Deconfined quantum criticality in the 2D J-Q model

The deconfined quantum critical point (DQCP) was proposed as a new scenario for quantum phase transitions fifteen years ago [1] and is still an enigmatic concept, with no general consensus on its existence. To test the DQCP proposal, which is based on a quantum field theory that cannot be solved, numerical studies of various lattice models have been considered. While no direct signs of discontinuities have been observed in the finite-size scaling, there are scaling anomalies that have led to speculations of a weak first-order transition described by a non-unitary conformal field theory [2]. Another possibility is that the transition is continuous but violates standard scaling laws. The observed finite-size scaling violations can be described phenomenologically by a scaling form with two relevant fields that are tuned by the same parameter in the Hamiltonian [3]. We will discuss recent work aimed at high-precision tests of this type of scaling by doing large scale calculation of the J-Q model which can realize the quantum phase transition between the antiferromagnetic state and a valence-bond solid state.

[1] Science 303, 1490 (2004).
[2] Phys. Rev. X 7, 031051 (2017).
[3] Science 352, 213 (2016).