The discovery of quantum spin-Hall (QSH) insulators has brought topology to the forefront of condensed matter physics. While a QSH state from spin-orbit coupling can be fully understood in terms of band theory, fascinating many-body effects are expected if it instead results from spontaneous symmetry breaking. Here, we introduce a model of interacting Dirac fermions where a QSH state is dynamically generated. Our tuning parameter further allows us to destabilize the QSH state in favour of a superconducting state through proliferation of charge-2e topological defects. This route to superconductivity put forward by Grover and Senthil is an instance of a deconfined quantum critical point (DQCP). Our model offers the possibility to study DQCPs without a second length scale associated with the reduced symmetry between field theory and lattice realization and, by construction, is amenable to large-scale fermion quantum Monte Carlo simulations.
We investigate the two-dimensional q = 3 and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number z of equivalent neighbors. For not-too-large z, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges, the transitions become discontinuous. For q = 3 we locate a tricritical point separating the continuous and discontinuous transitions near z = 80, and a critical fixed point between z = 8 and 12. For q = 4 the transition becomes discontinuous for z > 16. The scaling behavior of the q = 4 model with z = 16 approximates that of the q = 4 merged critical-tricritical fixed point predicted by the renormalization scenario.
A unique property of a dynamically generated quantum spin Hall state are Goldstone modes that correspond to the long-wavelength fluctuations of the spin-orbit coupling order parameter whose topological Skyrmion excitations carry charge 2e. Within the model considered here, upon varying the chemical potential, we observe two transitions: An s-wave superconducting order parameter develops at a critical chemical potential µc1, corresponding to the excitation gap of pairs of fermions, and at µc2 the SO(3) order parameter of the quantum spin Hall state vanishes. Using negative-signfree, large-scale quantum Monte Carlo simulations, we show that µc1 = µc2 within our accuracy-we can resolve dopings away from half filling down to δ = 0.0017. The length scale associated with the fluctuations of the quantum spin Hall order parameter grows down to our lowest doping, suggesting either a continuous or a weakly first-order transition. Contrary to mean-field expectations, the doping versus chemical potential curve is not linear, indicating a dynamical critical exponent z > 2 if the transition is continuous.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.