Related papers: Continuous and Discrete (Classical) Heisenberg Spi…
A generalized Hitchin equation was proposed as the BPS equation for a large class of four dimensional N=1 theories engineered using M5 branes. In this paper, we show how to write down the spectral curve for the moduli space of generalized…
We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for relating discrete and continuous min-max problems. This also…
By means of a variational calculation using Matrix Product States with periodic boundary conditions, we accurately determine the extension of the spin-supersolid phase predicted to exist in the spin-1 anisotropic Heisenberg chain. We…
Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing…
We present a new method to compute short-time expectation values in large collective spin systems with generic Markovian decoherence. Our method is based on a Taylor expansion of a formal solution to the equations of motion for Heisenberg…
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…
The Hoft structure of the central extension of the $U_q \left( \widehat{sl\left( n \right) }\right)$ algebra is considered. The intertwine matrix induces new integrable spin chain models. We show the relation of these models and the…
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties $V_{n,r}$. The systems are integrable in the non-commutative sense, and by applying a $2r\times…
The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a…
We present new integrable models of interacting spin-1/2 chains, which can be interpreted as hard rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: dynamical hard rods of length $\ell$ and particles…
We study quantum quenches in the $S=1$ Heisenberg spin chain and show that the dynamics can be described by the recently developed semi-semiclassical method based on particles propagating along classical trajectories but scattering quantum…
The first half of this paper is largely expository, wherein we present a systematic combinatorial approach to the theory of polynomial (semi)invariants and multilinear invariants of several vectors and covectors, for the classical groups.…
The multiplicities of the decomposition of the product of an arbitrary number $n$ of spin $s$ states into irreducible $SU(2)$ representations are computed. Two complementary methods are presented, one based on random walks in representation…
In this thesis, we investigate various integral submodels and generalize them. In part I, we study the submodel of the nonlinear $\mathbf{C}P^1$-model and the related submodels in $(1+2)$ dimensions. In part II, we construct integrable…
The whole enterprise of spin compositions can be recast as simple enumerative combinatoric problems. We show here that enumerative combinatorics (EC)\citep{book:Stanley-2011} is a natural setting for spin composition, and easily leads to…
We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearest-neighbor interactions and a multiparameter family of spin-1/2…
We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based…
In this work, exact solutions are obtained for a class of generalized gauge-invariant $n$-chain Ising models ($n=1,2,3,4$) with arbitrary multi-spin interactions that are invariant under the local $\mathbb{Z}_2$ gauge group. On a strip…
Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…
We continue the study of the d=2,4,6 pure-spinor superstring models introduced in [1]. By explicitly solving the pure-spinor constraint we show that these theories have vanishing central charge and work out the (covariant) current algebra…