TY - JOUR
T1 - Confinement transition of ℤ<sub>2</sub> gauge theories coupled to massless fermions: Emergent quantum chromodynamics and <em>SO</em>(5) symmetry
JF - Proceedings of the National Academy of Sciences
JO - Proc Natl Acad Sci USA
SP - E6987
LP - E6995
M3 - 10.1073/pnas.1806338115
VL - 115
IS - 30
AU - Gazit, Snir
AU - Assaad, Fakher F.
AU - Sachdev, Subir
AU - Vishwanath, Ashvin
AU - Wang, Chong
Y1 - 2018/07/24
UR - http://www.pnas.org/content/115/30/E6987.abstract
N2 - Universal properties of quantum (zero-temperature) phase transitions are typically well-described by the classical Landau theory of spontaneous symmetry breaking. A paradigmatic counterexample is deconfined criticality, where quantum interference allows for a direct and continuous transition between states with distinct symmetry-breaking patterns, a phenomenon that is classically forbidden. In this work, we extend the scope of deconfined criticality to a case where breaking of a global symmetry coincides with confinement of a local (gauge) symmetry. Using Monte Carlo simulations, we investigate a lattice realization of this transition. Remarkably, we uncover emergent and enlarged global and gauge symmetries. These findings direct us in constructing a critical field theory description.We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit Z2 topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged SO(5) symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [SU(2)] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross–Neveu–Yukawa transition.
ER -