Measuring the Boundary Gapless State and Criticality via Disorder Operator
Abstract
The disorder operator is often designed to reveal the conformal field theory (CFT) information in quantum many-body systems. By using large-scale quantum Monte Carlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K . This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1 +1 )D boundary. At bulk critical point, the effective K is suppressed but it keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1 +1 )D SU (2 )1 CFT and (2 +1 )D O (3 ) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality.
- Publication:
-
Physical Review Letters
- Pub Date:
- May 2024
- DOI:
- 10.1103/PhysRevLett.132.206502
- arXiv:
- arXiv:2311.05690
- Bibcode:
- 2024PhRvL.132t6502L
- Keywords:
-
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 8 Pages,7 figures