Critical properties of homogeneous binary trees

Abstract

Many-body states whose wave-function admits a representation in terms of a uniform binary-tree tensor decomposition are shown to obey to power-law two-body correlations functions. Any such state can be associated with the ground state of a translational invariant Hamiltonian which, depending on the dimension of the systems sites, involve at most couplings between third-neighboring sites. A detailed analysis of their spectra shows that they admit an exponentially large ground space.

6 pages, 2 figures

References in corpus (10)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A class of quantum many-body states that can be efficiently simulated
• Matrix product states represent ground states faithfully
• Entanglement renormalization, scale invariance, and quantum criticality
• Quantum MERA Channels
• Ground state approximation for strongly interacting systems in arbitrary dimension
• Unifying variational methods for simulating quantum many-body systems
• Simulation of time evolution with the MERA
• The Generalized Lyapunov Theorem and its Application to Quantum Channels
• The matrix product representations for all valence bond states

Cited by in corpus (47)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Tensor networks for complex quantum systems
• Equivalence of restricted Boltzmann machines and tensor network states
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Review on novel methods for lattice gauge theories
• Lecture Notes of Tensor Network Contractions
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Tensor Network Algorithms: a Route Map
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• Entanglement negativity in the critical Ising chain
• Ergodic and Mixing Quantum Channels in Finite Dimensions
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Entanglement entropy of two disjoint intervals in c=1 theories
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Entanglement negativity and conformal field theory: a Monte Carlo study
• Time Dependent Variational Principle for Tree Tensor Networks
• Two-dimensional quantum-link lattice Quantum Electrodynamics at finite density
• Tensor Network Contractions for #SAT
• Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model
• Measurement-induced phase transitions on dynamical quantum trees
• Anyonic entanglement renormalization
• Automatic structural optimization of tree tensor networks
• Solving frustration-free spin systems
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Correlation-Enhanced Neural Networks as Interpretable Variational Quantum States
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Superfluid to Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
• Framework for discrete-time quantum walks and a symmetric walk on a binary tree
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Continuum limits of homogeneous binary trees and the Thompson group
• Bridging Entanglement and Magic Resources within Operator Space
• Quantum phase diagram of two-dimensional transverse field Ising model: unconstrained tree tensor network and mapping analysis
• Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study
• Capturing long-range memory structures with tree-geometry process tensors
• State Diagrams to determine Tree Tensor Network Operators
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Tensor networks and efficient descriptions of classical data
• Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Generating Generalised Ground-State Ansatzes from Few-Body Examples