Related papers: Pattern of Zeros
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the quasiparticle number is shown to arise…
We have studied here the newly observed families of fractional quantum Hall states in the framework of Berry phase. It has been shown that this approach embraces in a unified way the whole spectrum of quantum Hall states with their various…
We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. S{\o}rensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
We show that a suitable combination of geometric frustration, ferromagnetism and spin-orbit interactions can give rise to nearly flat bands with a large bandgap and non-zero Chern number. Partial filling of the flat band can give rise to…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
The fractal character of some quantum properties has been shown for systems described by continuous variables. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing,…
We show that the set of double-layer Fractional Quantum Hall (FQH) states with a given topological order form a finite Abelian group under a new product. This group structure makes it possible to construct new FQH states from known ones. We…
We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an…
We provide some new results of the ground state of quantum layers.
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
In this paper, we have considered the problem of general conclusive quantum state classification; the necessary and sufficient conditions for the existence of conclusive classification strategies have also been presented. Moreover, we have…
The Hamiltonian Theory of the fractional quantum Hall (FQH) regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this paper we include disorder in our treatment, and show…
A subspace of the space, L(n), of traceless complex $n\times n$ matrices can be specified by requiring that the entries at some positions $(i,j)$ be zero. The set, $I$, of these positions is a (zero) pattern and the corresponding subspace…
We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…
This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…