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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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Eigenstate Localization in a Many-Body Quantum System.

Chao Yin1, Rahul Nandkishore1, Andrew Lucas1

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This summary is machine-generated.

Researchers demonstrate many-body localization in quantum systems. Eigenstates below a certain energy density are confined to a tiny subset of configurations, detectable via correlation functions.

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Area of Science:

  • Quantum mechanics
  • Many-body physics
  • Condensed matter theory

Background:

  • Understanding the localization of quantum systems is crucial for quantum computing and information.
  • Many-body localization (MBL) prevents thermalization in isolated quantum systems, preserving quantum information.
  • Exploring MBL in diverse Hamiltonians is key to realizing robust quantum devices.

Purpose of the Study:

  • To prove the existence of many-body Hamiltonians exhibiting a many-body mobility edge.
  • To demonstrate that eigenstates below a nonzero energy density can be localized.
  • To propose a method for detecting this localization experimentally.

Main Methods:

  • Construction of many-body Hamiltonians with few-body interactions.
  • Introduction of quantum perturbations to a classical low-density parity check code.
  • Analysis of eigenstate localization within Hilbert space.

Main Results:

  • Existence of many-body Hamiltonians with a many-body mobility edge.
  • Localization of all eigenstates below a nonzero energy density.
  • Eigenstates confined to an exponentially small fraction of energetically allowed configurations.
  • Demonstration of localization in Hilbert space.

Conclusions:

  • The study proves the existence of a specific type of many-body localization.
  • Experimental detection of eigenstate localization is feasible through few-body correlation functions.
  • This finding has implications for the design of quantum systems resistant to decoherence.