arXiv subjects

F. F. Assaad

Publications and source records attributed to F. F. Assaad.

At least 19 recordsLinked to original sources

arXiv2023

Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions

The absence of screening of the non-local Coulomb interaction in Dirac systems at charge neutrality leads to the breakdown of the Fermi liquid and divergence of the Fermi velocity. On the other hand, Mott Hubbard physics and the concomitant formation of local moments is dominated by the local effective Hubbard interaction. Using quantum Monte Carlo methods combined with stochastic analytical continuation, we compute the single particle spectral function of fermions on the honeycomb lattice for a realistic interaction that includes both the Hubbard interaction and long-ranged Coulomb repulsion. To a first approximation, we find that the generic high-energy features such as the formation of the upper Hubbard band are independent of the long-ranged Coulomb repulsion and determined mostly by the local effective Hubbard interaction. The sub-leading effects of adding the long-range interaction include an enhancement of the bandwidth and a decrease of the spin-polaron quasi-particle weight and lifetime.

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arXiv2020

The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code

The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as $Z_2$ unconstrained lattice gauge theories coupled to fermionic and $Z_2$ matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.4 and sign in to file issues.

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arXiv2020

Coexistence and interaction of spinons and magnons in an antiferromagnet with alternating antiferromagnetic and ferromagnetic quantum spin chains

In conventional quasi-one-dimensional antiferromagnets with quantum spins, magnetic excitations are carried by either magnons or spinons in different energy regimes: they do not coexist independently, nor could they interact with each other. In this Letter, by combining inelastic neutron scattering, quantum Monte Carlo simulations and Random Phase Approximation calculations, we report the discovery and discuss the physics of the coexistence of magnons and spinons and their interactions in Botallackite-Cu2(OH)3Br. This is a unique quantum antiferromagnet consisting of alternating ferromagnetic and antiferromagnetic Spin-1/2 chains with weak inter-chain couplings. Our study presents a new paradigm where one can study the interaction between two different types of magnetic quasiparticles, magnons and spinons.

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arXiv2020

Response to Comment on "The role of electron-electron interactions in two-dimensional Dirac fermions"

Hesselmann {\it et al}.~question one of our conclusions, namely, the suppression of Fermi velocity at the Gross-Neveu critical point for the specific case of vanishing long-range interactions and at zero energy. The possibility they raise could occur in any finite-size extrapolation of numerical data. While we cannot definitively rule out this possibility, we provide mathematical bounds on its likelihood.

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arXiv2018

The role of electron-electron interactions in two-dimensional Dirac fermions

The role of electron-electron interactions on two-dimensional Dirac fermions remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. Most interestingly, experimental realizations of Dirac fermions span the crossover between these two regimes providing the physical mechanism that masks this velocity divergence. We explain several long-standing mysteries including why the observed Fermi velocity in graphene is consistently about 20 percent larger than the best values calculated using ab initio and why graphene on different substrates show different behavior.

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arXiv2017

Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions

Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo (QMC) simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.

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arXiv2016

A simple fermionic model of deconfined phases and phase transitions

Using Quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with $N$ flavors of fermions per site for $N=1,2$ and $3$. The models have an extensive number of conserved quantities but are not integrable, and have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond Landau-Ginzburg paradigm. In particular, one of the prominent phase for $N>1$ corresponds to $2N$ gapless Dirac fermions coupled to an emergent $\mathbb{Z}_2$ gauge field in its deconfined phase. However, unlike a conventional $\mathbb{Z}_2$ gauge theory, we do not impose the `Gauss's Law' by hand and instead, it emerges due to spontaneous symmetry breaking. Correspondingly, unlike a conventional $\mathbb{Z}_2$ gauge theory in two spatial dimensions, our models have a finite temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short range entangled phase, which corresponds to Néel/Superconductor for $N=2$ and a Valence Bond Solid for $N=3$. Furthermore, for $N=3$, the Valence Bond Solid further undergoes a transition to a Néel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.

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arXiv2015

Finite-size effects in Luther-Emery phases of Holstein and Hubbard models

The one-dimensional Holstein model and its generalizations have been studied extensively to understand the effects of electron-phonon interaction. The half-filled case is of particular interest, as it describes a transition from a metallic phase with a spin gap due to attractive backscattering to a Peierls insulator with charge-density-wave (CDW) order. Our quantum Monte Carlo results support the existence of a metallic phase with dominant power-law charge correlations, as described by the Luther-Emery fixed point. We demonstrate that for Holstein and also for purely fermionic models the spin gap significantly complicates finite-size numerical studies, and explains inconsistent previous results for Luttinger parameters and phase boundaries. On the other hand, no such complications arise in spinless models. The correct low-energy theory of the spinful Holstein model is argued to be that of singlet bipolarons with a repulsive, mutual interaction. This picture naturally explains the existence of a metallic phase, but also implies that gapless Luttinger liquid theory is not applicable.

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arXiv2015

Interaction driven metal-insulator transition in strained graphene

The question of whether electron-electron interactions can drive a metal to insulator transition in graphene under realistic experimental conditions is addressed. Using three representative methods to calculate the effective long-range Coulomb interaction between $π$-electrons in graphene and solving for the ground state using quantum Monte Carlo methods, we argue that without strain, graphene remains metallic and changing the substrate from SiO$_2$ to suspended samples hardly makes any difference. In contrast, applying a rather large -- but experimentally realistic -- uniform and isotropic strain of about $15\%$ seems to be a promising route to making graphene an antiferromagnetic Mott insulator.

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arXiv2015

Dynamical structure factors and excitation modes of the bilayer Heisenberg model

Using quantum Monte Carlo simulations along with higher-order spin-wave theory, bond-operator and strong-coupling expansions, we analyse the dynamical spin structure factor of the spin-half Heisenberg model on the square-lattice bilayer. We identify distinct contributions from the low-energy Goldstone modes in the magnetically ordered phase and the gapped triplon modes in the quantum disordered phase. In the antisymmetric (with respect to layer inversion) channel, the dynamical spin structure factor exhibits a continuous evolution of spectral features across the quantum phase transition, connecting the two types of modes. Instead, in the symmetric channel we find a depletion of the spectral weight when moving from the ordered to the disordered phase. While the dynamical spin structure factor does not exhibit a well-defined distinct contribution from the amplitude (or Higgs) mode in the ordered phase, we identify an only marginally-damped amplitude mode in the dynamical singlet structure factor, obtained from interlayer bond correlations, in the vicinity of the quantum critical point. These findings provide quantitative information in direct relation to possible neutron or light scattering experiments in a fundamental two-dimensional quantum-critical spin system.

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arXiv2014

Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices

We study the half-filled Hubbard model on a one-parameter family of vortex-full square lattices ranging from the isotropic case to weakly coupled Hubbard dimers. The ground-state phase diagram consists of four phases: A semi-metal and a band insulator which are connected to the weak-coupling limit, and a magnetically ordered Néel phase and a valence bond crystal (VBC) which are linked to the strong-coupling Mott limit. The phase diagram is obained by quantum Monte Carlo (QMC) and continuous unitary transformations (CUTs). The CUT is performed in a two-step process: Non-perturbative graph-based CUTs are used in the Mott insulating phase to integrate out charge fluctuations. The resulting effective spin model is tackled by perturbative CUTs about the isolated dimer limit yielding the breakdown of the VBC by triplon condensation. We find three scenarios when varying the interaction for a fixed anisotropy of hopping amplitudes: i) one direct phase transition from Néel to semi-metal, ii) two phase transitions VBC to Néel and Néel to semi-metal, or iii) a smooth crossover from VBC to the band insultor. Our results are consistent with the absence of spin-liquid phases in the whole phase diagram.

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arXiv2014

Phase diagram of the Kane-Mele-Coulomb model

We determine the phase diagram of the Kane-Mele model with a long-range Coulomb interaction using an exact quantum Monte Carlo method. Long-range interactions are expected to play a role in honeycomb materials because the vanishing density of states in the semimetallic weak-coupling phase suppresses screening. According to our results, the Kane-Mele-Coulomb model supports the same phases as the Kane-Mele-Hubbard model. The nonlocal part of the interaction promotes short-range sublattice charge fluctuations, which compete with antiferromagnetic order driven by the onsite repulsion. Consequently, the critical interaction for the magnetic transition is significantly larger than for the purely local Hubbard repulsion. Our numerical data are consistent with $SU(2)$ Gross-Neveu universality for the semimetal to antiferromagnet transition, and with 3D XY universality for the quantum spin Hall to antiferromagnet transition.

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arXiv2013

Correlation effects in two-dimensional topological insulators

Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.

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arXiv2013

Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators

The adiabatic insertion of a πflux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that πfluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z_2 topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a πflux gives rise to a Kramers doublet of spinon states with a Curie law signature in the magnetic susceptibility. Electronic correlations also provide a bosonic mode of magnetic excitons with tunable energy that act as exchange particles and mediate a dynamical interaction of adjustable range and strength between spinons. πfluxes can therefore be used to build models of interacting spins. This idea is applied to a three-spin ring and to one-dimensional spin chains. Due to the freedom to create almost arbitrary spin lattices, correlated topological insulators with πfluxes represent a novel kind of quantum simulator potentially useful for numerical simulations and experiments.

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arXiv2012

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 Landé 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.

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arXiv2012

Quantum phase transitions in the Kane-Mele-Hubbard model

We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard U is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.

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arXiv2012

Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges

We investigate electronic correlation effects on edge states of quantum spin-Hall insulators within the Kane-Mele-Hubbard model by means of quantum Monte Carlo simulations. Given the U(1) spin symmetry and time-reversal invariance, the low-energy theory is the helical Tomanaga-Luttinger model, with forward scattering only. For weak to intermediate interactions, this model correctly describes equal-time spin and charge correlations, including their doping dependence. As apparent from the Drude weight, bulk states become relevant in the presence of electron-electron interactions, rendering the forward-scattering model incomplete. Strong correlations give rise to slowly decaying transverse spin fluctuations, and inelastic spin-flip scattering strongly modifies the single-particle spectrum, leading to graphene-like edge state signatures. The helical Tomanaga-Luttinger model is completely valid only asymptotically in the weak-coupling limit.

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arXiv2011

Coherent heavy quasiparticles in CePt5 surface alloy

We report on the results of a high-resolution angle-resolved photoemission (ARPES) study on the ordered surface alloy CePt5. The temperature dependence of the spectra show the formation of the coherent low-energy heavy-fermion band near the Fermi level. This experimental data is supported by a multi-band model calculation in the framework of the dynamical mean field theory (DMFT).

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