Related papers: Spin quantum Hall transition on random networks: e…
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum…
Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of $S_{n}$-permutation…
A careful study of the supersymmetric version of Pruisken's nonlinear sigma model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting…
Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the…
We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is…
In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way which allows them to back-react. As a consequence, they become dynamical…
The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…
Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we…
We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the…
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes…
We study a number of hierarchical network models related to the Chalker-Coddington model of quantum percolation. Our aim is to describe the physics of the quantum Hall transition. The hierarchical network models are constructed by combining…
We show that the interplay of geometric criticality and quantum fluctuations leads to a novel universality class for the percolation quantum phase transition in diluted magnets. All critical exponents involving dynamical correlations are…
We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such…
The spin and integer quantum Hall effects are two cousins of topological phase transitions in two-dimensional electronic systems. Their close relationship makes it possible to transform spin to integer quantum Hall effect in two-dimensional…
Non-local twist operators are introduced for the O(n) and Q-state Potts models in two dimensions which, in the limits n -> 0 (resp. Q -> 1) count the numbers of self-avoiding loops (resp. percolation clusters) surrounding a given point.…
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle…
We show that the localization transition in the integer quantum Hall effect as described by the Chalker-Coddington network model is quantum critical. We first map the anisotropic network model to the problem of diagonalizing a…
We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations formulation of Euclidean quantum gravity in two dimensions. For…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…