相关论文: Quantum Integrable System with Multi-components in…
We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as $q$-deformed Lie algebras. In particular, we show that if the symmetry of a free quantum particle corresponds to a Lie…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable…
The Tavis-Cummings model (the Dicke model treated in the rotating wave approximation) describing many two-level systems coupled to a single bosonic mode, has been long known to show collective semiclassical oscillations when prepared in an…
Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
We study the quantum phase transition of a N two-level atomic ensemble interacting with an optical degenerate parametric process, which can be described by the finite size Dicke Hamiltonian plus counter-rotating and quadratic field terms.…
The squeezing process of a three-dimensional quantum system by use of an external deformed one-body oscillator potential can also be described by the $d$-method, without external field and where the dimension can take non-integer values. In…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
Using twisted commutation relations we show that the quantum sinh-Gordon model on noncommutative space is integrable, and compute the exact two-particle scattering matrix. The model possesses a strong-weak duality, just like its commutative…
We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
Complete spectrum of exact interdimensional degeneracies for a quantum $N$-body system in $D$-dimensions is presented by the method of generalized spherical harmonic polynomials. In an $N$-body system all the states with angular momentum…
A new approach is developed to derive the complete spectrum of exact interdimensional degeneracies for a quantum three-body system in D-dimensions. The new method gives a generalization of previous methods.
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems…