Improved numerical methods for infinite spin chains with long-range interactions

Abstract

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed multi-optimization (SMO) method, which allows an efficient optimization of exponentially many MPS of different length at different sites all in one step. Hereby the algorithm becomes protected against position dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the systems translational symmetry was accessible. Further, we investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance braking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply the new methods to polar bosons with long-range interactions. We calculate several detailed Devil's Staircases with the corresponding phase diagrams and investigate some supersolid properties.

Main text: 17 pages plus references, 8 figures. Supplementary info: 6 pages. v2: improved presentation and more results added

References in corpus (25)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement renormalization
• An Area Law for One Dimensional Quantum Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• From density-matrix renormalization group to matrix product states
• Matrix product operator representations
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Scaling of entanglement support for Matrix Product States
• Applying matrix product operators to model systems with long-range interactions
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Ultracold Dipolar Gases in Optical Lattices
• Finite automata for caching in matrix product algorithms
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Dynamical crystal creation with polar molecules or Rydberg atoms in optical lattices
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Tensor operators: constructions and applications for long-range interaction systems
• Devil's staircases and supersolids in a one-dimensional dipolar Bose gas
• The computational difficulty of finding MPS ground states
• Suppression of finite-size effects in one-dimensional correlated systems
• On calculation of vector spin chirality for zigzag spin chains
• Computational Difficulty of Global Variations in the Density Matrix Renormalization Group
• Concatenated tensor network states
• Renormalization algorithm with graph enhancement
• Uniform Matrix Product State in the Thermodynamic Limit
• Incommensurate Matrix Product State for Quantum Spin Systems

Cited by in corpus (17)

• Spread of correlations in long-range interacting quantum systems
• Kitaev chains with long-range pairing
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Topological phases in ultracold polar-molecule quantum magnets
• Information propagation and equilibration in long-range Kitaev chains
• Random transverse-field Ising chain with long-range interactions
• Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit
• Structured Chaos in a Devil's Staircase of the Josephson Junction
• Conformal and chiral phase transitions in Rydberg chains
• Long-range random transverse-field Ising model in three dimensions
• Devil's Staircases and Continued Fractions in the Josephson Junctions
• Devil's Staircases in SFS Josephson Junctions
• Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models
• Phase-transitions of the random bond Potts chain with long-range interactions
• Controllable quantum spin glasses with magnetic impurities embedded in quantum solids
• Floating Phases in One-Dimensional Rydberg Ising Chains
• An efficient perturbation theory of density matrix renormalization group