2]. Namely, 1. S_2 which depends on two sets of Bethe roots, b_1 and b_2, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit b_1 -> infinity, and/or b_2 -> infinity, into a product of determinants, 2. Each of the latter determinants is an A_1 vertex-model partition function., Comment: 28 pages, LaTeX figures included in the text. Minor corrections and clarifications added. Version published in Nuclear Physics B

We consider the rational six-vertex model on an L-by-L lattice with domain wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition function is an (L-2N)-parameter extension of Slavnov's scalar product of a Bethe eigenstate and a generic state, with N magnons each, on a length-L XXX spin-1/2 chain. Decoupling the extra parameters, we obtain a third determinant expression for the scalar product, where the first is due to Slavnov [1], and the second is due to Kostov and Matsuo [2]. We show that the new determinant is a discrete KP tau-function in the inhomogeneities, and consequently that tree-level N = 4 SYM structure constants that are known to be determinants, remain determinants at 1-loop level., Comment: 17 pages

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 changes

We consider a generalized model with SU(3)-invariant R-matrix, and review the nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum formula for the scalar product between generic Bethe vectors, originally obtained by Reshetikhin [11], is discussed. This formula depends on a certain partition function Z(\{\lambda\},\{\mu\}|\{w\},\{v\}), which we evaluate explicitly. In the limit when the variables \{\mu\} or \{v\} approach infinity, this object reduces to the domain wall partition function of the six-vertex model Z(\{\lambda\}|\{w\}). Using this fact, we obtain a new expression for the off-shell scalar product (between a generic Bethe vector and a Bethe eigenvector), in the case when one set of Bethe variables tends to infinity. The expression obtained is a product of determinants, one of which is the Slavnov determinant from SU(2) theory. It extends a result of Caetano [13]., Comment: 28 pages, 12 figures, greatly lengthened exposition in v3; 2 appendices and extra references added

Using Slavnov's scalar product of a Bethe eigenstate and a generic state in closed XXZ spin-1/2 chains, with possibly twisted boundary conditions, we obtain determinant expressions for tree-level structure constants in 1-loop conformally-invariant sectors in various planar (super) Yang-Mills theories. When certain rapidity variables are allowed to be free rather than satisfy Bethe equations, these determinants become discrete KP tau-functions., Comment: 34 pages. Minor formatting and verbal changes. To appear in "Symmetries, Integrable Systems and Representations", K Iohara, S Morier-Genoud and B R\'emy, Editors, Springer Proceedings in Mathematics and Statistics, Springer, 2012

We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de Santos, we derive a completely factorized expression for the $F$-matrix of such models and prove its equivalence to the expression obtained by Albert, Boos, Flume and Ruhlig. A new relation between the $F$-matrices and the Bethe eigenvectors of these spin chains is given., Comment: 30 pages

This thesis studies the role of free fermions in certain classical and quantum integrable models. The classical models studied are the KP and BKP hierarchies of partial differential equations. We review the presence of free fermions in the theory of these hierarchies, a topic which was established in the work of the Kyoto school. The quantum models studied are descendents and relatives of the XYZ model, or its lattice equivalent, the eight-vertex model. We give a number of new results in the context of these models, revealing the presence of fermions in typical quantities such as Bethe eigenvectors, partition functions and scalar products., Comment: 2010 PhD thesis, Department of Mathematics and Statistics, University of Melbourne. 293 pages

Using the framework of the algebraic Bethe Ansatz, we study the scalar product of the inhomogeneous XXZ spin-1/2 chain. Inspired by the Izergin-Korepin procedure for evaluating the domain wall partition function, we obtain a set of conditions which uniquely determine the scalar product. Assuming the Bethe equations for one set of variables within the scalar product, these conditions may be solved to produce a determinant expression originally found by Slavnov. We also consider the inhomogeneous XX spin-1/2 chain in an external magnetic field. Repeating our earlier procedure, we find a set of conditions on the scalar product of this model and solve them in the presence of the Bethe equations. The expression obtained is in factorized form., Comment: 32 pages, 24 figures

Using notation inherited from the six-vertex model, we construct diagrams that represent the action of the factorizing $F$-matrices associated to the finite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorize the tensor $R^{\sigma}_{1... n}$ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor $R^{\sigma_c}_{1... n}$, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators $S_i^{\pm}$ and $S_i^{z}$ in terms of the monodromy matrix operators., Comment: 26 pages, extra references added, typographical errors corrected

Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP tau function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter., Comment: 14 pages, LaTeX2E

We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization)., Comment: 16 pages, LaTeX2e

MacMahon's classic generating function of random plane partitions, which is related to Schur polynomials, was recently extended by Vuletic to a generating function of weighted plane partitions that is related to Hall-Littlewood polynomials, S(t), and further to one related to Macdonald polynomials, S(t,q). Using Jing's 1-parameter deformation of charged free fermions, we obtain a Fock space derivation of the Hall-Littlewood extension. Confining the plane partitions to a finite s-by-s square base, we show that the resulting generating function, S_{s-by-s}(t), is an evaluation of a tau-function of KP., Comment: 17 pages, minor changes, added a subsection and comments to clarify content, no changes made to conclusions, version to appear in IMRN

We use free fermion methods to re-derive a result of Okounkov and Reshetikhin relating charged fermions to random plane partitions, and to extend it to relate neutral fermions to strict plane partitions., Comment: 21 pages, figures included in latex

We obtain factorized domain wall partition functions in two elliptic height models: 1. A Felderhof-type model, which is new, and 2. A Perk-Schultz-type gl(1|1) model of Deguchi and Martin., Comment: 14 pages