TY - JOUR
T1 - Extracting Higher Central Charge from a Single Wave Function
AU - Kobayashi, Ryohei
AU - Wang, Taige
AU - Soejima, Tomohiro
AU - Mong, Roger S.K.
AU - Ryu, Shinsei
N1 - Publisher Copyright:
© 2024 American Physical Society.
PY - 2024/1/5
Y1 - 2024/1/5
N2 - A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c- is vanishing. Recently, it was discovered that a quantity regarded as a "higher"version of chiral central charge gives a further obstruction beyond c- to gapping out the edge. In this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν=1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c-, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.
AB - A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c- is vanishing. Recently, it was discovered that a quantity regarded as a "higher"version of chiral central charge gives a further obstruction beyond c- to gapping out the edge. In this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν=1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c-, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.
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U2 - 10.1103/PhysRevLett.132.016602
DO - 10.1103/PhysRevLett.132.016602
M3 - Article
C2 - 38242664
AN - SCOPUS:85182864413
SN - 0031-9007
VL - 132
JO - Physical review letters
JF - Physical review letters
IS - 1
M1 - 016602
ER -