Related papers: Entanglement renormalization and wavelets
Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is…
The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…
Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme…
We show that regularizing divergent integrals is crucially important when applied to the loop diagrams corresponding to quantum corrections to the coupling of the ``gravitational" scalar field due to the interaction among matter fields. We…
Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the…
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or…
We review White's density matrix renormalisation group method, an increasingly popular method for the solution of low dimensional quantum Hamiltonians. We describe some applications to frustrated spin systems, quantum critical phenomena,…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
We investigate the multi-particle states of the (1+1)-dimensional Ising model using a spectroscopy scheme based on the tensor renormalization group method. We start by computing the finite-volume energy spectrum of the model from the…
Imperfections in experimental measurement schemes can lead to falsely identifying, or over estimating, entanglement in a quantum system. A recent solution to this is to define schemes that are robust to measurement imperfections -…
The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…
The Ryu-Takayanagi (RT) formula is a crucial concept in current theory of gauge-gravity duality and emergent phenomena of geometry. Recent reinterpretation of this formula in terms of a set of "bit threads" is an interesting effort in…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
A novel approach to understanding the hierarchy problem is presented making use of topological aspects of the renormalisation group and the ER-EPR interpretation of entanglement. A common discussion of the renormalisation group, the black…
We introduce bipartite projected ensembles (BPEs) for quantum many-body wave functions, which consist of pure states supported on two local subsystems, with each state associated with the outcome of a projective measurement of the…
The density-matrix renormalization-group (DMRG) algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…