Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements

We propose a method to mitigate heavy-tailed distributions in fermion Quantum Monte Carlo simulations originating from zeros of the fermion determinant. In this case the second moment of the observables might be not well defined, and we show that by merely changing the synchronization between local updates and computation of observables, one can reduce the prefactor of the heavy-tailed distribution, thus substantially suppressing statistical fluctuations of observables. We also show that the average, or the first moment, is well defined and hence is independent on our measuring scheme. The method is especially suitable for local observables similar to e.g. double occupancy, where the resulting speedup can reach two orders of magnitude. For observables, containing spatial correlators, the speedup is more moderate, but still ranges between five and ten. Our results are independent on the nature of the auxiliary field, discrete or continuous, and pave the way to improve measurement strategies for Hybrid Monte Carlo simulations.Comment: A proof for the independence of the mean value on the synchronization scheme is added. The style of the figures is update

On the validity of SLAC fermions for the 1+1D helical Luttinger liquid

The Nielson-Ninomiya theorem states that a chirally invariant free fermion lattice action, which is local, translation invariant, and real necessarily has fermion doubling. The SLAC approach gives up on locality and long range hopping leads to a linear dispersion with singularity at the zone boundary. We introduce a SLAC Hamiltonian formulation of the U(1) helical Luttinger liquid and compare our results to bosonization. We argue that non-locality and concomitant singularity at the zone edge has important implications. Large momentum transfers yield spurious features already in the non-interacting case. Upon switching interactions non-locality invalidates the Mermin-Wagner theorem and allows for long ranged magnetic ordering such that a single particle gap opens at the Dirac point. Nonetheless, since non-locality allows for charge fluctuations at any length scale, the ground state remains metallic. Hence, SLAC and bosonization results show marked differences already at intermediate coupling strengths

Bridging the gap between numerics and experiment in free standing graphene

We report results of large-scale quantum Monte Carlo (QMC) simulations of graphene. Using cutting-edge algorithmic improvements, we are able to consider spatial volumes, corresponding to 20808 electrons, that allow us to access energy scales of direct relevance to experiments. Using constrained random phase approximation (cRPA) estimates of short-ranged interactions combined with a Coulomb tail, we are able to successfully confront numerical and experimental estimates of the Fermi velocity renormalization. These results and their comparison with perturbation theory not only show the non-Fermi liquid character of graphene, but also prove the importance of lattice-scale physics and higher-order perturbative corrections beyond RPA for the quantitative description of the experimental data for the Fermi velocity renormalization in suspended graphene.Comment: Higher quality low temperature numerical data added, clear-cut suggestions for further experiment

Collective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model

In this article, we discuss the nontrivial collective charge excitations (plasmons) of the extended square lattice Hubbard model. Using a fully nonperturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly correlated phase. The momentum-resolved charge susceptibility also is computed on the basis of the Euclidean charge-density-density correlator. In agreement with previous extended dynamical mean-field theory studies, we find that, at high strength of the electron-electron interaction, the plasmon dispersion develops two branches

Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice

Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling. We determine the phase diagram in the space of on-site and nearest-neighbor couplings $U$ and $V$ in the region $V<U/3$, which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large $U$ for basically all $V$. Tracing the corresponding phase boundary from $V=0$ to the $V=U/3$ line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary. With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered. We also discuss several improvements of the HMC algorithm which are crucial to reach these conclusions, in particular the improved fermion action with exact sublattice symmetry and the complexification of the Hubbard-Stratonovich field to ensure the ergodicity of the algorithm

Interelectron interactions and the RKKY potential between H adatoms in graphene

We use first-principles quantum Monte Carlo simulations to study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between hydrogen adatoms attached to a graphene sheet. We find that the pairwise RKKY interactions at distances of a few lattice spacings are strongly affected by interelectron interactions, in particular, the potential barrier between widely separated adatoms and the dimer configuration becomes wider and thus harder to penetrate. We also point out that antiferrromagnetic and charge density wave orderings have very different effects on the RKKY interaction. Finally, we analyze the stability of several regular adatom superlattices with respect to small displacements of a single adatom, distinguishing the cases of adatoms which populate either both or only one sublattice of the graphene lattice

Hybrid Monte Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density

We report on Hybrid Monte Carlo simulations at finite spin density of the p-band electrons in monolayer graphene with realistic interelectron interactions. Unlike simulations at finite charge-carrier density, these are not affected by a fermion-sign problem. Our results are in qualitative agreement with an interaction-induced warping of the Fermi contours and a reduction of the bandwidth as observed in angle-resolved photoemission spectroscopy experiments on charge-doped graphene systems. Furthermore, we find evidence that the neck-disrupting Lifshitz transition, which occurs when the Fermi level traverses the van Hove singularity (VHS), becomes a true quantum phase transition due to interactions. This is in line with an instability of the VHS toward the formation of ordered electronic phases, which has been predicted by a variety of different theoretical approaches

Quantum phase transitions on the hexagonal lattice

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.Comment: Contributed to the 8th International Conference on New Frontiers in Physics (ICNFP 2019). Revised version, accepted for publicatio