Entanglement renormalization for disordered systems

Abstract

We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. This method makes use of the strong disorder renormalization group to determine the order in which lattice sites are coarse-grained, which sets the overall structure of the corresponding tensor network ansatz, before optimization using variational energy minimization. Benchmark results from the disordered XXZ model demonstrates that this approach accurately captures ground state entanglement in disordered systems, even at long distances. This approach leads to a new class of efficiently contractible tensor network ansatz for 1D systems, which may be understood as a generalization of the multi-scale entanglement renormalization ansatz for disordered systems.

14 pages, 21 figures

References in corpus (33)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Universal dynamics and renormalization in many body localized systems
• Strong disorder RG approach of random systems
• Entanglement entropy of random quantum critical points in one dimension
• Recent progress in many-body localization
• Algorithms for entanglement renormalization
• Tensor network states and geometry
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Entanglement renormalization, scale invariance, and quantum criticality
• Ground State and Finite Temperature Lanczos Methods
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• The entanglement negativity in random spin chains
• Phase transition of one dimensional bosons with strong disorder
• Random Quantum Spin Chains: A Real-Space Renormalization Group Study
• Faster identification of optimal contraction sequences for tensor networks
• From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
• Entanglement entropy of the random spin-1 Heisenberg chain
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Boundary quantum critical phenomena with entanglement renormalization
• Numerical renormalization-group study of spin correlations in one-dimensional random spin chains
• Self-assembling tensor networks and holography in disordered spin chains
• A numerical study of the Random Dimerized XX spin-1/2 chain
• Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
• Extracting entanglement geometry from quantum states
• Quantum Ising model in a transverse random field: A density-matrix renormalization group analysis
• Emergent SU(3) symmetry in random spin-1 chains

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• Conformal Properties of Hyperinvariant Tensor Networks
• Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions
• Adaptive Density Matrix Renormalization Group for Disordered Systems
• Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain
• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Tensor network method for reversible classical computation
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain
• Entanglement-based tensor-network strong-disorder renormalization group
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