Related papers: Perfect Integrability and Gaudin Models
We show that a perfect quantum state transmission can be realized through a spin chain possessing a commensurate structure of energy spectrum, which is matched with the corresponding parity. As an exposition of the mirror inversion symmetry…
We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…
We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices…
The integrability of a quantum many-body system, which is characterized by the presence or absence of local conserved quantities, drastically impacts the dynamics of isolated systems, including thermalization. Nevertheless, a rigorous and…
We find families of integrable n-leg spin-1/2 ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to su(N) spin chains with N=2^n. Arbitrary rung interactions in the spin tubes and…
This paper present the important role that random system with complete connections played in solving the Gauss problem associated to the regular continued fractions. Hence, using the ergodic behavior of homogeneous random system with…
A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and…
We study exact effective superpotentials of four-dimensional {\cal N} = 2 supersymmetric gauge theories with gauge group U(N) and various amounts of fundamental matter on R^3 x S^1, broken to {\cal N} = 1 by turning on a classical…
Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…
We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction.…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
Establishing the completeness of a Bethe Ansatz solution for an exactly solved model is a perennial challenge, which is typically approached on a case by case basis. For the rational, spin-1/2 Richardson--Gaudin system it will be argued…
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory,…
We study an observable-based notion of equilibration and its application to realistic systems like spin qubits in quantum dots. On the basis of the so-called distinguishability, we analytically derive general equilibration bounds, which we…
Nekrasov functions were conjectured in \cite{Mironov:2009uv} to be related to exact Bohr-Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for the case of the pure $SU(N_c)$ gauge theory in…
This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…
We suggest a protocol for perfect quantum communication through spin chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success…