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Related Concept Videos

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An ideal Y-Y transformer, grounded through neutral impedances, displays per-unit sequence networks akin to those of a single-phase ideal transformer when subjected to balanced positive- or negative-sequence currents. These currents do not produce neutral currents, and their associated voltage drops.
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Related Experiment Videos

Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.

G Evenbly1, G Vidal2

  • 1Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA.

Physical Review Letters
|November 28, 2015
PubMed
Summary
This summary is machine-generated.

We present a new method to construct multiscale entanglement renormalization ansatz (MERA) representations for quantum many-body systems. This tensor network renormalization approach efficiently generates ground and thermal states, applicable to classical statistical systems.

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Area of Science:

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

Background:

  • Accurate representation of quantum many-body ground states is crucial for understanding complex physical phenomena.
  • Previous methods for constructing multiscale entanglement renormalization ansatz (MERA) often involve computationally expensive energy minimization.
  • Tensor network methods are powerful tools for simulating quantum systems but require efficient algorithms for state representation.

Purpose of the Study:

  • To develop a novel and efficient method for building MERA representations of quantum many-body states.
  • To apply tensor network renormalization to Euclidean time evolution for constructing MERA states.
  • To extend the MERA formalism and tensor network renormalization to thermal states and classical statistical systems.

Main Methods:

  • Utilized the recently proposed tensor network renormalization technique.
  • Applied this renormalization to the Euclidean time evolution operator e(-βH) for infinite and finite inverse temperatures (β).
  • Developed a construction that bypasses traditional energy minimization in MERA algorithms.

Main Results:

  • Successfully demonstrated the construction of MERA representations for the ground state of a many-body Hamiltonian.
  • Showed that applying the method to finite β yields a MERA representation of a thermal Gibbs state.
  • Established a renormalization group flow in the space of wave functions and Hamiltonians, not just tensors.

Conclusions:

  • The proposed tensor network renormalization approach provides an efficient alternative to energy minimization for MERA construction.
  • This method naturally extends to describing thermal states in quantum systems.
  • The formalism is applicable to classical statistical systems, broadening the scope of tensor network renormalization.