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Register a new userQuantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene
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We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Horava in relation to the quantum theory of gravity. In such vacua the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED
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The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field $B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field $E$ at $E/B ll 1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field $E$ and the lowest order correction to it due to the magnetic field ($B/E ll 1$).
Some astrophysical objects are supposed to have very strong electromagnetic fields above the critical strength. Quantum fluctuations due to strong electromagnetic fields modify the Maxwell theory and particularly electric fields make the vacuum unstable against pair production of charged particles. We study the strong field effect such as the effective action and the Schwinger pair production in scalar QED.
We examine the entanglement properties of the spin-half Heisenberg model on the two-dimensional square-lattice bilayer based on quantum Monte Carlo calculations of the second Renyi entanglement entropy. In particular, we extract the dominant area-law contribution to the bipartite entanglement entropy that shows a non-monotonous behavior upon increasing the inter-layer exchange interaction: a local maximum in the area-law coefficient is located at the quantum critical point separating the antiferromagnetically ordered region from the disordered dimer-singlet regime. Furthermore, we consider subleading logarithmic corrections to the Renyi entanglement entropy scaling. Employing different subregion shapes, we isolate the logarithmic corner term from the logarithmic contribution due to Goldstone modes that is found to be enhanced in the limit of decoupled layers. At the quantum critical point, we estimate a contribution of $0.016(1)$ due to each $90^{circ}$ corner. This corner term at the SU(2) quantum critical point deviates from the Gaussian theory value, while it compares well with recent numerical linked cluster calculations on the bilayer model.
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the correlated insulating states at $pm 1/2$ filling and at the charge neutrality point are all valley polarized sates which break $C_{2z}$ and time-reversal ($mathcal{T}$) symmetries, but preserves $C_{2z}mathcal{T}$ symmetry. Such valley polarized states exhibit moire orbital antiferromagnetic ordering on an emergent honeycomb lattice with compensating circulating current pattern in the moire supercell. Within the same theoretical framework, our calculations indicate that the $C!=!mp 1$ QAH states at $pm 3/4$ fillings of the magic-angle TBG are spin and orbital ferromagnetic states, which emerge when a staggered sublattice potential is present. We find that the nonlocalness of the exchange interactions tend to enhance the bandwidth of the low-energy bands due to the exchange-hole effect, which reduces the gaps of the correlated insulator phases. The nonlocal exchange interactions also dramatically enhance the spin polarization of the system, which significantly stabilize the orbital and spin ferromagnetic QAH state at $3/4$ filling of TBG aligned with hexagonal boron nitride (hBN). We also predict that, by virtue of the orbital ferromagnetic nature, the QAH effects at electron and hole fillings of hBN-aligned TBG would exhibit hysteresis loops with opposite chiralities.
By using Density Matrix Renormalization Group (DMRG) technique we study the 1D extended anisotropic Heisenberg model. We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions (QPTs) induced by frustration. By increasing the next-nearest-neighbor (NNN) interaction, the ground state of the system changes smoothly from a completely polarized state to a NNN correlated one. On the contrary, letting the in-plane interaction to be greater than the out-of-plane one, the ground state changes abruptly.
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