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Register a new userRenormalization group study of systems with quadratic band touching
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Lifshitz transitions in two 2D systems with a single quadratic band touching point as the chemical potential is varied have been studied here. The effects of interactions have been studied using the renormalization group (RG) and it is found that at the transition a repulsive interaction is marginally relevant and an attractive interaction is marginally irrelevant. We corroborate the results obtained from the RG calculation by studying a microscopic model whose ground state and Greens functions can be obtained exactly. We find that away from the transition, the system displays an instability towards forming and excitonic condensate.
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Phase diagrams of the two-dimensional one-band t-t Hubbard model are obtained within the two-patch and the temperature-cutoff many-patch renormalization group approach. At small t and at van Hove band fillings antiferromagnetism dominates, while with increasing t or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t=t/2 and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.
The formation of bound states between mobile impurity particles and fermionic atoms has been demonstrated in spin-polarized Fermi gases with attractive interspecies interaction. We investigate bound states of mobile impurities immersed in a two-dimensional system with a symmetry-protected quadratic band touching. In addition to the standard s-wave interaction, we consider an anisotropic dipolar exchange interaction that locally breaks point group symmetries. Using a weak-coupling renormalization group approach and a ladder approximation for the impurity-fermion propagator, we establish that the number of bound states can be controlled by varying the anisotropy of the exchange interaction. Our results show that the degeneracy and momentum dependence of the binding energies reflect some distinctive properties of the quadratic band touching.
We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite $U/t$, despite the $U=0$ hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with a dynamical critical exponent $z=1$ as expected for 2+1 d Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.
The ground state of a hole-doped t-t-J ladder with four legs favors a striped charge distribution. Spin excitation from the striped ground state is known to exhibit incommensurate spin excitation near q=(pi,pi) along the leg direction (qx direction). However, an outward dispersion from the incommensurate position toward q=(0,pi) is strong in intensity, inconsistent with inelastic neutron scattering (INS) experiment in hole-doped cuprates. Motivated by this inconsistency, we use the t-t-J model with m x n=96 lattice sites by changing lattice geometry from four-leg (24x4) to rectangle (12x8) shape and investigate the dynamical spin structure factor by using the dynamical density matrix renormalization group. We find that the outward dispersion has weak spectral weights in the 12x8 lattice, accompanied with the decrease of excitation energy close to q=(pi,pi), being consistent with the INS data. In the 12x8 lattice, weakening of incommensurate spin correlation is realized even in the presence of the striped charge distribution. For further investigation of geometry related spin dynamics, we focus on direction dependent spin excitation reported by recent resonant inelastic x-ray scattering (RIXS) for cuprate superconductors and obtain a consistent result with RIXS by examining an 8x8 t-t-J square lattice.
We use Wilsons weak coupling ``momentum shell renormalization group method to show that two-particle interaction terms commonly neglected in bosonization of one-dimensional correlated electron systems with open boundaries are indeed irrelevant in the renormalization group sense. Our study provides a more solid ground for many investigations of Luttinger liquids with open boundaries.
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