arXiv subjects

Fakher F. Assaad

Publications and source records attributed to Fakher F. Assaad.

At least 73 records · Page 4Linked to original sources

arXiv2021

Doping-induced quantum spin Hall insulator to superconductor transition

A unique property of a dynamically generated quantum spin Hall state are Goldstone modes that correspond to the long-wavelength fluctuations of the spin-orbit coupling order parameter whose topological Skyrmion excitations carry charge 2$e$. Within the model considered here, upon varying the chemical potential, we observe two transitions: An s-wave superconducting order parameter develops at a critical chemical potential $μ_{c1}$, corresponding to the excitation gap of pairs of fermions, and at $μ_{c2}$ the SO(3) order parameter of the quantum spin Hall state vanishes. Using negative-sign-free, large-scale quantum Monte Carlo simulations, we show that $μ_{c1}=μ_{c2}$ within our accuracy -- we can resolve dopings away from half filling down to $δ= 0.0017$. The length scale associated with the fluctuations of the quantum spin Hall order parameter grows down to our lowest doping, suggesting either a continuous or a weakly first-order transition. Contrary to mean-field expectations, the doping versus chemical potential curve is not linear, indicating a dynamical critical exponent $z > 2$ if the transition is continuous.

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arXiv2021

Gross-Neveu Heisenberg criticality: dynamical generation of quantum spin Hall masses

We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O(N) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of N such that in the large-N limit it is of particular importance to consider susceptibilities rather than equal time correlations so as to minimize contributions from the background. For the N=3 case, we obtain $1/ν=1.11(4)$, $η_ϕ=0.80(9)$, and $η_ψ=0.29(2)$ for respectively the correlation length exponent, bosonic and fermionic anomalous dimensions.

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arXiv2021

Local moments versus itinerant antiferromagnetism: magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model

Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain $t$ and interchain $t_{\perp}$ hopping amplitudes at half-filling. A fixed value of the next-nearest-neighbor hopping $t'=-t_{\perp}/2$ removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime $t_{\perp}/t\lesssim 0.3$ displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.

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arXiv2021

Quantum Monte Carlo Simulation of Generalized Kitaev Models

Frustrated spin systems generically suffer from the negative sign problem inherent to Monte Carlo methods. Since the severity of this problem is formulation dependent, optimization strategies can be put forward. We introduce a phase pinning approach in the realm of the auxiliary field quantum Monte Carlo algorithm. If we can find an anti-unitary operator that commutes with the one body Hamiltonian coupled to the auxiliary field, then the phase of the action is pinned to $0$ and $π$. For generalized Kitaev models, we can successfully apply this strategy and observe a remarkable improvement of the average sign. We use this method to study thermodynamical and dynamical properties of the Kitaev-Heisenberg model down to temperatures corresponding to half of the exchange coupling constant. Our dynamical data reveals finite temperature properties of ordered and spin-liquid phases inherent to this model.

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arXiv2021

Fermi-surface reconstruction without symmetry breaking

We present a sign-problem free quantum Monte Carlo study of a model that exhibits quantum phase transitions without symmetry breaking and associated changes in the size of the Fermi surface. The model is an Ising gauge theory on the square lattice coupled to an Ising matter field and spinful `orthogonal' fermions at half-filling, both carrying Ising gauge charges. In contrast to previous studies, our model hosts an electron-like, gauge-neutral fermion excitation providing access to Fermi liquid phases. One of the phases of the model is a previously studied orthogonal semi-metal, which has $\mathbb{Z}_2$ topological order, and Luttinger-volume violating Fermi points with gapless orthogonal fermion excitations. We elucidate the global phase diagram of the model: along with a conventional Fermi liquid phase with a large Luttinger-volume Fermi surface, we also find a `deconfined' Fermi liquid in which the large Fermi surface co-exists with fractionalized excitations. We present results for the electron spectral function, showing its evolution from the orthogonal semi-metal with a spectral weight near momenta $\{\pm π/2, \pm π/2\}$, to a large Fermi surface.

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arXiv2020

Kondo breakdown in a spin-1/2 chain of adatoms on a Dirac semimetal

We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the \textit{decoupled} fixed-point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.

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arXiv2020

Topological terms on topological defects: a quantum Monte Carlo study

Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekulé valence-bond solid (KVBS) masses map onto a field theory with a topological $θ$-term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $θ$-term implies that a domain wall of the Z$_2$ KVBS order parameter harbors a spin-$1/2$ Heisenberg chain, as described by a $1+1$ dimensional SO(3) non-linear sigma model with $θ$-term at $θ= π$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1/2$ chain at the Z$_2$ topological defect. This concept can be generalized to higher dimensions where $2+1$ dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.

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arXiv2020

Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term

We use the half-filled zeroth Landau level in graphene as a regularization scheme to study the physics of the SO(5) non-linear sigma model subject to a Wess-Zumino-Witten topological term in 2+1 dimensions. As shown by Ippoliti et al. [PRB 98, 235108 (2019)], this approach allows for negative sign free auxiliary field quantum Monte Carlo simulations. The model has a single free parameter, $U_0$, that monitors the stiffness. Within the parameter range accessible to negative sign free simulations, we observe an ordered phase in the large $U_0$ or stiff limit. Remarkably, upon reducing $U_0$ the magnetization drops substantially, and the correlation length exceeds our biggest system sizes, accommodating 100 flux quanta. The implications of our results for deconfined quantum phase transitions between valence bond solids and anti-ferromagnets are discussed.

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arXiv2020

The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations

We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition between a Dirac semi-metal and the antiferromagnetic insulator. The aim of this article is to provide a detailed comparison between these approaches by computing static properties, notably ground-state energy, single-particle gap, double occupancy, and staggered magnetization, as well as dynamical quantities such as the single-particle spectral function. At the static mean-field level local moments cannot be generated without breaking the SU(2) spin symmetry. The DMFT approximation accounts for temporal fluctuations, thus captures both the evolution of the double occupancy and the resulting local moment formation in the paramagnetic phase. As a consequence, the DMFT approximation is found to be very accurate in the Dirac semi-metallic phase where local moment formation is present and the spin correlation length small. However, in the vicinity of the fermion quantum critical point the spin correlation length diverges and the spontaneous SU(2) symmetry breaking leads to low-lying Goldstone modes in the magnetically ordered phase. The impact of these spin fluctuations on the single-particle spectral function -- \textit{waterfall} features and narrow spin-polaron bands -- is only visible in the lattice QMC approach.

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arXiv2020

Phase diagram and dynamics of the SU($\boldsymbol N$) symmetric Kondo lattice model

In heavy-fermion systems, the competition between the local Kondo physics and intersite magnetic fluctuations results in unconventional quantum critical phenomena which are frequently addressed within the Kondo lattice model (KLM). Here we study this interplay in the SU($N$) symmetric generalization of the two-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ up to 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spin systems typically gives way to spin-singlet ground states with spontaneously broken lattice symmetry, we find that the SU($N$) KLM is unique in that for each finite $N$ its ground-state phase diagram hosts only two phases -- AF order and the Kondo-screened phase. The absence of any intermediate phase between the $N=2$ and large-$N$ cases establishes adiabatic correspondence between both limits and confirms that the large-$N$ theory is a correct saddle point of the KLM fermionic path integral and a good starting point to include quantum fluctuations. In addition, we determine the evolution of the single-particle gap, quasiparticle residue of the doped hole at momentum $(π,π)$, and spin gap across the magnetic order-disorder transition. Our results indicate that increasing $N$ modifies the behavior of the coherence temperature: while it evolves smoothly across the magnetic transition at $N=2$ it develops an abrupt jump -- of up to an order of magnitude -- at larger but finite $N$. We discuss the magnetic order-disorder transition from a quantum-field-theoretic perspective and comment on implications of our findings for the interpretation of experiments on quantum critical heavy-fermion compounds.

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arXiv2020

Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation

The magnetic properties of graphene on finite geometries are studied using a self-consistent mean-field theory of the Hubbard model. This approach is known to predict ferromagnetic edge states close to the zig-zag edges in single-layer graphene quantum dots and nanoribbons. In order to assess the accuracy of this method, we perform complementary exact diagonalization and quantum Monte Carlo simulations. We observe good quantitative agreement for all quantities investigated provided that the Coulomb interaction is not too strong.

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arXiv2019

A search for correlation-induced adiabatic paths between distinct topological insulators

Correlations in topological states of matter provide a rich phenomenology, including a reduction in the topological classification of the interacting system compared to its non-interacting counterpart. This happens when two phases that are topologically distinct on the non-interacting level become adiabatically connected once interactions are included. We use a quantum Monte Carlo method to study such a reduction. We consider a 2D charge-conserving analog of the Levin-Gu superconductor whose classification is reduced from $\mathbb{Z}$ to $\mathbb{Z}_4$. We may expect any symmetry-preserving interaction that leads to a symmetric gapped ground state at strong coupling, and consequently a gapped symmetric surface, to be sufficient for such reduction. Here, we provide a counter example by considering an interaction which (i) leads to a symmetric gapped ground state at sufficient strength and (ii) does not allow for any adiabatic path connecting the trivial phase to the topological phase with $w=4$. The latter is established by numerically mapping the phase diagram as a function of the interaction strength and a parameter tuning the topological invariant. Instead of the adiabatic connection, the system exhibits an extended region of spontaneous symmetry breaking separating the topological sectors. Frustration reduces the size of this long-range ordered region until it gives way to a first order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free fermion states into each other. We conclude that an interaction which trivializes the surface of a gapped topological phase is necessary but not sufficient to establish an adiabatic path within the reduced classification. In other words, the class of interactions which trivializes the surface is different from the class which establishes an adiabatic connection in the bulk.

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arXiv2019

Orthogonal metal in the Hubbard model with liberated slave spins

A two-dimensional Falicov-Kimball model, equivalent to the Hubbard model in an unconstrained slave-spin representation, is studied by quantum Monte Carlo simulations. The focus is on a fractionalized metallic phase that is characterized in terms of spectral, thermodynamic, and transport properties, including a comparison to the half-filled Hubbard model. The properties of this phase, most notably a single-particle gap but gapless spin and charge excitations, can in principle be understood in the framework of orthogonal metals. However, important and interesting differences arise in the present setting compared to single-particle mean-field theories and other models. We also discuss the role of the local constraints from the slave-spin representation within an extended phase diagram that includes the spatial dimension as a parameter, thereby making contact with previous work in infinite dimensions. Finally, we highlight the absence of $π$-flux configurations in the slave-spin formulation, in particular in the context of topologically ordered fractional phases predicted at the mean-field level.

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arXiv2019

Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory

Using linear flavor-wave theory (LFWT) and auxiliary field quantum Monte Carlo (QMC), we investigate the properties of the SU(4) Heisenberg model on the anisotropic square lattice in the fully antisymmetric six-dimensional irreducible representation, a model that describes interacting fermions with four flavors at half-filling. Thanks to the calculations on very large systems, we have been able to convincingly demonstrate that QMC results are consistent with a small but finite antiferromagnetic moment at the isotropic point, in qualitative agreement with LFWT obtained earlier [F. H. Kim {\it{et al.}}, Phys. Rev. B {\bf 96}, 205142 (2017)], and in quantitative agreement with results obtained previously on the Hubbard model [D. Wang {\it{et al.}}, Phys. Rev. Lett. {\bf 112}, 156403 (2014)] after extrapolation to infinite $U/t$. The presence of a long-range antiferromagnetic order has been further confirmed by showing that a phase transition takes place into a valence-bond solid (VBS) phase not too far from the isotropic point when reducing the coupling constant along one direction on the way to decoupled chains.

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arXiv2019

Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions

Recent experimental and numerical evidence suggest an intriguing universal relationship between the Fermi surface anisotropy of the non-interacting parent two-dimensional electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filing. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed non-perturbative and numerically-exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the half-filled composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual HLR state. The importance of the long-range interaction, expected for Dirac systems, is also consistent with recent transport measurements. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators organic conductors, and magic-angle twisted bilayer graphene.

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arXiv2019

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are an incarnation of exotic states of matter, $i.e.$ the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, $N_f = 4$, our data suggests a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

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arXiv2019

Mutual information in heavy-fermion systems

A key notion in heavy-fermion systems is the entanglement between conduction electrons and localized spin degrees of freedom. To study these systems from this point of view, we compute the mutual information in a ferromagnetic and antiferromagnetic Kondo lattice model in the presence of geometrical frustration. Here the interplay between the Kondo effect, the Ruderman-Kittel-Kasuya-Yosida interaction, and geometrical frustration leads to partial Kondo screened, conventional Kondo insulating, and antiferromagnetic phases. In each of these states the mutual information follows an area law, the coefficient of which shows sharp crossovers (on our finite lattices) across phase transitions. Deep in the respective phases, the area law coefficient can be understood in terms of simple direct product wave functions thereby yielding an accurate measure of the entanglement in each phase. The above-mentioned results stem from approximation-free auxiliary field quantum Monte Carlo simulations.

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arXiv2019

Entanglement studies of interacting fermionic models

Recent advances in the field of strongly correlated electron systems allow to access the entanglement properties of interacting fermionic models, by means of Monte Carlo simulations. We briefly review the techniques used in this context to determine the entanglement entropies and correlations of the entanglement Hamiltonian. We further apply these methods to compute the spin two-point function of entanglement Hamiltonian for a stripe embedded into a correlated topological insulator. Further we discuss a recent method that allows an unbiased, numerically exact, direct determination of the entanglement Hamiltonian by means of auxiliary field quantum Monte Carlo simulations.

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