arXiv subjects

Fakher F. Assaad

Publications and source records attributed to Fakher F. Assaad.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Monte Carlo studies of U(1) lattice gauge models of Kondo breakdown

In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. Motivated by this perspective, we study a minimal compact U(1) lattice gauge model describing a spin chain coupled to two-dimensional Dirac conduction electrons. The spin chain is described by fermionic partons carrying spin and U(1) gauge charge. The heavy-fermion quasiparticle is a bound state of a U(1) matter field carrying unit electric charge and U(1) gauge charge, and the fermionic parton. Using sign-problem-free determinant quantum Monte Carlo simulations, we identify two symmetry-equivalent regimes: a heavy-fermion metal with a sharp composite-fermion resonance and robust low-frequency transport, and a Kondo-breakdown metal with an incoherent resonance and vanishing low-frequency transport. For any finite lattice extent in the direction perpendicular to the chain, the Luttinger volume of the heavy-fermion phase counts both composite and conduction electrons, while in the Kondo-breakdown phase it counts only the conduction electrons. The evolution of the composite-fermion spectrum, dynamical spin structure factor, and optical conductivity provides a nonperturbative demonstration of gauge-mediated Kondo breakdown and establishes transport fingerprints of an orbital-selective Mott transition in the context of U(1) gauge theories of heavy fermions.

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arXiv2026

Strain-Tuned Incommensurate Kekulé Spiral Order in Twisted Bilayer Graphene: a Quantum Many-Body Study

The physics of twisted bilayer graphene away from the exactly solvable chiral limit and the quantum Monte Carlo sign-problem-free charge neutrality point is elusive due to the exponential increase in the computational complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factor $ν=\pm2$ and address the question of the strain dependence of the interacting ground state by approximate quantum Monte Carlo (AQMC), state-of-the-art exact diagonalization (ED) and Hartree-Fock (HF) mean field, in order to investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekulé spiral (IKS) state. While all three methods capture the KIVC order, only ED and HF detect the weaker IKS order that AQMC does not capture adequately. As the AQMC is still capable of capturing stronger orders like the KIVC, our combined protocol may open the door for further understanding of the rich phases of twisted bilayer graphene and other strongly-correlated systems.

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arXiv2026

Numerical evidence of a critical point in the (2+1)D SO(5) nonlinear sigma model with Wess-Zumino-Witten term

We develop an optimized continuous-field quantum Monte Carlo (QMC) algorithm to investigate the projected SO(5) nonlinear sigma model with a Wess-Zumino-Witten term, which describes half-filled Dirac fermions in 2+1 space-time dimensions akin to graphene and Yukawa coupled to a quintuplet of compatible mass terms. Our algorithm reduces the computational complexity to $O(βN_{\mathbf{q}} N_ϕ^2)$, yielding a speedup of a factor of $N_ϕ$ (the number of magnetic fluxes, i.e., system size) relative to prior works [1-4]. This advance enables us to simulate system sizes up to $N_ϕ=140$ on the torus and $N_ϕ=59$ on the sphere, far exceeding the maximum sizes previously accessed, and to map out the universal phase diagram of the model on both geometries. Most notably, we identify and characterize a critical point that separates an SO(5)-broken ordered phase at small coupling from an SO(5)-symmetric disordered phase at large coupling. The critical point becomes multicritical upon the inclusion of terms that break the SO(5) symmetry down to $\mathrm{U}(1) \times \mathrm{SU}(2)$, relevant for the deconfined phase transition between Néel antiferromagnetic and valence-bond-solid orders in quantum magnets. Our finding of a multicritical point in the phase diagram of the SO(5) nonlinear sigma model with Wess-Zumino-Witten term resolves the long-standing open question of its global structure, and our QMC algorithm opens a new avenue for systematic studies of projected Hamiltonians, ranging from correlated flat bands to fractional quantum (anomalous) Hall systems.

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arXiv2026

Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet

Low dimensionality enhances quantum fluctuations, triggering novel states of quantum matter to emerge. In real materials, low dimensionality usually arises from spatially strongly anisotropic couplings. Here, we demonstrate a different mechanism: in two-dimensional systems with coupled alternating ferromagnetic (FM) and antiferromagnetic (AFM) spin-$1/2$ chains, an applied magnetic field may drive a dimensional reduction. Under magnetic field, the FM chains polarize and stiffen, suppressing the propagation of transverse AFM fluctuations from one chain to another, and effectively induce one-dimensional behavior at low energies. For a model describing botallackite, Cu$_2$(OH)$_3$Br, quantum Monte Carlo dynamics show that beyond a critical magnetic field, the low-energy spectrum reduces to that of a one-dimensional AFM Heisenberg spin-$1/2$ chain with field-dependent incommensurate two-spinon fluctuations, providing clear signatures for inelastic neutron scattering.

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arXiv2026

Thermalization Dynamics in the Two-Dimensional Hubbard Model with Neural-Network Quantum States

Thermalization in strongly correlated fermionic systems remains a central open problem in quantum many-body physics. In this work, we investigate the real-time dynamics and the approach to thermalization in the two-dimensional Hubbard model, a paradigmatic framework for correlated electrons, relevant to high-temperature superconductivity and ultracold quantum simulation. Focusing on the half-filled square lattice, we monitor the time evolution of the double occupancy following a quench in the on-site interaction $U$, and assess whether its long-time value is captured by a canonical thermal ensemble. We employ time-dependent variational Monte Carlo methods combined with transformer-based Neural-Network Quantum States to accurately describe the nonequilibrium dynamics of fermions, especially for the behavior at long times, thereby accessing regimes that were previously inaccessible to numerical simulations. Our results reveal two dynamical behaviors: for weak to intermediate interactions, the double occupancy rapidly approaches the thermal prediction, consistent with ergodic evolution; beyond a critical interaction $U_{C}$, the dynamics remains distinct from the thermal expectation on the timescales investigated, revealing signatures of a prethermal plateau delaying fast relaxation. These results establish numerical simulation as a powerful tool to probe nonequilibrium quantum phenomena in correlated fermionic matter.

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arXiv2026

Antiferromagnetism and Stripe Channel Order in the $\mathrm{SU}(N)$-Symmetric Two-Channel Kondo Lattice Model

We carry out large-scale, sign-problem-free determinant quantum Monte Carlo simulations of the square lattice $\mathrm{SU}(N)$-symmetric two-channel Kondo lattice model at half-filling. We map out the zero-temperature phase diagram for $N = 2, 4, 6$, and $8$, as a function of the Kondo coupling strength. In the weak-coupling regime, we observe antiferromagnetic order of the localized moments. Remarkably, for $N \geq 6$, sufficiently strong Kondo coupling induces spontaneous channel symmetry breaking, forming a stripe dimerization pattern with a wave vector $\boldsymbol{k}=(π,0)$ alternating between channels. These findings are supported by a complementary large-$N$ saddle point analysis, which identifies the striped hybridization pattern as the energetically preferred configuration. The spatial symmetry breaking results in an anisotropic Fermi surface reconstruction.

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arXiv2026

Observation of an emergent energy scale close to dimensional reduction in a quasi-two-dimensional quantum magnet

By appropriately perturbing a critical transverse-field Ising chain away from its critical point, the system can develop a finite correlation length with a characteristic purely massive spectrum, whose ratios and correlations are precisely described by an integrable field theory and an infinite set of integrals of motion corresponding to the $E_8$ Lie algebra. In this work, we report on experimental observation of a characteristic massive spectrum close to transverse field-induced dimensional reduction in a quasi-two-dimensional quantum magnet Cu$_2$(OH)$_3$Br, providing evidence for an emergent $E_8$ symmetry and the corresponding excitations of bound states in the sublattice of its ferromagnetic chains. These results demonstrate the power of integrable field theory in describing emergent many-body quantum critical phenomena in condensed matter systems.

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arXiv2026

Scale-invariant magnetic anisotropy in $α$-RuCl$_3$: A quantum Monte Carlo study

We compute the rotational anisotropy of the free energy of $α$-RuCl$_3$ in an external magnetic field. This quantity, known as the magnetotropic susceptibility, $k$, relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of $α$-RuCl$_3$ and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to $30~\mathrm{K}$, an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic spin susceptibility in this model of $α$-RuCl$_3$ displays scaling behavior $k = T f(B/T)$ at high temperatures. Once the uniform susceptibility departs from the Curie law (i.e., at the energy scale of the exchange interactions), it appears to transition to an emergent scalinglike behavior, characterized by a different function $f$ at lower temperatures, stemming from the locality of torque fluctuations. We observe a remarkable numerical match between experiment and simulations and we also find qualitative agreement with the pure Kitaev model. In comparison, for the XXZ Heisenberg Hamiltonian, the scaling $k = T f(B/T)$ breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law and never reemerges at low temperatures.

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arXiv2026

Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\textrm{O}(4N)$ symmetry breaking at repulsive coupling

Gross-Neveu model in 2+1 dimensions exhibits a continuous transition from gapless Dirac semimetal to the gapped quantum anomalous Hall (QAH) insulator at a finite (attractive) coupling, at which the inversion and time-reversal symmetry become spontaneously broken, and the flavor O($M$) symmetry remains preserved. A unification of leading order parameters of 2+1 dimensional $N$ four-component Dirac fermions collects all Lorentz-singlet mass-like fermion bilinears, except the one condensing in the QAH state, into an irreducible representation of the O($M=4N$), and predicts another phase transition in the Gross-Neveu model to occur at a strong (repulsive) coupling. Here, a fermionic auxiliary-field quantum Monte Carlo algorithm is employed in order to study a lattice realization of the Gross-Neveu field theory in the repulsive regime, where the sign problem is absent. We indeed find the O($4N$) symmetry breaking transition out of Dirac semimetal to occur and to be weakly first-order for $N=2$, relevant to graphene. The size of the discontinuity and the magnitude of the critical coupling, however, both grow with $N$. Adding a finite chemical potential is found to break the symmetry and cause superconductivity. These results are in broad agreement with the predictions of the unified field theory. Our lattice model also displays an interesting exact O($2N$) symmetry, a subgroup of the low-energy O($4N$), and has the ordered ground state with the order parameter that belongs to its $N(2N-1)$-dimensional representation. Other order parameters are also examined, and a certain hierarchy among those that belong to different representations of the exact $O(2N)$ is observed.

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arXiv2026

Mott transition of photons: quantum Monte Carlo study of Gross-Neveu criticality in a cavity

The Hubbard model on the honeycomb lattice is a pristine realisation of a semimetal-to-insulator Mott transition belonging to the Gross-Neveu O(3) universality class. We couple this system to a single linearly polarised cavity photon mode. The light-matter coupling is such that the photon number remains an intensive quantity as is the case for an empty cavity. For this interacting light-matter model, we formulate a negative-sign-free fermion quantum Monte Carlo algorithm that allows for bias-free results on finite system sizes. Our numerical results show that the coupling to the cavity is irrelevant at criticality, even at strong electron-photon coupling. On the other hand, we observe, and show analytically, that the photon spectral function couples to the optical conductivity of the electronic system. The cavity photons thereby undergo a Mott transition, and the photon spectral function acts as a contact-free non-invasive probe for Mott criticality.

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arXiv2026

Dynamical magnetotropic susceptibility as a new probe of Kitaev materials and beyond

The magnetotropic susceptibility $k(\omega)$ probes ultra-low-frequency uniform fluctuations. For a crystal mounted on an oscillating cantilever in a magnetic field, it is defined as the ratio of torque to angular-displacement amplitude. Its real and imaginary parts determine the oscillation-frequency shift and crystal-induced damping. It is a low-energy probe of uniform $q=0$ spin and charge degrees of freedom. We demonstrate this by deriving $k(\omega)$ within linear response theory for a generic correlated-electron Hamiltonian with charge and spin degrees of freedom. Although it covers metallic and insulating magnets, correlated paramagnets, and exotic quantum critical points, we focus on limiting cases. For insulating spin systems $k(0)$ is sensitive to magnetic anisotropy whereas its finite-frequency imaginary part probes uniform dynamical spin susceptibility even in spin-symmetric models. For metallic systems we identify when eddy currents cause low-frequency damping. Our numerical results focus on Kitaev-material magnetotropic response. Using auxiliary-field quantum Monte Carlo with machine-learning-based sign-problem optimization we compute $k(\omega)$ for several models proposed for $\alpha$-RuCl$_3$. The observed low-temperature scaling of $k(0)/T$ with $B/T$ results from dominant Kitaev couplings: parameter sets without dominant Kitaev coupling do not exhibit this scaling. It remains robust upon inclusion of optical phonons. Beyond the static response, $k''(\omega)$ for the $\alpha$-RuCl$_3$ parameter set reproducing the experimental $k(0)$ data shows local-moment features at high and low $T$, with a single peak at the Larmor frequency. Beyond Kitaev systems we highlight broader applications. Probing ultra-low-energy uniform charge fluctuations is pertinent to Kondo destruction quantum criticality, of broad interest in strange metallicity and unconventional superconductivity.

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arXiv2026

Generating ferro-spinetic polarizations in altermagnetic insulators

Altermagnets are a novel class of fully spin-compensated magnetic materials that nevertheless have spin-split electronic bands, offering novel perspectives for spintronics applications. Based on a rigorous analysis of altermagnetic many-body models and their symmetry we establish the important role of two fundamental types of polarizations in altermagnetic insulators: the charge and the spinetic one, where the latter corresponds to a macroscopic spin-displacement field. First principles calculations confirm and quantify their presence in real materials. The two polarizations are directly coupled and emerge in orthogonal directions when inversion symmetry is broken, either by the system developing a spontaneously ferroelectric polarization (in ferroelectric altermagnets), or by a charge displacement induced by an external electric field (for inversion invariant altermagnetic insulators). This presence of large and switchable spin accumulations constitute an attractive fundamental feature of altermagnetic insulators.

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arXiv2026

Revealing altermagnetic Fermi surfaces with two Kondo impurities

Motivated by recent advances in the study of altermagnetism, or unconventional magnetism, and in the realization and manipulation of two-impurity Kondo physics in real materials, we propose a phase-sensitive method to explore unconventional magnetic symmetries. Our method can be implemented with spin-resolved scanning tunneling microscopy to study two-impurity Kondo phenomena on altermagnetic metals by varying the distance and orientation between magnetic impurities. Using quantum Monte Carlo simulations, we analyze the spin splitting of the Kondo resonance, whose spatial distribution sensitively captures the symmetry of the underlying altermagnetic order. Furthermore, the impurity spin correlations reflects the anisotropy of the RKKY interaction due to the altermagnetic Fermi surface splitting. This work provides a framework for studying the competition between the Kondo effect, the RKKY interaction and altermagnetism, in the simplest possible system.

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arXiv2025

The two-dimensional optical Su-Schrieffer-Heeger model: ground state and thermodynamic properties

We investigate the two-dimensional optical Su-Schrieffer-Heeger (SSH) model, in which the electron hopping amplitude is modulated by the difference between neighboring phonon coordinates. Using sign-problem-free auxiliary-field quantum Monte Carlo simulations, complemented by mean-field analysis, we determine the long-range ordered phases as a function of the electron-phonon coupling and phonon frequency. By examining both adiabatic and antiadiabatic regimes, we reveal the emergence of staggered and armchair valence bond solid (VBS) phases, as well as the O(4) antiferromagnetic phase. In addition, finite-temperature simulations show that the VBS transition occurs at critical temperatures significantly higher than in models with local electron-phonon coupling, consistent with the presence of lighter polarons in the metallic regime. These findings establish the ground-state and finite-temperature phase diagrams of the optical SSH model, which emphasize its similarities and contrasts with other electron-phonon systems.

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arXiv2025

Dimensionality-Changing Transition from a Non-Fermi Liquid to a Spin-Solid in a Multichannel Kondo Lattice

A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.

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arXiv2025

The Two-Dimensional Rashba-Holstein Model: A Quantum Monte Carlo Approach

In this work, we investigate the impact of Rashba spin-orbit coupling (RSOC) on the formation of charge-density wave (CDW) and superconducting (SC) phases in the Holstein model on a half-filled square lattice. Using unbiased finite-temperature Quantum Monte Carlo simulations, we go beyond mean-field approaches to determine the ground state order parameter as a function of RSOC and phonon frequency. Our results reveal that the Rashba metal is unstable due to particle-hole instabilities, favoring the emergence of a CDW phase for any RSOC value. In the limit of a pure Rashba hopping, the model exhibits a distinct behavior with the appearance of four Weyl cones at half-filling, where quantum phase transitions are expected to occur at strong interactions. Indeed, a quantum phase transition, belonging to the Gross-Neveu Ising universality class between a semi-metal and CDW emerges at finite phonon frequency dependent coupling $λ_c$. In the antiadiabatic limit we observe an enhanced symmetry in the infrared that unifies SC and CDW orders. These results advance our understanding of competing CDW and SC phases in systems with spin-orbit coupling, providing insights that may help clarify the behavior of related materials.

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arXiv2025

Phases and phase transitions of an $S=3/2$ chain on metallic and semi-metallic surfaces

Motivated by recent scanning tunneling microscopy experiments on chains of Co adatoms on Cu surfaces, we investigate the physics of a spin-$3/2$ Heisenberg chain with single-ion anisotropy ($D$) on metallic and semi-metallic surfaces. In the strong Kondo coupling ($J_k$) limit, a perturbative analysis maps the system onto a Haldane spin-1 chain with single-ion anisotropy, ferromagnetically coupled to the metallic surface. This Haldane state, arising from underscreening of the $S=3/2$ chain, is stable against small $D$ and characterized by topological edge modes. The nature of the $D$-driven transitions out of this state depends on the environment. Coupling to a metal (semi-metal) is a relevant (irrelevant) perturbation at the decoupled fixed point between the spin-1 chain and the two-dimensional electron gas. In the large positive $D$ limit, the system maps onto an anisotropic spin-$1/2$ Kondo system. For large negative $D$, in the Ising phase, spins are frozen. For small $J_k$, the nature of the metallic phase dominates. On a two-dimensional semi-metal, the Kondo coupling is irrelevant at the decoupled fixed point ($J_k= 0$), leading to a Kondo breakdown phase at weak coupling, irrespective of $D$. In contrast, on a two-dimensional metal, the resulting dissipative Ohmic bath is a marginally relevant perturbation, inducing antiferromagnetic ordering along the chain. In this case, $D$ drives a spin-flop transition between Ising and XY ordered phases. At $D=0$, we observe continuous transitions between the Kondo breakdown or dissipation-induced long-range ordered phases and the underscreened Haldane phase. These phase diagrams are supported by scaling arguments and sign-free auxiliary-field quantum Monte Carlo simulations.

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arXiv2025

Edge modes of topological Mott insulators and deconfined quantum critical points

Topology and anomalies lead to edge modes that can interact with critical bulk fluctuations. To study this setup, pertaining to boundary criticality, we consider a model exhibiting a deconfined quantum critical point (DQCP) between a dynamically generated quantum spin Hall state (i.e.a topological Mott insulator) and an s-wave superconductor. For the topological Mott insulator, the bulk Goldstone modes are shown to be irrelevant at the helical Luttinger liquid fixed points. The deconfined quantum critical point is an instance of an emergent anomaly, and we observe a sharp localized edge state at this point. The sharpness of the edge mode is consistent with an ordinary phase in which electronic edge modes decouple from critical edge bosonic fluctuations. At the DQCP, the scaling dimension of the edge electron shows a jump, a feature argued to be a signature of the emergent anomaly. Our results are based on large-scale auxiliary-field quantum Monte Carlo simulations.We also carry out calculations for the Kane-Mele-Hubbard model to confirm spectral features of the ordinary and extraordinary-log phases in the vicinity of the bulk critical point.

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