Abstract
This paper studies quantum critical loop models by defining topological types of local operators, studying their renormalization group transformation, and obtaining analytical and numerical results on various scaling exponents.
Highlights
Much of quantum criticality can be understood in terms of long-wavelength fluctuations of quantum fields
We use an exact correspondence between the imaginary-time dynamics of the 2 + 1D quantum models and a classical Markovian dynamics for 2D classical loop models with a nonlocal Boltzmann weight
We use the idea of Ref. [6], which is to create an excited state of the loop model by twisting the phase of the wave function (C) as a function of a slow “mode.” Our observation here is that using the area of a large loop for the slow mode gives a stronger bound than using the length, as was done previously
Summary
Much of quantum criticality can be understood in terms of long-wavelength fluctuations of quantum fields. The quantum loop models have a second special property, distinct from the dynamical constraint, which is a type of quantum-classical correspondence Thanks to this correspondence, we can obtain analytical results despite the lack of a 2 + 1D field theory. We map correlation functions of local quantum operators to nonlocal, “geometrical” correlation functions in the classical model The latter are well understood [20,21,22], so we obtain numerous exact critical exponents in the quantum models. We generalize the quantum-classical correspondence to dynamical correlation functions in the loop model, using the ideas of Refs. X, we discuss open questions worth studying in the future
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
