Encoding the structure of many-body localization with matrix product operators

Abstract

Anderson insulators are non-interacting disordered systems which have localized single particle eigenstates. The interacting analogue of Anderson insulators are the Many-Body Localized (MBL) phases. The natural language for representing the spectrum of the Anderson insulator is that of product states over the single-particle modes. We show that product states over Matrix Product Operators of small bond dimension is the corresponding natural language for describing the MBL phases. In this language all of the many-body eigenstates are encode by Matrix Product States (i.e. DMRG wave function) consisting of only two sets of low bond-dimension matrices per site: the $G_i$ matrix corresponding to the local ground state on site $i$ and the $E_i$ matrix corresponding to the local excited state. All $2^n$ eigenstates can be generated from all possible combinations of these matrices.

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Cited by in corpus (38)

• Many-body localization: an introduction and selected topics
• The Ergodic Side of the Many-Body Localization Transition
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• Many-Body Localization in the Age of Classical Computing
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• Finding matrix product state representations of highly-excited eigenstates of many-body localized Hamiltonians
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Fixed points of Wegner-Wilson flows and many-body localization
• Bimodal entanglement entropy distribution in the many-body localization transition
• Signatures of the Many-body Localized Regime in Two Dimensions
• Cluster Truncated Wigner Approximation in Strongly Interacting Systems
• Efficient representation of fully many-body localized systems using tensor networks
• One-particle density matrix characterization of many-body localization
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• Behavior of l-bits near the many-body localization transition
• Emergent local integrals of motion without a complete set of localized eigenstates
• One-particle-density-matrix occupation spectrum of many-body localized states after a global quench
• Exploring many body localization and thermalization using semiclassical method
• Local integrals of motion and the quasiperiodic many-body localization transition
• Exploring one particle orbitals in large Many-Body Localized systems
• Numerical evidence for many-body localization in two and three dimensions
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• Length scales in the many-body localized phase and their spectral signatures
• Localization-protected order in spin chains with non-Abelian discrete symmetries
• Almost-conserved operators in nearly many-body localized systems
• Beyond many-body localized states in a spin-disordered Hubbard model with pseudo-spin symmetry
• Approximating observables on eigenstates of large many-body localized systems
• Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
• Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
• Ultraslow Growth of Number Entropy in an l-bit Model of Many-Body Localization
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Many-body-localization protection of eigenstate topological order in two dimensions
• Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Renormalization view on resonance proliferation between many-body localized phases
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold