arXiv subjects

Abolhassan Vaezi

Publications and source records attributed to Abolhassan Vaezi.

At least 19 recordsLinked to original sources

arXiv2025

Phase diagram of the Kitaev-Hubbard model: $\mathbb{Z}_2$ slave-spin and QMC approaches

Recent experiments show that the ground state of some layered materials with localized moments is in close proximity to the Kitaev spin liquid, calling for a proper model to describe the measurements. The Kitaev-Hubbard (KHu) model is the minimal model that captures the essential ingredients of these systems; it yields the Kitaev-Heisenberg spin model at the strong coupling limit and contains the charge fluctuations present in these materials as well. Despite its relevance, the phase diagram of the KHu model has not been rigorously revealed yet. In this work, we study the full phase diagram of the KHu model using the $\mathbb{Z}_2$ slave-spin mean-field theory as well as the auxiliary field quantum Monte Carlo on rather large systems and at low temperatures. The Mott transition is signaled by a vanishing quasiparticle weight evaluated using the slave-spin construction. Moreover, we demonstrate that there are multiple magnetic phase transitions within the Mott phase including magnetically ordered phases and most notably a quantum spin liquid phase for $1.0 \lesssim t^{\prime}/t \lesssim 1.11 $ at $U/t=5$.

cond-mat.str-el↗

arXiv2025

Nontrapping Tunable Topological Photonic Memory

We propose a novel topological photonic memory that encodes information through dynamically controllable Chern numbers in a two-band topological photonic system. Utilizing a honeycomb lattice photonic crystal, the memory leverages topologically protected edge states that remain robust against fabrication imperfections and environmental perturbations. By applying a synthetic time-dependent magnetic field, we achieve real-time tunability of the Chern number, enabling rapid and efficient memory switching without the need for light-trapping mechanisms. Our computational study evaluates critical performance metrics, including write speed, read stabilization time, energy gap stability, and nonadiabatic transition probabilities. The results demonstrate that the system supports GHz-range write speeds (approximately 1-10 GHz), with stable data retention due to the large energy gap between bands. The system enables scalable multi-bit memory encoding based on quantized Chern numbers and exhibits superior speed, fault tolerance, and robustness compared to conventional photonic memory architectures. This work introduces a scalable, high-speed, and nontrapping optical memory paradigm, paving the way for future applications in quantum information processing and optical communication technologies.

physics.optics↗

arXiv2024

Stoner ferromagnetism, correlated metal and thermoelectricity in partially flat-band materials

Recent discovery of correlated electronic phases in twisted heterostructures raised a surge of interests in studying models and materials with flat bands where the electronic excitations are nearly dispersionless in momentum space. As such, the kinetic energy is quenched and the correlations are enhanced, giving rise to a plethora of unusual magnetic, superconducting and transport behaviors. Finding materials whose energy bands are completely flat is rather challenging, yet those whose dispersion is flat only in a portion of the momentum space might be more accessible in material search. In this work, we propose a partially flat-band system on a square lattice. Using the Hubbard model, it is demonstrated that the suppression of the electronic kinetic energy in the flat portion of the band dispersion drives the system to Stoner ferromagnetism even at very weak interactions, i.e., much smaller than the bandwidth, with significantly enhanced Curie temperature. While the low-energy magnon modes are well defined collective excitations, flat magnon bands can be observed at high energies. We show that the strong interaction leads to reduction of the flat portion of the magnon band. However, tuning the chemical potential at a strong interaction regime may lead to spin density wave at finite wave vectors. Then, focusing on the non-magnetic correlated phase and using dynamical mean-field theory, we demonstrate the appearance of a flat-band induced sharp peak in the density of states in addition to the correlation-induced Mott bands. Furthermore, the large seebeck coefficient and the figure of merit of the proposed partially flat-band model, compared to symmetric regular band models, put them in the category of efficient thermoelectric materials.

cond-mat.str-el↗

arXiv2023

Nematicity-enhanced superconductivity in systems with a non-Fermi liquid behavior

We explore the interplay between nematicity~(spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a systematic manner on the $T_{\rm c}$ dome. There, a $s_{x^2+y^2} - d_{x^2-y^2} - d_{xy}$-wave symmetry, in place of the conventional $d_{x^2-y^2}$-wave, governs the nematicity-enhanced pairing with a sharp rise in the $T_{\rm c}$ dome on the filling axis. When the sixfold symmetry is spontaneously broken, the pairing becomes more compact in real space than in the case when the symmetry is enforced. These are accompanied by a non-Fermi character of electrons in the partially flat bands with many-body interactions.

cond-mat.supr-con↗

arXiv2022

Phase transition and fractionalization in superconducting Kondo lattice model

Topology, symmetry, electron correlations, and the interplay between them have formed the cornerstone of our understanding of quantum materials in recent years and are used to identify new emerging phases. While the first two give a fair understanding of noninteracting and, in many cases, weakly interacting wave function of electron systems, the inclusion of strong correlations could change the picture substantially. The Kondo lattice model is a paradigmatic example of the interplay of electron correlations and conduction electrons of a metallic system, describing heavy fermion materials and also fractionalized Fermi liquid pertaining to an underlying gauge symmetry and topological orders. In this work, we study a superconducting Kondo lattice model, a network of 1D Kitaev superconductors Kondo coupled to a lattice of magnetic moments. Using slave-particle representation of spins and exact numerical calculations, we obtain the phase diagram of the model in terms of Kondo coupling $J_K$ and identify a topological order phase for $J_{K} J_{K}^c$, where $J_{K}^c$ is the critical point. Setting the energy scales of electron hopping and pairing to unity, the mean-field theory calculations achives $J_{K}^c=2$ and in exact numerics we found $J_{K}^c\simeq 1.76$, both of which show that the topological order is a robust phase. We argue that in terms of slave particles, the compensated phase corresponds to an invertible phase, and a Mott insulating transition leads to a topological order phase. Furthermore, we show that in the regime $J_{K}<J_{K}^c$ in addition to the low-energy topological states, a branch of subgap states appears inside the superconducting gap.

cond-mat.str-el↗

arXiv2022

Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study

We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with $N=2$ spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength $U_c = 7.28 \pm 0.02$ in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding $N=2$ chiral Ising Gross-Neveu universality class: the inverse correlation length exponent $ν^{-1} = 1.19 \pm 0.03$, the order parameter anomalous dimension $η_ϕ = 0.31 \pm 0.01$, and the fermion anomalous dimension $η_ψ = 0.136 \pm 0.005$.

cond-mat.str-el↗

arXiv2021

An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo

We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground-state if the evolution time is long enough. We demonstrate that the AQMC enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC vis-à-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum Monte Carlo formalism. Next, we test the AQMC against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at $p=1/8$ doping for a $16\times 8$ system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of $U(1)_2\sim SU(2)_1$ topological order in a strongly correlated Chern insulator.

cond-mat.str-el↗

arXiv2021

Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond

We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians. In this letter, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz symmetry, and (c) for subsystems with non-flat boundaries, up to relatively strong interactions. We show that the mentioned local temperature at a given point decays inversely proportional to its distance from the boundary between the subsystem and the environment. We find the subdominant terms in the EH as well and show that they are severely suppressed away from the boundaries of subsystem and are relatively small near them.

cond-mat.str-el↗

arXiv2020

Engineering Quantum Hall Phases in Synthetic Bilayer Graphene System

Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diagonalization (ED), we show that the system exhibits a non-abelian bilayer Fibonacci phase at filling fraction $ν= 2/3$. Moreover, at integer filling $ν= 1$, the SQHB exhibits quantum Hall ferromagnetism. Using Hartree-Fock theory and exact diagonalization, we show that excitations of the quantum Hall ferromagnet are topological textures known as skyrmions.

cond-mat.str-el↗

arXiv2019

Pairing and non-Fermi liquid behavior in partially flat-band systems

While multiband systems are usually considered for flat-band physics, here we study one-band models that have flat portions in the dispersion to explore correlation effects in the 2D repulsive Hubbard model in an intermediate coupling regime. The FLEX+DMFT~(the dynamical mean-field theory combined with the fluctuation exchange approximation) is used to show that we have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied, which triggers a crossover from triplet to singlet pairings with a peculiar filling dependence that is dominated by the size of the flat region in the dispersion. A curious manifestation of the flat part appears as larger numbers of nodal lines associated with pairs extended in real space. We further detect non-Fermi liquid behavior in the momentum distribution function, frequency dependence of the self-energy and spectral function. These indicate correlation physics peculiar to flat-band systems.

cond-mat.supr-con↗

arXiv2018

Momentum-dependent relaxation dynamics of the doped repulsive Hubbard model

We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and nonlocal (momentum-dependent) observables evolve toward a thermal state, although the temperature of the final state depends on the ramp duration and the chemical doping. We further reveal a momentum-dependent relaxation rate of the distribution function in doped systems, and trace back its physical origin to the anisotropic self-energies in the momentum space.

cond-mat.str-el↗

arXiv2018

Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study

Motivated by recent experiments realizing correlated phenomena and superconductivity in 2D van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model, and a partially flat band structure containing a non-dispersing region, with identical total non-interacting bandwidth $W$. For both repulsive and attractive weak interactions ($|U| \ll W$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with $U$ an order of magnitude smaller than $W$, we find the presence of a Mott insulating state near half-filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the non-interacting electronic dispersion.

cond-mat.str-el↗

arXiv2018

A unified theory of variational and quantum Monte Carlo methods and beyond

We present a unified theory of the variational Monte Carlo (VMC) and determinant quantum Monte Carlo (DQMC) methods using a novel density matrix formulation of VMC. We introduce an efficient algorithm for VMC to compute correlation functions and expectation values based on the auxiliary field Hirsch-Hubbard-Stratonovic transformation. We show that this new approach to VMC converges significantly faster than its traditional implementations. Furthermore, we generalize the Trotter-Suzuki decomposition to finite imaginary time steps $τ\sim O(1)$ and develop a variational quantum Monte Carlo (VQMC) method accordingly, which is more accurate than VMC and can incorporate quantum fluctuations more efficiently. The two extreme limits of the VQMC method, namely infinitesimal and infinite imaginary time steps, correspond to the DQMC and VMC techniques, respectively. We demonstrate that our VQMC allows us to access lower temperatures in comparison with the conventional DQMC before the sign problem comes into play. We finally show that our VQMC can also enhance the accuracy of the projector Monte Carlo methods by providing better and less biased candidates for the trial wave functions, requiring shorter projection times for a given accuracy and alleviating the sign problem further.

cond-mat.str-el↗

arXiv2018

Topological Quantum Computation Based on Chiral Majorana Fermions

Chiral Majorana fermion is a massless self-conjugate fermion which can arise as the edge state of certain two-dimensonal topological matters. It has been theoretically predicted and experimentally observed in a hybrid device of quantum anomalous Hall insulator and a conventional superconductor. Its closely related cousin, Majorana zero mode in the bulk of the corresponding topological matter, is known to be applicable in topological quantum computations. Here we show that the propagation of chiral Majorana fermions lead to the same unitary transformation as that in the braiding of Majorana zero modes, and propose a new platform to perform quantum computation with chiral Majorana fermions. A Corbino ring junction of the hybrid device can utilize quantum coherent chiral Majorana fermions to implement the Hadamard gate and the phase gate, and the junction conductance yields a natural readout for the qubit state.

cond-mat.mes-hall↗

arXiv2018

Does the SYK model have a spin glass phase?

We argue that the Sachdev-Ye-Kitaev model has no spin glass phase, based on calculations involving both the nearly-conformal limit and the strongly-coupled Schwarzian limit of the model. This conclusion is supported by numerical computations of eigenvalue statistics with up to 46 Majorana fermions. In addition, we find numerically that the distribution of the ground state energy is Gaussian.

hep-th↗

arXiv2017

Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality

No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. Moreover, whether spacetime SUSY in 2+1 and higher dimensions can occur or emerge in generic microscopic models remains open. Here, we introduce a lattice realization of a \textit{single} Dirac fermion with attractive Hubbard interactions that preserves both time-reversal and chiral symmetries. By performing numerically-exact sign-problem-free determinant quantum Monte Carlo simulations, we show that the interacting single Dirac fermion in 2+1 dimensions features a superconducting quantum critical point (QCP). More remarkably, we demonstrate that the ${\mathcal N}$=2 spacetime SUSY in 2+1D emerges at the superconducting QCP by showing that the fermions and bosons have \textit{identical} anomalous dimensions 1/3, a hallmark of the emergent SUSY. To the best of our knowledge, this is the first observation of emergent 2+1D spacetime SUSY in quantum microscopic models. We further show some experimental signatures which can be measured to test such emergent SUSY in candidate systems such as the surface of 3D topological insulators.

cond-mat.str-el↗

arXiv2017

Quantum phase transition of chiral Majorana fermion in the presence of disorder

We study the quantum phase transitions of a disordered two-dimensional quantum anomalous Hall insulator with $s$-wave superconducting proximity, which are governed by the percolation theory of chiral Majorana fermions. Based on symmetry arguments and a renormalization group analysis, we show there are generically two phase transitions from Bogoliubov-de Gennes Chern number $\mathcal{N}=0$ to $\mathcal{N}=1$ ($p+ip$ chiral topological superconductor) and then to $\mathcal{N}=2$, in agreement with the conclusion from the band theory without disorders. Further, we discuss the critical scaling behavior of the $e^2/2h$ conductance half plateau induced by $\mathcal{N}=1$ chiral topological superconductor recently observed in the experiment. In particular, we compare the critical behavior of the half plateau induced by topological superconductor with that predicted recently by alternative explanations of the half plateau, and show that they can be distinguished in experiments.

cond-mat.mes-hall↗

arXiv2017

Entanglement distance between quantum states and its implications for density-matrix-renormalization-group study of degenerate ground-states

We study the concept of entanglement distance between two quantum states which quantifies the amount of information shared between their reduced density matrices (RDMs). Using analytical arguments combined with density-matrix-renormalization-group (DMRG) and exact diagonalization (ED) calculations, we show that for gapless systems the entanglement distance has power law dependence on the energy separation and subsystem size with $α_E$ and $α_{\ell}$ exponents, respectively. Using conformal field theory (CFT) we find $α_E = 2$ and $α_{\ell} = 4$ for Abelian theories with $c=1$ such as free fermions. For non-Abelian CFTs $α_E = 0$ , and $α_{\ell}$ is twice the conformal dimension of the thermal primary fields. For instance for $Z_3$ parafermion CFT $α_E = 1$ and $α_{\ell} = 4/5$. For gapped 1+1D fermion systems, we show that the entanglement distance divides the low energy excitations into two branches with different values of $α_E$ and $α_{\ell}$. These two branches are related to momentum transfers near zero and $π$. We also demonstrate that the entanglement distance reaches its maximum for degenerate states related through nonlocal operators such as Wilson loops. For example, degenerate ground-states (GSs) of 2+1 D topological states have maximum entanglement distance. On the contrary, degenerate GSs related through confined anyon excitations such as genons have minimum entanglement distance. Various implications of this concept for quantum simulations are discussed. Finally, based on the ideas developed we discuss the computational complexity of DMRG algorithms that are capable of finding all degenerate GSs.

cond-mat.str-el↗