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Register a new userQuantum phase transitions in Dirac fermion systems
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A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.
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Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)$times$U(1) symmetry. Using large-scale auxiliary- field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.
Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase structure. Here, we review the present status of our work in this direction.
We report measurements of magnetic quantum oscillations and specific heat at low temperatures across a field-induced antiferromagnetic quantum critical point (QCP)(B_{c0}approx50T) of the heavy-fermion metal CeRhIn_5. A sharp magnetic-field induced Fermi surface reconstruction is observed inside the antiferromagnetic phase. Our results demonstrate multiple classes of QCPs in the field-pressure phase diagram of this heavy-fermion metal, pointing to a universal description of QCPs. They also suggest that robust superconductivity is promoted by unconventional quantum criticality of a fluctuating Fermi surface.
We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of $Z_N$ models in the $Ntoinfty$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.
The tilted balance among competing interactions can yield a rich variety of ground states of quantum matter. In most Ce-based heavy fermion systems, this can often be qualitatively described by the famous Doniach phase diagram, owing to the competition between the Kondo screening and the Ruderman-Kittel-Kasuya-Yoshida exchange interaction. Here, we report an unusual pressure-temperature phase diagram beyond the Doniach one in CeCuP2. At ambient pressure, CeCuP2 displays typical heavy-fermion behavior, albeit with a very low carrier density. With lowering temperature, it shows a crossover from a non Fermi liquid to a Fermi liquid at around 2.4 K. But surprisingly, the Kondo coherence temperature decreases with increasing pressure, opposite to that in most Ce-based heavy fermion compounds. Upon further compression, two superconducting phases are revealed. At 48.0 GPa, the transition temperature reaches 6.1 K, the highest among all Ce-based heavy fermion superconductors. We argue for possible roles of valence tuning and fluctuations associated with its special crystal structure in addition to the hybridization effect. These unusual phase diagrams suggest that CeCuP2 is a novel platform for studying the rich heavy fermions physics beyond the conventional Doniach paradigm.
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