Related papers: Integrable spin chains and cellular automata with …
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals…
We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin…
Recently, the one dimensional model of $N$ spins with $S=\frac{1}{2}$ on a circle, interacting with an exchange that falls off with the inverse square of the separation: $H_{\rm ISE} =\sum_{i\neq j} \frac{1}{[\frac{N}{\pi}…
We revisit the integrability of quantum circuits constructed from two-qubit unitary gates $U$ that satisfy the Yang-Baxter equation. A brickwork arrangement of $U$ typically corresponds to an integrable Trotterization of some Hamiltonian…
We investigate the integrable structures in an N=2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the…
We extend our study of the field-theoretic description of matrix-vector models and the associated many-body problems of one dimensional particles with spin. We construct their Yangian-su(R) invariant Hamiltonian. It describes an interacting…
Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
Two integrable quantum spin ladder systems will be introduced associated with the fundamental su(2|2) solution of the Yang-Baxter equation. The first model is a generalized quantum Ising system with Ising rung interactions. In the second…
A class of quasi two and three dimensional quantum lattice spin models with nearest and next nearest neighbour interactions is proposed. The basic idea of construction is to introduce interactions in an array of XXZ spin chains through…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
We study the many-body instabilities of correlated electrons on the half-filled honeycomb lattice with enhanced exchange coupling. The system is described by an extended Hubbard model including the next-nearest-neighbor Coulomb repulsion…
In this paper we study an su$(m)$-invariant open version of the Haldane-Shastry spin chain whose ground state can be obtained from the chiral correlator of the $c=m-1$ free boson boundary conformal field theory. We show that this model is…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
This paper deals with the treatment of quantum interferences in the semiclassical initial value theory of rotationally inelastic scattering in the interaction picture [C. W. McCurdy and W. H. Miller, J. Chem. Phys. 67, 463 (1977)]. It is…
A study of the integrability of one-dimensional quantum mechanical many-body systems with general point interactions and boundary conditions describing the interactions which can be independent or dependent on the spin states of the…
We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain…