Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

Abstract

The practical success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad, Landau, Vazirani, and Vidick. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce an efficient implementation of the theoretical RRG procedure which finds MPS ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in situations of practical interest. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a tree-like manner. We evaluate the algorithm numerically, finding similar performance to DMRG in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, or large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

13 pages, 10 figures

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Cited by in corpus (10)

• Ground-state properties of the one-dimensional transverse Ising model in a longitudinal magnetic field
• Gauging tensor networks with belief propagation
• Locally accurate MPS approximations for ground states of one-dimensional gapped local Hamiltonians
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Infinite randomness with continuously varying critical exponents in the random XYZ spin chain
• Variational adiabatic transport of tensor networks
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach
• Adiabatic ground state preparation in an expanding lattice
• Sample complexity of matrix product states at finite temperature