Adaptive-weighted tree tensor networks for disordered quantum many-body systems

Abstract

We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that considers a tunable weight parameter to prevent completely unbalanced trees. Using this approach, we compute the ground state of the two-dimensional quantum Ising model in the presence of quenched random disorder and frustration, with lattice size up to $32\times 32$. We compare the results with the ones obtained using the standard homogeneous tree tensor networks and the completely self-assembled tree tensor networks, demonstrating a clear improvement of numerical precision as a function of the weight parameter, especially for large system sizes.

8 pages, 6 figures. Published version

References in corpus (15)

• Anderson Transitions
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Criticality, the area law, and the computational power of PEPS
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Recent progress in many-body localization
• Ergodicity breaking in a model showing many-body localization
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• On the quantum spin glass transition on the Bethe lattice
• Entanglement-based tensor-network strong-disorder renormalization group

Cited by in corpus (19)

• Tree tensor network state approach for solving hierarchical equations of motion
• Automatic structural optimization of tree tensor networks
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Simulating quantum circuits using tree tensor networks
• Entanglement bipartitioning and tree tensor networks
• Ground state search by local and sequential updates of neural network quantum states
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Hybrid Tree Tensor Networks for quantum simulation
• Efficient calculation of three-dimensional tensor networks
• Digital quantum simulation of lattice fermion theories with local encoding
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Quantum Gauge Networks: A New Kind of Tensor Network
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm
• Angular Momentum Inheritance from the Schwinger Effect in (Chromo)electromagnetic Fields
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States
• Dynamical cluster-based strategy for improving tensor network algorithms in quantum circuit simulations
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Hierarchical Search of Tree Tensor Networks for High-Dimensional Data