Scaling theory for two-dimensional quantum critical points using tensor network states

Novel quantum critical behaviors beyond the traditional Landau-Ginzberg-Wilson paradigm can happen in strongly correlated quantum many-body systems. Although great efforts have been spent both numerically and theoretically, many of them are still remaining controversial in two dimensions (2D). To resolve these problems, we propose to develop a new scaling theory using tensor network states, specifically projected entangled pair states (PEPS) in 2D. We plan to introduce finite time scales into PEPS by driving the system to evolve near the critical point. Unlike the finite correlation length in a PEPS, the finite time scale can be freely adjusted to construct dimensionless operators. State-of-the-art time evolution methods will be used to establish an efficient update algorithm and the finite scaling theory. With this scaling theory, we can not only perform standard finite scaling analysis to study the critical behaviors but also investigate the critical dynamics to explore the mechanism of the corresponding phase transition. This approach is promising to be a unified and standard PEPS based finite scaling analysis method for critical properties of fermion, boson, and spin models in 2D.