Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions

We show that the two recently proposed methods to compute Renyi entanglement entropies in the realm of determinant quantum Monte Carlo methods for fermions are in principle equivalent, but differ in sampling strategies. The analogy allows to formulate a numerically stable calculation of the entanglement spectrum at strong coupling. We demonstrate the approach by studying static and dynamical properties of the entanglement hamiltonian across the interaction driven quantum phase transition between a topological insulator and quantum antiferromagnet in the Kane-Mele Hubbard model. The formulation is not limited to fermion systems and can readily be adapted to world-line based simulations of bosonic systems.Comment: 8 pages, 5 figure

Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice

In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is {\it small}, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry breaking field, and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary field quantum Monte Carlo algorithm. With our enhanced resolution we find a direct and continuous quantum phase transition between the semi-metallic and the insulating antiferromagnetic states with increase of the interaction. The single particle gap in units of the Hubbard $U$ tracks the staggered magnetization. An excellent data collapse is obtained by finite size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.Comment: 7 pages, 6 figures, Published versio

Metamagnetism and Lifshitz Transitions in Models for Heavy Fermions

We investigate metamagnetic transitions in models for heavy fermions by considering the doped Kondo lattice model in two dimensions. Results are obtained within the framework of dynamical mean field and dynamical cluster approximations. Universal magnetization curves for different temperatures and Kondo couplings develop upon scaling with the lattice coherence temperature. Furthermore, the coupling of the local moments to the magnetic field is varied to take into account the different Land\'e factors of localized and itinerant electrons. The competition between the lattice coherence scale and the Zeeman energy scale allows for two interpretations of the metamagnetism in heavy fermions: Kondo breakdown or Lifshitz transitions. By tracking the single-particle residue through the transition, we can uniquely conclude in favor of the Lifshitz transition scenario. In this scenario, a quasiparticle band drops below the Fermi energy which leads to a change in topology of the Fermi surface.Comment: 8 pages, 7 figure

Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing "photon" of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.Comment: 16 pages, 7 figures, published versio