Entanglement renormalization and wavelets

Abstract

We establish a precise connection between discrete wavelet transforms (WTs) and entanglement renormalization (ER), a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multi-scale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.

Main text: 5 pages, 2 figures. Appendices: 5 pages, 5 figures. Revised version with minor corrections

References in corpus (24)

• Entanglement renormalization
• A class of quantum many-body states that can be efficiently simulated
• Entanglement Renormalization and Holography
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Renormalization and tensor product states in spin chains and lattices
• Tensor Network Renormalization
• Algorithms for entanglement renormalization
• Tensor network states and geometry
• Entanglement renormalization, scale invariance, and quantum criticality
• Entanglement renormalization in two spatial dimensions
• Ground State and Finite Temperature Lanczos Methods
• A class of highly entangled many-body states that can be efficiently simulated
• Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
• Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
• Entanglement renormalization in fermionic systems
• Multi-scale quantum simulation of quantum field theory using wavelets
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Tensor Network and Black Hole
• Fourier transform of fermionic systems and the spectral tensor network
• MERA for Spin Chains with Continuously Varying Criticality
• Representation and design of wavelets using unitary circuits
• A real space decoupling transformation for quantum many-body systems
• Non-local scaling operators with entanglement renormalization
• Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization

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• Measurement as a shortcut to long-range entangled quantum matter
• Tensor Networks from Kinematic Space
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Sequential Quantum Circuits as Maps between Gapped Phases
• Tensor network and ($p$-adic) AdS/CFT
• Rigorous free fermion entanglement renormalization from wavelet theory
• Approximating many-body quantum states with quantum circuits and measurements
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• Boundary Tensor Renormalization Group
• Representation and design of wavelets using unitary circuits
• Holographic rainbow networks for colorful Motzkin and Fredkin spin chains
• Matrix product state algorithms for Gaussian fermionic states
• Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture
• Exact holographic tensor networks for the Motzkin spin chain
• Wavelet representation of light-front quantum field theory
• Efficient Quantum Algorithm for All Quantum Wavelet Transforms
• Scaling limits of lattice quantum fields by wavelets
• Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions
• Conformal field theory from lattice fermions
• Multiresolution decomposition of quantum field theories using wavelet bases
• Entanglement in quantum field theory via wavelet representations
• Generalized Exact Holographic Mapping with Wavelets
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Wavelet Conditional Renormalization Group
• Chemical accuracy from small, system-adapted basis functions
• A Multi-Scale Tensor Network Architecture for Classification and Regression
• Méthodes de calcul avec réseaux de tenseurs en physique (Basic tensor network computations in physics)
• Single-shot holographic compression from the area law
• Bosonic entanglement renormalization circuits from wavelet theory
• Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
• Variational quantum simulation of critical Ising model with symmetry averaging
• Preparing Renormalization Group Fixed Points on NISQ Hardware
• Renormalization in Wavelet basis
• Renormalization of lattice field theories with infinite-range wavelets
• Operator-algebraic renormalization and wavelets
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Hamiltonian Flow Equations in Daubechies Wavelet Basis
• Adiabatic ground state preparation in an expanding lattice
• Machine Learning Entanglement Freedom Or: How I Learned to Stop Worrying and Love Linear Regression
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Scale limited fields and the Casimir effect
• Approximating Maximally Localized Wannier Functions with Position Scaling-Eigenfunction
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Hamiltonian formulation of the $1+1$-dimensional ${\varphi }^4$ theory in a momentum-space Daubechies wavelet basis
• Are there any Landau poles in wavelet-based quantum field theory?
• Holographic entanglement renormalisation for fermionic quantum matter
• An efficient Wavelet-Based Hamiltonian Formulation of Quantum Field Theories using Flow-Equations