Related papers: From Baxter Q-Operators to Local Charges
For a generic $n$-qubit system, local invariants under the action of $SL(2,\mathbb{C})^{\otimes n}$ characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we…
The course of 5 lectures given at the seminar "Integrable Systems: from Classical to Quantum" (Universite de Montreal, Jul 26 -- Aug 6, 1999) contains a detailed comment on the recently discovered (Gaudin-Pasquier, 1992) connection between…
We investigate various aspects of invariance under local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin-Vilkovisky (BV) operator, on-shell, can be…
Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic…
We investigate the effect of introducing a boundary inhomogeneity in the transfer matrix of an integrable open quantum spin chain. We find that it is possible to construct a local Hamiltonian, and to have quantum group symmetry. The…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
We study the ground state quantum spin fluctuations around the N\'eel ordered state for the one-band ($t,U$) Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian, $H_{\rm s}^{(4)}$, is generated using the canonical…
We go beyond a systematic review of the semiclassical approaches for determining the scaling dimensions of fixed-charge operators in $U(1)$ and $O(N)$ models by introducing a general strategy apt at determining the relation between a given…
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
In this article we propose a new construction of the spatial scalar curvature operator in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a…
This paper examines the features of a generalized position-dependent mass Hamiltonian in a supersymmetric framework in which the constraints of pseudo-Hermiticity and CPT are naturally embedded. Different representations of the charge…
The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order…
In this work we give a mechanical (Hamiltonian) interpretation of the so called spectrality property introduced by Sklyanin and Kuznetsov in the context of B\"acklund transformations (BTs) for finite dimensional integrable systems. The…
We present a conjectural description of the space of local operators on a stack of finitely many fivebranes in $M$ theory at the level of the holomorphic twist. Our approach is through the lens of twisted holography and utilizes a…
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
Instead of using local field equations - like the Dirac equation for spin-1/2 and the Klein-Gordon equation for spin-0 particles - one could try to use non-local field equations in order to describe scattering processes. The latter…
We present a hierarchy of commuting operators in Fock space containing the q-boson Hamiltonian on $\mathbb{Z}$ and show that the operators in question are simultaneously diagonalized by Hall-Littlewood functions. As an application, the…
A transport methodology to study the electron transport between quantum dots arrays based in Transfer Hamiltonian approach is presented. The interactions between the quantum dots and between the quantum dots and the electrodes are…
The lattice model of scalar quantum electrodynamics (Maxwell field coupled to a complex scalar field) in the Hamiltonian framework is discussed. It is shown that the algebra of observables ${\cal O}({\Lambda})$ of this model is a…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…