Yao Daoxin, a professor in the School of Physics of Sun Yat sen University, and his collaborators have made important progress in the study of the scaling behavior of disordered operators in quantum phase transitions. They first proposed that disordered operators can be used to detect boundary states and the critical behavior of boundaries, and analyzed their scaling behavior. Relevant achievements were published in Physical Review Letters on May 17, and were recommended by editors.
Quantum phase transition has always been one of the important and interesting topics in condensed matter physics. The boundary of the lattice system shows more abundant phase transition behavior than that in the body due to its different coordination number, that is, the surface critical behavior. Because the boundary mode is coupled with the critical fluctuation of the body, the boundary will induce novel phase transition behavior, which has attracted many researchers' attention. How to extract the information of boundary critical behavior in multibody computing and further verify the reliability of surface critical theory is an important direction of quantum multibody computing.
In recent years, the research of nonlocal operators has gradually arisen, which can understand the phase and phase transition from the perspective of generalized symmetry and domain wall. As a non local measurement operator, the disorder operator can reveal the high valence symmetry and conformal field theory information of phase and phase transition point, and understand the information of phase transition universality from a global perspective.
The research team took the lead in using the disorder operator to study the boundary properties of the two-dimensional quantum spin chain (AKLT) model with symmetric protective topological phase. In the AKLT phase, the spin of the boundary forms an effective Heisenberg chain. The disorder operator can reflect the physical properties of the edge state, extract the Luttinger parameter of the Heisenberg chain, and reveal the physics of the (1+1) dimensional boundary SU (2) 1. When the system is close to the phase transition point, the edge mode of the void free gap is gradually coupled with the critical fluctuation of the body. The disorder operator can not only reflect the (1+1) dimensional SU (2) 1 physics of the edge state, extract Luttinger parameters, but also extract the conformal field theory information of the critical behavior of the body O (3) critical mode.
On this basis, the research team proposed a conjecture about the scaling behavior of disordered operators. At the critical point, the marginal mode of the void free and the critical mode of the body will enter the scaling behavior of the disorder operator in the form of superposition, which is reflected in its logarithmic term. The team used the quantum Monte Carlo method to study the corresponding relationship between the entanglement spectrum and the energy spectrum of the two-dimensional AKLT model. The famous Li Haldane conjecture points out that the low-energy part of the entanglement spectrum in the topological state has a one-to-one correspondence with the energy spectrum of the open boundary. The research team found that the entanglement spectrum does not always correspond to the energy spectrum when perturbation is applied at the boundary of the AKLT model. In some cases, even if the boundary becomes energy gap, its entanglement spectrum and energy spectrum also have a corresponding relationship.
The research team also used new wormhole images to better understand these numerical results, and revealed that wormhole images can be a powerful tool to understand the changes in the entanglement spectrum of complex systems. Prior to this, the research team used the quantum Monte Carlo method to study the excitation spectrum of the model body and boundary, providing an important numerical basis for understanding the excitation of symmetric protective topological phase and magnetic order.
Relevant paper information: https://doi.org/10.1103/PhysRevLett.132.206502
