Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

Abstract

We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in TEBD and DMRG-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond- or local dimension, of up to 24 times in quasi-2D cylindrical systems.

10 pages, 6 figures

References in corpus (52)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Efficient simulation of one-dimensional quantum many-body systems
• Entanglement entropy and conformal field theory
• Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Entanglement renormalization
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• A class of quantum many-body states that can be efficiently simulated
• Time-dependent variational principle for quantum lattices
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Violation of the entropic area law for Fermions
• Corner Transfer Matrix Renormalization Group Method
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Entanglement spectrum in one-dimensional systems
• Entanglement Properties of the Harmonic Chain
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Tensor network decompositions in the presence of a global symmetry
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Density matrix renormalization group algorithms with a single center site
• General entanglement scaling laws from time evolution
• A positive tensor network approach for simulating open quantum many-body systems
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• Functional renormalization for spontaneous symmetry breaking in the Hubbard model
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Lattice Gauge Tensor Networks
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation
• Critical properties of homogeneous binary trees
• Entanglement and tensor network states
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model
• Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
• Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition

Cited by in corpus (11)

• Efficient simulation of finite-temperature open quantum systems
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Dissipation-assisted matrix product factorization
• Quantum probing beyond pure dephasing
• Tensor Renormalization Group with Randomized Singular Value Decomposition
• Fingerprint and universal Markovian closure of structured bosonic environments
• Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism
• Continuous-time quantum walks in the presence of a quadratic perturbation
• Efficient construction of tensor-network representations of many-body Gaussian states
• Quantum Fisher information from tensor network integration of Lyapunov equation