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Fakher Assaad

Publications and source records attributed to Fakher Assaad.

13 recordsLinked to original sources
arXiv2026

Analytic continuation of Green's functions with a neural network

An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic kernel diverges exponentially for large frequencies, numerical noise generically causes instabilities. We use a convolutional neural network to obtain the spectral density for a given imaginary time Green's function. The network is trained by data which we generate using random Gaussians. We improve the training data set available by including collision centers for the Gaussians rather than employing uniformly distributed Gaussians. Our network is constructed in such a way that its output fulfills positive semidefiniteness. We compare the results of our network with results of the Maximum Entropy method (MaxEnt), a standard method for the same reconstruction problem for the spectral density. This comparison is performed for three different cases, namely our Gaussian based test data as well as two physical models, the 1d Hubbard model showing spin-charge separation, and the two-dimensional SSH model in the self-consistent Born approximation. We find that the network outperforms MaxEnt when presented data close to the training set. For the physical models considered, MaxEnt recognizes physical features more precisely as compared to our network prediction. While it is hard to improve MaxEnt, the quality of the network depends on the training data set which can be systematically enhanced and improved.

cond-mat.str-el↗
arXiv2025

Two-site entanglement in the two-dimensional Hubbard model

The study of entanglement in strongly correlated electron systems typically requires knowledge of the reduced density matrix. Here, we apply the parquet dynamical vertex approximation to study the two-site reduced density matrix at varying distance, in the Hubbard model at weak coupling. This allows us to investigate the spatial structure of entanglement in dependence of interaction strength, electron filling, and temperature. We compare results from different entanglement measures, and benchmark against quantum Monte Carlo.

cond-mat.str-el↗
arXiv2024

Hydrodynamics of particle-hole symmetric systems: a quantum Monte Carlo study

The emergence of hydrodynamic behavior in electronic flow within clean, particle-hole-symmetric systems at half-filling is a non-trivial problem. Navier-Stokes (NS) equations describe the momentum flow, while experimental measurements typically capture the current flow profiles. However, in particle-hole-symmetric systems, electric current and momentum flow are entirely decoupled because electrons and holes move in opposite directions with equal distribution functions. This makes it challenging to link NS equations to observed flow patterns. In this work, we demonstrate that the hydrodynamic behavior of the charge current at half filling can emerge despite the absence of momentum flow. By combining Boltzmann transport theory with numerically exact Quantum Monte Carlo simulations of clean graphene samples, we show that NS-type equations can be derived directly for the charge current, eliminating the need for any additional mechanism coupling the velocity field and charge current in explaining the experimentally observed hydrodynamic flow profiles in graphene at half-filling. We show that a new transport quantity - the current diffusion coefficient - replaces viscosity and expect this description to be valid for any particle-hole symmetric system. Our results provide new insights into the interpretation of experimental data and demonstrate how Quantum Monte Carlo calculations can serve as an alternative to experiments in transport measurements to verify the kinetic theory results.

cond-mat.mes-hall↗
arXiv2023

Flat band projections: Sign problem mapping for frustrated spin systems

Projection of the Coulomb potential onto flat bands paves the way to design various interactions in the particle-hole and particle-particle channels. Here we pose the question if we can use this mapping to overcome the negative sign problem for the simplest possible frustrated spin system consisting a trimer of spins-1/2 coupled with an antiferromagnetic exchange interaction. While the answer is negative, we show that we can map the sign problem for frustrated spin systems onto a problem where we need to simulate particle-hole symmetric systems but with long-ranged Coulomb interactions prevailing over short-ranged ones. While the latter systems are currently not accessible to auxiliary field determinant quantum Monte Carlo, this mapping motivates algorithmic development that may overcome this issue.

cond-mat.str-el↗
arXiv2022

Validity of SLAC fermions for the (1 + 1)-dimensional 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 that is expected to realize a U(1) helical Luttinger liquid in a naive continuum limit. 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 on interactions non-locality invalidates the Mermin-Wagner theorem and allows for long ranged magnetic ordering. In fact, in the strong coupling limit the model maps onto an XXZ-spin chain with $1/r^2$ exchange. Here, both spin-wave and DMRG calculations support long ranged order. While the long-ranged order opens a single particle gap the Dirac point, the singularity at the zone-boundary persists for any finite value of the interaction strength such that the ground state remains metallic. Hence, SLAC Hamiltonian does not flow to the $1$d helical Luttinger liquid fixed point. Aside from DMRG simulations, we have used auxiliary field quantum Monte Carlo simulations to arrive to the above conclusions.

cond-mat.str-el↗
arXiv2022

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.

cond-mat.str-el↗
arXiv2022

Instanton gas approach to the Hubbard model

In this article we consider a path integral formulation of the Hubbard model based on a SU(2)-symmetrical Hubbard-Stratonovich transformation that couples auxiliary field to the local electronic density. This decoupling is known to have a regular saddle-point structure: each saddle point is a set of elementary field configurations localized in space and imaginary time which we coin instantons. We formulate a classical partition function for the instanton gas that has predictive power. Namely, we can predict the distribution of instantons and show that the instanton number is sharply defined in the thermodynamic limit, thus defining a unique dominant saddle point. Despite the fact that the instanton approach does not capture the magnetic transition inherent to the Hubbard model on the honeycomb lattice, we were able to describe the local moment formation accompanied by short-ranged anti-ferromagnetic correlations. This aspect is also seen in the single particle spectral function that shows clear signs of the upper and lower Hubbard bands. Our instanton approach bears remarkable similarities to local dynamical approaches, such as dynamical mean field theory, in the sense that it has the unique property of allowing for local moment formation without breaking the SU(2) spin symmetry. In contrast to local approaches, it captures short-ranged magnetic fluctuations. Furthermore, it also offers possibilities for systematic improvements by taking into account fluctuations around the dominant saddle point. Finally, we show that the saddle point structure depends upon the choice of lattice geometry. For the square lattice at half-filling, the saddle point structure reflects the itinerant to localized nature of the magnetism as a function of the coupling strength. The implications of our results for Lefschetz thimbles approaches to alleviate the sign problem are also discussed.

cond-mat.str-el↗
arXiv2021

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.

cond-mat.str-el↗
arXiv2019

Exploring the Kondo effect of an extended impurity with chains of Co adatoms in a magnetic field

Motivated by recent STM experiments, we explore the magnetic field induced Kondo effect that takes place at symmetry protected level crossings in finite Co adatom chains. We argue that the effective two-level system realized at a level crossing acts as an extended impurity coupled to the conduction electrons of the substrate by a distribution of Kondo couplings at the sites of the chain. Using auxiliary-field quantum Monte Carlo simulations, which quantitatively reproduce the field dependence of the zero-bias signal, we show that a proper Kondo resonance is present at the sites where the effective Kondo coupling dominates. Our modeling and numerical simulations provide a theoretical basis for the interpretation of the STM spectrum in terms of level crossings of the Co adatom chains.

cond-mat.str-el↗
arXiv2016

Coexistence of charge and ferromagnetic order in fcc Fe

Phase coexistence phenomena have been intensively studied in strongly correlated materials where several ordered states simultaneously occur or compete. Material properties critically depend on external parameters and boundary conditions, where tiny changes result in qualitatively different ground states. However, up to date, phase coexistence phenomena have exclusively been reported for complex compounds composed of multiple elements. Here we show that charge- and magnetically ordered states coexist in double-layer Fe on Rh(001). Scanning tunneling microscopy and spectroscopy measurements reveal periodic charge order stripes below a temperature of 130 K. Close to liquid helium temperature, they are superimposed by ferromagnetic domains as observed by spin-polarized scanning tunneling microscopy. Temperature-dependent measurements reveal a pronounced cross-talk between charge and spin order at the ferromagnetic ordering temperature about 70 K, which is successfully modeled within an effective Landau theory including sixth-order terms. Our results show that subtle balance between structural modifications can lead to competing ordering phenomena.

cond-mat.mtrl-sci↗
arXiv2014

Optical conductivity of topological Kondo insulating states

Using real-space dynamical mean field quantum Monte Carlo simulations, we study the optical conductivity of two-dimensional topological Kondo insulating states. We consider model parameters which allow us to consider mixed valence and local moment regimes. The real space resolution inherent to our approach reveals a renormalization of the hybridization gap as one approaches the edge. Low energy transport is dominated by the helical edge state and the corresponding Drude weight scales as the coherence scale of the heavy fermion state. The concomitant renormalization of the edge state velocity leads to a constant edge local density of states. We discuss the implication of our results for the three dimensional case.

cond-mat.str-el↗
arXiv2012

Periodic Anderson model with electron-phonon correlated conduction band

This paper reports dynamical mean field calculations for the periodic Anderson model in which the conduction band is coupled to phonons. Motivated in part by recent attention to the role of phonons in the $γ$-$α$ transition in Ce, this model yields a rich and unexpected phase diagram which is of intrinsic interest. Specifically, above a critical value of the electron-phonon interaction, a first order transition with two coexisting phases develops in the temperature-hybridization plane, which terminates at a second order critical point. The coexisting phases display the familiar Kondo screened and local moment character, yet they also exhibit pronounced polaronic and bipolaronic properties, respectively.

cond-mat.str-el↗