相关论文: Notes on index of quantum integrability

The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit…

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…

We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium which is based on the influence matrix approach. By replacing the dynamical map of a large fermionic quantum environment with an…

In this paper we consider a semigroup of completely positive maps $\tau=(\tau_t,t \ge 0)$ with a faithful normal invariant state $\phi$ on a type-$II_1$ factor $\cla_0$ and propose an index theory. We :achieve this via a more general…

We discuss certain integrable quantum field theories in (1+1)-dimensions consisting of coupled sine/sinh-Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that…

The structure and dynamics of quantum many-body systems are the result of a delicate interplay between underlying interactions, which leads to intricate entanglement structures. Despite this apparent complexity, symmetries emerge and have…

The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…

We study a model of Ising-coupled Kondo impurities that can be applied to quantum dots with capacitance coupling, coupled qubits with an incoherent environment, etc. We show that this model becomes equivalent to a Anderson impurity model…

The Noncommutative Index Theorem is used to prove that the Chern character of quantum Hopf line bundles over the standard Podles quantum sphere equals the winding number of the representations defining these bundles. This result gives an…

Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…

We report on the status of our programme to simulate Sp($2N$) gauge theories on the lattice. Motivated by the potential realization of an SU($4$)/Sp($4$)$\sim$SO($6$)/SO($5$) composite Higgs model and the applications to self interacting…

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 study some sorts of dimensionally-deconstructed models for supersymmetric (Euclidean) quantum mechanics, or zero-dimensional field theory. In these models, we assign bosonic and fermionic variables to vertices and edges of a graph. We…

Several dynamical aspects of the SU(2) Seiberg-Witten models with N_f quark hypermultiplets are explored. We first clarify the meaning of the number of the singularities of the space of vacua. CP invariance of the theories are then studied…

The quantization procedure for both N=1 and N=2 supersymmetric Korteweg-de Vries (SUSY KdV) hierarchies is constructed. Namely, the quantum counterparts of the monodromy matrices, built by means of the integrated vertex operators, are shown…

Phenomenologically viable string vacua may require incorporating Kac-Moody algebras at level $\geq 2$. We exploit the free fermionic formulation to construct N=(0,2) world-sheet supersymmetric string models with specific phenomenological…

We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite…

The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC)…

We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…

This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…