On Many-Body Localization for Quantum Spin Chains
By J. Imbrie. 2014
607 citations recorded by the source corpus.
For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.
Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6b47fe576dcc5812c1d7595d9ee94d8cde26d3f9
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In Atomic and Molecular Physics, and Optics
In Geometry and Topology
Citations in the corpus
- Many-body localization: An introduction and selected topics (2017, neutral): “…for closed, isolated systems, a situation problematic for experiments due to the inevitable coupling with the environment While initial development of the MBL field was driven by theory (with numerics contributing actively), several major experiments, mostly on cold-atoms, changed the situation.”
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains (2016, background): “non-conducting, non-thermalising phase, in which the system violates the Eigenstate Thermalisation hypothesis [25, 26, 27, 28, 29, 30, 31].”
- Many-body localization and delocalization in large quantum chains (2018, background): “Analytically, the existence of an MBL region in the phase diagram of a disordered quantum spin chain has been proven based on an assumption about energy level repulsion [17].”
- Local integrals of motion in many‐body localized systems (2016, methodology): “This follows straightforwardly from the construction in [52], where the conserved quantities of a disordered spin chain are obtained from the Pauli operators Sz a by means of a quasilocal rotation Ω, Iα = ΩS z aΩ ∗ and I± α = ΩS ± a Ω ∗, that obviously preserves the spectrum and the commutation rela”
- A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems (2015, methodology): “to perform a KAM step, see [21] for a celebrated recent application and an account of the technique.”
- Slow scrambling in disordered quantum systems (2016, background): “As discussed in [45,48], this fixed-point Hamiltonian is expected to be sufficient to describe the coarse-grained physics of an entire many-body localized phase.”
- Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “(56) has zero bipartite entanglement; in the thermal phase, h < hc, the half-chain entanglement entropy grows rapidly (red curve) towards a value which is extensive in system size; the growth on the MBL side, h > hc, in contrast is much slower, first achieving a sub-extensive level similar to that o”
- Random Operators: Disorder Effects on Quantum Spectra and Dynamics (2015, background): “Mathematical approaches to localization in more general many-body models, such as [14], are still rare and incomplete.”
- Avalanches and many-body resonances in many-body localized systems (2021, methodology): “This is numerical confirmation, at the accessible system sizes, of the modest assumption of limited level attraction in the proof of MBL [66], albeit for Floquet systems, which were not the original target of the proof.”