Detecting Emergent Continuous Symmetries at Quantum Criticality

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New or enlarged symmetries can emerge at the low-energy spectrum of a Hamiltonian that does not possess the symmetries, if the symmetry breaking terms in the Hamiltonian are irrelevant under the renormalization group flow. We propose a tensor network based algorithm to numerically extract lattice operator approximation of the emergent conserved currents from the ground state of any quantum spin chains, without the necessity to have prior knowledge about its low-energy effective field theory. Our results for the spin-1/2 J−Q Heisenberg chain and a one-dimensional version of the deconfined quantum critical points demonstrate the power of our method to obtain the emergent lattice Kac-Moody generators. It can also be viewed as a way to find the local integrals of motion of an integrable model and the local parent Hamiltonian of a critical gapless ground state.
Original languageEnglish
Article number036505
Number of pages7
JournalPhysical Review Letters
Issue number3
Publication statusPublished - 21 Jul 2023

Austrian Fields of Science 2012

  • 103015 Condensed matter
  • 103025 Quantum mechanics

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