Robustness in Projected Entangled Pair States

Abstract

We analyze a criterion which guarantees that the ground states of certain many body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restricted version of the Local Topological Quantum Order (LTQO) condition provides a checkable criterion which allows to assess the stability of local properties of PEPS under physical perturbations. We moreover show that LTQO itself is stable under perturbations which preserve the spectral gap, leading to nontrivial examples of PEPS which possess LTQO and are thus stable under arbitrary perturbations.

arXiv comment11 pages, 4 figures

References in corpus (15)

• Entanglement spectrum of a topological phase in one dimension
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classifying quantum phases using Matrix Product States and PEPS
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Topological quantum order: stability under local perturbations
• PEPS as ground states: degeneracy and topology
• A short proof of stability of topological order under local perturbations
• Stability of Frustration-Free Hamiltonians
• Resonating valence bond states in the PEPS formalism
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
• A quantum version of Wielandt's inequality
• A canonical form for Projected Entangled Pair States and applications
• Gapless Hamiltonians for the toric code using the PEPS formalism

Cited by in corpus (23)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Purifications of multipartite states: limitations and constructive methods
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Entanglement and tensor network states
• Edge theories in Projected Entangled Pair State models
• Frustration free gapless Hamiltonians for Matrix Product States
• Quantum many-body systems in thermal equilibrium
• Fundamental Tensor Operations for Large-Scale Data Analysis in Tensor Train Formats
• Product Vacua and Boundary State Models in d Dimensions
• Approximating local observables on projected entangled pair states
• Topological quantum error correction in the Kitaev honeycomb model
• Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces
• Long range order and symmetry breaking in Projected Entangled Pair State models
• Graph states as ground states of two-body frustration-free Hamiltonians
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in ${\mathbb{R}}^d$
• Connected components of irreducible maps and 1D quantum phases
• Perturbation Theory for Parent Hamiltonians of Matrix Product States
• How local is the information in MPS/PEPS tensor networks?
• From decay of correlations to locality and stability of the Gibbs state
• Locality optimization for parent Hamiltonians of Tensor Networks
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States
• Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States