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Detecting Emergent Continuous Symmetries at Quantum Criticality.

Mingru Yang1, Bram Vanhecke1, Norbert Schuch1,2

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This summary is machine-generated.

We developed a new tensor network algorithm to find emergent symmetries in quantum spin chains. This method identifies conserved currents and local integrals of motion without needing prior knowledge of the system's effective field theory.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Computational Physics

Background:

  • Symmetries can emerge in low-energy spectra even if not present in the original Hamiltonian.
  • Renormalization group flow determines the relevance of symmetry-breaking terms.

Purpose of the Study:

  • To propose a novel tensor network algorithm for extracting emergent conserved currents.
  • To demonstrate the algorithm's ability to identify symmetries without prior effective field theory knowledge.

Main Methods:

  • Tensor network based numerical algorithm.
  • Analysis of ground states of quantum spin chains.
  • Application to spin-1/2 J-Q Heisenberg chain and 1D deconfined quantum critical points.

Main Results:

  • Successfully extracted lattice operator approximations of emergent conserved currents.
  • Identified emergent lattice Kac-Moody generators.
  • Demonstrated the method's power for various quantum spin systems.

Conclusions:

  • The proposed tensor network algorithm is effective for discovering emergent symmetries and conserved quantities.
  • The method provides a way to find local integrals of motion and parent Hamiltonians for critical states.