Related papers: Localization renormalization and quantum Hall syst…
Nonlocality is an essential concept that distinguishes quantum from classical models and has been extensively studied in systems of qubits. For higher-dimensional systems, certain results for their two-level counterpart, like Bell…
To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We show that model states of fractional quantum Hall fluids at all experimentally detected plateau can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation motivated from physical…
The location of electrons governs phenomena ranging from chemical bonding and electric polarization to the topological classification of band insulators and the emergence of correlated states in quantum matter. While a prescription exists…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent \nu. This class…
Hilbert spaces of states can be constructed in standard quantum field theory only for infinitely extended spacelike hypersurfaces, precluding a more local notion of state. In fact, the Reeh-Schlieder Theorem prohibits the localization of…
We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. Previously it was demonstrated that the RG approach reproduces the critical distribution…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
We present a method of short-distance analysis in quantum field theory that does not require choosing a renormalization prescription a priori. We set out from a local net of algebras with associated pointlike quantum fields. The net has a…
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\ell_1$ regularization to the free energy of the quantum system. Based on the…
As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from…
The functional renormalization group method is used to take into account the vacuum polarization around localized bound states generated by external potential. The application to Atomic Physics leads to improved Hartree-Fock and Kohn-Sham…
Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature (T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with…
Using the conformal equivalence of translational KMS states on chiral theories with dilational KMS states obtained from restricting the vacuum state to an interval (the chiral inversion of the Unruh-effect) it was shown in a previous…
The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length $\xi$ of…
We investigate the localization transition of interacting particles in a one-dimensional correlated disorder system. The disorder which we investigate allows for vanishing backwards scattering processes. We derive by two renormalization…