arXiv subjects

Mahmoud Abdelshafy

Publications and source records attributed to Mahmoud Abdelshafy.

4 recordsLinked to original sources

arXiv2025

Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study

We study Yang-Lee zeros in the thermodynamic limit of the 2D nearest-neighbor antiferromagnetic Ising model on square and triangular lattices. We employ the Numerical Linked Cluster Expansion (NLCE) equipped with Exact Enumeration (EE) of the partition function to estimate the Laplacian of the free energy, which is proportional to the zeros density. Using a modified NLCE, where the expansion can be carried directly on the Yang-Lee zeros of the involved clusters, we estimate the density of Yang-Lee zeros in the thermodynamic limit. NLCE gives significantly more zeros than EE in the complex field plane providing more insights on how the root curves look in the thermodynamic limit. For the square lattice at $T \ll T_c$, the results suggest that two vertical lines at $\pm h_c(T)$ in the complex field plane (i.e two concentric circles in the complex fugacity plane) are the thermodynamic root curves. A similar picture is expected for the triangular lattice for phase transitions at large values of magnetic field while further study is needed for phase transitions at smaller values of magnetic field. The convergence of the NLCE and (EE) calculations of the partition function to the thermodynamic limit is studied in both lattices and the temperature-field phase diagram is obtained from Yang-Lee zeros using both methods. This NLCE-based approach will facilitate the study of different types of phase transitions using Yang-Lee zeros in future research.

cond-mat.stat-mech↗

arXiv2025

Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces

We show that in systems with highly degenerate energy spectra, such as the 2D transverse-field Ising model (2DTFIM) in the strong-field limit, quantum chaos can emerge in finite systems for arbitrary small perturbations. In this regime, the presence of extensive quasiconserved quantities can prevent finite systems from becoming ergodic. We study the ensuing crossover to ergodicity in a family of models that includes the 2DTFIM, in which the onset of ergodic behavior exhibits universality and occurs for perturbation strengths that decrease polynomially with increasing system size. We discuss the behaviors of quantum chaos indicators, such as level spacing statistics and bipartite entanglement, and of the fidelity susceptibilities and spectral functions across the crossover.

quant-ph↗

arXiv2024

Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions

We show that numerical linked cluster expansions (NLCEs) based on sufficiently large building blocks allow one to obtain accurate low-temperature results for the thermodynamic properties of spin lattice models with continuous disorder distributions. Specifically, we show that such results can be obtained computing the disorder averages in the NLCE clusters before calculating their weights. We provide a proof of concept using three different NLCEs based on L, square, and rectangle building blocks. We consider both classical (Ising) and quantum (Heisenberg) spin-$\frac{1}{2}$ models and show that convergence can be achieved down to temperatures that are up to two orders of magnitude lower than the relevant energy scale in the model. Additionally, we provide evidence that in one dimension one can obtain accurate results for observables such as the energy down to their ground-state values.

cond-mat.stat-mech↗

arXiv2023

L-based numerical linked cluster expansion for square lattice models

We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of the bare sums than that of the (larger) square-shaped clusters, and can be used with resummation techniques (like the site- and bond-based expansions) to obtain results at even lower temperatures. We compare the performance of weak- and strong-embedding versions of this expansion in various spin-1/2 models, and show that the strong-embedding version is preferable because of its convergence properties and lower computational cost. Finally, we show that the expansion based on the L-shape cluster can be naturally used to study properties of lattice models that smoothly connect the square and triangular lattice geometries.

cond-mat.stat-mech↗