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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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General entanglement scaling laws from time evolution.

Jens Eisert1, Tobias J Osborne

  • 1Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE, United Kingdom.

Physical Review Letters
|December 13, 2006
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Summary
This summary is machine-generated.

We found a general entanglement-boundary law for quantum spin chains, applicable to ground and dynamic states. This law shows geometric entropy saturates, with exceptions in specific fermionic systems.

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Area of Science:

  • Quantum Information Theory
  • Condensed Matter Physics
  • Quantum Many-Body Systems

Background:

  • Entanglement is a key resource in quantum information and a probe of quantum many-body states.
  • Understanding entanglement scaling in quantum spin chains is crucial for characterizing phases of matter and dynamics.
  • Previous studies focused on specific models, necessitating a general framework for entanglement scaling laws.

Purpose of the Study:

  • To establish a general scaling law for entanglement in quantum spin chains.
  • To investigate the applicability of this law to both ground states and dynamically evolving states.
  • To explore conditions under which this entanglement-boundary law may be violated.

Main Methods:

  • Utilizing concepts from quantum information theory.
  • Applying Lieb-Robinson bounds to analyze the dynamics of quantum systems.
  • Investigating ground states of gapped models and states generated by sudden quenches.

Main Results:

  • A general entanglement-boundary law is established for a broad class of quantum spin chain states.
  • Geometric entropy of a distinguished block saturates, following the established law.
  • Noncritical fermionic systems and specific spin chains with decaying interactions were identified as violating this law.

Conclusions:

  • The entanglement-boundary law provides a universal description for entanglement scaling in many quantum spin systems.
  • The identified exceptions highlight the importance of system properties and interactions in determining entanglement behavior.
  • These findings have implications for understanding the classical simulatability of quantum systems.