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Numerical renormalization group for continuum one-dimensional systems.

Robert M Konik1, Yury Adamov

  • 1CMPMS Department, Brookhaven National Laboratory, Upton, New York 11973, USA.

Physical Review Letters
|May 16, 2007
PubMed
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We developed a new renormalization group (RG) procedure for one-dimensional interacting models. This method combines numerical RG with conformal field theory, allowing for both numerical and analytical studies of physical observables.

Area of Science:

  • Condensed matter physics
  • Quantum field theory
  • Statistical mechanics

Background:

  • Renormalization group (RG) methods are crucial for understanding critical phenomena and quantum systems.
  • Continuum conformal and integrable models provide exactly solvable frameworks for theoretical physics.

Purpose of the Study:

  • To introduce a novel RG procedure applicable to a broad range of interacting one-dimensional models.
  • To integrate Wilson's numerical RG with Zamolodchikov's truncated conformal spectrum approach.
  • To enable both numerical and analytical investigations of RG flow for physical observables.

Main Methods:

  • The procedure combines Wilson's numerical renormalization group with Zamolodchikov's truncated conformal spectrum approach.
  • It leverages exactly understood eigenstates from continuum conformal and integrable models for precise matrix element computation.

Related Experiment Videos

  • The method allows for the study of renormalization group flow of physical observables.

    • Main Results:

    • The developed RG procedure is demonstrated to be effective on interacting one-dimensional models.
    • The study successfully analyzes the spectrum of coupled quantum Ising chains.
    • Correlation functions in a single quantum Ising chain under a magnetic field are investigated.

    Conclusions:

    • The presented RG procedure offers a powerful hybrid approach for studying complex quantum systems.
    • It bridges numerical and analytical techniques, enhancing the understanding of renormalization group flows.
    • The method provides new insights into the behavior of quantum Ising chains in external fields.