The frustration-free fully packed loop model
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The frustration-free fully packed loop model. / Zhang, Zhao; Roising, Henrik Schou.
I: Journal of Physics A: Mathematical and Theoretical, Bind 56, Nr. 19, 194001, 12.05.2023.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The frustration-free fully packed loop model
AU - Zhang, Zhao
AU - Roising, Henrik Schou
PY - 2023/5/12
Y1 - 2023/5/12
N2 - We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. A boundary Hamiltonian is added to favor domain-wall boundary conditions and link ground state properties to the combinatorics and six-vertex model literature. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace, leading to a series of energy-equidistant exact eigenstates in the lower end of the spectrum. Among them we systematically classify both finitely entangled eigenstates and product eigenstates. Using a recursion relation for enumerating half-plane configurations, we compute numerically the exact entanglement entropy of the ground state, confirming area law scaling. Finally, the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
AB - We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. A boundary Hamiltonian is added to favor domain-wall boundary conditions and link ground state properties to the combinatorics and six-vertex model literature. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace, leading to a series of energy-equidistant exact eigenstates in the lower end of the spectrum. Among them we systematically classify both finitely entangled eigenstates and product eigenstates. Using a recursion relation for enumerating half-plane configurations, we compute numerically the exact entanglement entropy of the ground state, confirming area law scaling. Finally, the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
KW - self-avoiding walks
KW - two-dimensional spin models
KW - lattice models in condensed matter
KW - quantum entanglement
KW - exact enumeration
KW - combinatorics and graph theory
KW - QUANTUM
KW - LATTICE
KW - ENTANGLEMENT
KW - PHASE
U2 - 10.1088/1751-8121/acc76f
DO - 10.1088/1751-8121/acc76f
M3 - Journal article
VL - 56
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 19
M1 - 194001
ER -
ID: 346141137