Under the support of the National Natural Science Foundation of China (Grant No.: 62034004, 62122036), etc., Prof. Feng Miao from Nanjing University and his collaborators adopted the “Atomic Lego-like” means to build a new solid-state quantum simulator, observing a new electron crystal state pinned on the moire superlattice. This work was published in Nature on September 14, 2022, entitled "Tunable quantum criticalities in an isospin extended Hubbard model simulator" (article link: www.nature.com/articles/s41586-022-05106-0). This work was also reported by the Nature News & Views in the article entitled "Simple solids mimic complex electronic states", saying that this work "offers a platform in which the simplest possible simulator can be tuned to exhibit complex quantum phase transitions".

Giant electron-electron coulomb interactions in strongly correlated systems can induce rich and exotic quantum many-body states, including unconventional superconductors, Mott insulators, Wigner crystal states, non-Fermi liquids, and quantum spin liquids. The exploration and in-depth understanding of these novel states have been the constant force for the development of the field of condensed matter physics in the past few decades. Meanwhile, in the vicinity of correlation-induced quantum phase transitions, various energy scales are comparable, and the quantum fluctuations become prominent, providing an ideal platform for exploring new quantum many-body states and physics. Especially when the system involves multiple physical degrees of freedom, the strong competition between quantum fluctuations of different order parameters may lead to novel quantum critical phases and critical behaviors beyond the Landau’s phase transition paradigm.

In order to grasp the essence of correlated physics, physicists have developed several abstract models to understand the quantum many-body systems. The most famous one is the Hubbard model, as well as the extended version when long-range Coulomb interactions are considered. Although these paradigmatic models are already simplified compared to the actual physical systems, there are still huge theoretical challenges in solving these strongly correlated models. Especially when the strongly correlated electron system with multiple degrees of freedom is near the quantum critical region, the huge order parameter quantum fluctuation and various comparable energy scales make the problem extremely difficult to solve. In recent years, the rise of various quantum simulators has provided new experimental methods and platforms for solving such problems. In particular, if different types of quantum phase transitions and quantum critical behaviors, as well as the controllable evolution among them can be realized in a single system by in-situ tuning the parameters, it will provide unprecedented opportunities for the new development of strongly correlated physics.

Facing the above opportunities and challenges, Feng Miao, Bin Cheng and their collaborators built a SU(4) isospin extended Hubbard model simulator based on twisted double bilayer graphene fabricated by "Atomic Lego-like" means. For the first time, a new type of electronic crystal state pinned to the Moiré superlattice, i.e., generalized isospin Wigner crystal, has been observed. In the experiment, the collaborative team realized quantum melting of this electron crystal through the in-situ tuning of the electron correlation strength by varying the vertical electric field, observing the quantum two-stage criticality for the first time. Based on the decoupled valley and spin degrees of freedom in this system, the research team continuously evolve the intrinsic degrees of freedom of this quantum simulator from SU(4) to SU(2) by turning on the parallel magnetic field, and for the first time observed quantum pseudo criticality (see figure).

This "Atom Lego-like" quantum simulator successfully simulates the tunable quantum phase transitions from a highly symmetric SU(4) strongly correlated electron system with a critical intermediate phase to a weak first-order case in a low symmetric SU(2) electron system. This controllable evolution not only makes it possible to enable the simulation and in-depth understanding of strongly correlated electronic systems with tunable intrinsic degrees of freedom, but also takes a key step towards the future development of high-density integratable, highly tunable, and easy-to-read solid-state quantum simulators.

Figure Quantum pseudo criticality in high parallel magnetic field. a, Line plots of resistance-temperature (R-T) curves at different perpendicular electric fields (D). The dashed box indicates the almost unchanged resistance. b, 2D map of dR/dT as a function of D and T in high magnetic field. c, Successful and failed (upper inset) collapse of R-T curves by performing the scaling analysis in the Wigner crystal regime for temperatures only above the critical temperature and for full temperature range. d, Quantum simulator with intrinsic degrees of freedom continuously evolving from SU(4) and SU(2).