Related papers: Dual algebraic structures for the two-level pairin…
Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
We consider a generic two-dimensional system of fermionic particles with attractive interactions and no disorder. If time-reversal symmetry is absent, it is possible to obtain incompressible insulating states in addition to the superfluid…
Toroidal classification and geometric duality in quantum spin systems is presented. Through our classification and duality, we reveal that various bipartite quantum features in magnon-systems can manifest equivalently in both bipartite…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
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 (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an…
Exactly solvable solution for the spherical to gamma - unstable transition in transitional nuclei based on dual algebraic structure and nuclear supersymmetry concept is proposed. The duality relations between the unitary and quasispin…
We consider a (2+1) dimensional Wilson-Fisher boson coupled to a (3+1) dimensional U(1) gauge field. This theory possesses a strong-weak duality in terms of the coupling constant e, and is self-dual at a particular value of $e$. We derive…
We discuss some aspects and examples of applications of dual algebraic pairs $({\cal G}_1,{\cal G}_2)$ in quantum many-body physics. They arise in models whose Hamiltonians $H$ have invariance groups $G_i$. Then one can take ${\cal G}_1 =…
We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}.…
We use the chain of simple heuristic expedients to obtain perturbative and exactly solvable relativistic spectra for a family of two-fermionic bound systems with Coulomb-like interaction. In the case of electromagnetic interaction the…
Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field…
Chains of first-order SUSY transformations for the spin equation are studied in detail. It is shown that the transformation chains are related with a olynomial pseudo-supersymmetry of the system. Simple determinant formulas for the final…
It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to…
We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg…
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice…
Solvable supersymmetric algebraic model for descriptions of the spherical to gama unstable shape- phase transition in even and odd mass nuclei is proposed. This model is based on dual algebraic structure and Richardson - Gaudin method,…
We analyze the 2+1 dimensional gauge theory with two fermions in the real adjoint representation with non-zero Chern-Simons level. We propose a new fermion-fermion dualities between strongly-coupled theories and determine the quantum phase…