Self-assembling tensor networks and holography in disordered spin chains

Abstract

We show that the numerical strong disorder renormalization group algorithm (SDRG) of Hikihara et. al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems.

12 pages, 17 figures

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• New Trends in Density Matrix Renormalization
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• Robustness of a perturbed topological phase
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Finite automata for caching in matrix product algorithms
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Tensor operators: constructions and applications for long-range interaction systems
• Correlation amplitude and entanglement entropy in random spin chains
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Entanglement entropy of the random spin-1 Heisenberg chain
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain

Cited by in corpus (27)

• Strong Disorder RG approach - a short review of recent developments
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model
• Automatic structural optimization of tree tensor networks
• Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
• Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid
• Entanglement in low-energy states of the random-hopping model
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Entanglement renormalization for disordered systems
• Entanglement bipartitioning and tree tensor networks
• Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions
• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Adaptive Density-Matrix Renormalization-Group study of the disordered antiferromagnetic spin-1/2 Heisenberg chain
• Adaptive Density Matrix Renormalization Group for Disordered Systems
• Dynamical properties of the Haldane chain with bond disorder
• 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
• Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs
• Extended Delta-map: a map-based foreground removal method for CMB polarization observations
• Improving accuracy of tree-tensor network approach by optimization of network structure
• Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain
• Numerical methods for localization
• Leaf-to-leaf distances in Catalan trees
• Entanglement-based tensor-network strong-disorder renormalization group
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains