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Register a new userMonte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
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We report on Hybrid-Monte-Carlo simulations of the tight-binding model with long-range Coulomb interactions for the electronic properties of graphene. We investigate the spontaneous breaking of sublattice symmetry corresponding to a transition from the semimetal to an antiferromagnetic insulating phase. Our short-range interactions thereby include the partial screening due to electrons in higher energy states from ab initio calculations based on the constrained random phase approximation [T.O.Wehling {it et al.}, Phys.Rev.Lett.{bf 106}, 236805 (2011)]. In contrast to a similar previous Monte-Carlo study [M.V.Ulybyshev {it et al.}, Phys.Rev.Lett.{bf 111}, 056801 (2013)] we also include a phenomenological model which describes the transition to the unscreened bare Coulomb interactions of graphene at half filling in the long-wavelength limit. Our results show, however, that the critical coupling for the antiferromagnetic Mott transition is largely insensitive to the strength of these long-range Coulomb tails. They hence confirm the prediction that suspended graphene remains in the semimetal phase when a realistic static screening of the Coulomb interactions is included.
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In this work, results are presented of Hybrid-Monte-Carlo simulations of the tight-binding Hamiltonian of graphene, coupled to an instantaneous long-range two-body potential which is modeled by a Hubbard-Stratonovich auxiliary field. We present an investigation of the spontaneous breaking of the sublattice symmetry, which corresponds to a phase transition from a conducting to an insulating phase and which occurs when the effective fine-structure constant $alpha$ of the system crosses above a certain threshold $alpha_C$. Qualitative comparisons to earlier works on the subject (which used larger system sizes and higher statistics) are made and it is established that $alpha_C$ is of a plausible magnitude in our simulations. Also, we discuss differences between simulations using compact and non-compact variants of the Hubbard field and present a quantitative comparison of distinct discretization schemes of the Euclidean time-like dimension in the Fermion operator.
We present a method for direct hybrid Monte Carlo simulation of graphene on the hexagonal lattice. We compare the results of the simulation with exact results for a unit hexagonal cell system, where the Hamiltonian can be solved analytically.
We report on Hybrid-Monte-Carlo simulations at finite spin density of the $pi$-band electrons in monolayer graphene with realistic inter-electron 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 towards the formation of electronic ordered phases, which has been predicted by a variety of different theoretical approaches.
We study the properties of two electrons with Coulomb interactions in a tight-binding model of La-based cuprate superconductors. This tight-binding model is characterized by long-range hopping obtained previously by advanced quantum chemistry computations. We show analytically and numerically that the Coulomb repulsion leads to a formation of compact pairs propagating through the whole system. The mechanism of pair formation is related to the emergence of an effective narrow energy band for Coulomb electron pairs with conserved total pair energy and momentum. The dependence of the pair formation probability on an effective filling factor is obtained with a maximum around a filling factor of 20 (or 80) percent. The comparison with the case of the nearest neighbor tight-binding model shows that the long-range hopping provides an increase of the phase space volume with high pair formation probability. We conjecture that the Coulomb electron pairs discussed here may play a role in high temperature superconductivity.
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
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