We derive the renormalization group equations describing all the short-range interactions in bilayer graphene allowed by symmetry and the long range Coulomb interaction. For certain range of parameters, we predict the first order phase transition to the uniaxially deformed gapless state accompanied by the change of the topology of the electron spectrum. PACS numbers: 73.22.Pr, 73.21.-bIntroduction-The Lifshitz transition (LiTr) [1] is the simplest topological effect in physics of metals. It consists of the change of connectivity of isoenergetic surfaces, either as a function of electron density or external parameters, such as strain. As the change of the topology of the e.g. Fermi surface can not be continuous, all the observables in the system should experience singularities at the LiTr also known as a half-integer-order phase transition (PT). Alternatively, the reconstruction of the Fermi surface may occur via an underlaying spontaneous symmetry breaking PT. The observation of the LiTr in the bulk metals is an extremely challenging task: a variation of the Fermi level in metals requires doping which introduces disorder and obscures the transition, whereas application of strain requires high pressure experiments.

We analyze the phase diagram of bilayer graphene (BLG) at zero temperature and zero doping. Assuming that at high energies the electronic system of BLG can be described within a weak-coupling theory (consistent with the experimental evidence), we systematically study the evolution of the couplings with going from high to low energies. The divergences of the couplings at some energies indicate the tendency towards certain symmetry breakings. Carrying out this program, we found that the phase diagram is determined by microscopic couplings defined on the short distances (initial conditions). We explored all plausible space of these initial conditions and found that the three states have the largest phase volume of the initial couplings: nematic, antiferromagnetic, and spin flux (a.k.a. quantum spin Hall). In addition, ferroelectric and two superconducting phases appear only near the very limits of the applicability of the weak-coupling approach. The paper also contains the derivation and analysis of the renormalization group equations and the group theory classification of all the possible phases which might arise from the symmetry breakings of the lattice, spin rotation, and gauge symmetries of graphene.

Results are presented for the time evolution of fermions initially in a non-zero temperature normal phase, following the switch on of an attractive interaction. The dynamics are studied in the disordered phase close to the critical point, where the superfluid fluctuations are large. The analysis is conducted within a two-particle irreducible, large N approximation. The system is considered from the perspective of critical quenches where it is shown that the fluctuations follow universal model A dynamics. A signature of this universality is found in a singular correction to the fermion lifetime, given by a scaling form, where d is the spatial dimension, t is the time since the quench, and ε is the fermion energy. The singular behavior of the spectral density is interpreted as arising due to incoherent Andreev reflections off superfluid fluctuations.

Periodically driven Kitaev chains show a rich phase diagram as the amplitude and frequency of the drive is varied, with topological phase transitions separating regions with different number of Majorana zero and π modes. We explore whether the critical point separating different phases of the periodically driven chain may be characterized by a universal central charge. We affirmatively answer this question by studying the entanglement entropy (EE) numerically and analytically for the lowest entangled many particle eigenstate at arbitrary nonstroboscopic and stroboscopic times. We find that the EE at the critical point scales logarithmically with a time-independent central charge, and that the Floquet micromotion gives only subleading corrections to the EE. This result also generalizes to multicritical points where the EE is found to have a central charge that is the sum of the central charges of the intersecting critical lines.