Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians

Yu, Xiongjie; Pekker, David; Clark, Bryan K.

doi:10.1103/physrevlett.118.017201

Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians

Journal Article · Mon Jan 02 23:00:00 EST 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.118.017201· OSTI ID:1536467

Yu, Xiongjie ^[1]; Pekker, David ^[2]; Clark, Bryan K. ^[3]

Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics; DOE/OSTI
Univ. of Pittsburgh, PA (United States). Pittsburgh Quantum Inst. Dept. of Physics and Astronomy
Univ. of Illinois at Urbana-Champaign, IL (United States). Dept. of Physics

A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0008692

OSTI ID:: 1536467

Alternate ID(s):: OSTI ID: 1338136

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 1 Vol. 118; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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