arXiv subjects

Paul L. Ebert

Publications and source records attributed to Paul L. Ebert.

6 recordsLinked to original sources

arXiv2026

Incommensurate Spin-Density Waves in a Frustrated Maple-Leaf Lattice Ferromagnet

We study how ferromagnetism breaks down in the spin-$\tfrac12$ nearest-neighbor Heisenberg model on the maple-leaf lattice with ferromagnetic $J_t,J_d$ and antiferromagnetic $J_h$, motivated by the mixed ferro-antiferromagnetic interactions in Na$_2$Mn$_3$O$_7$. Exact diagonalization shows that the ferromagnetic boundary does not feature a zero-field spin-nematic phase on the clusters studied here, but an extended regime of incommensurate spin-density-wave correlations with continuously evolving ordering vector. The phase diagram also contains collinear Néel, canted $120^\circ$, and hexagonal-singlet regimes, separated by regions that remain difficult to classify from exact diagonalization alone. Variational tests of fully symmetric Gutzwiller-projected Abrikosov-fermion U(1) and $\mathbb{Z}_2$ states find no competitive spin-liquid description of the interior unresolved regions. By contrast, on the ruby-lattice boundary we identify a point between the collinear Néel and hexagonal-singlet phases where a projected $\mathbb{Z}_2$ Ansatz reproduces the finite-size energy and spin correlations with good accuracy.

cond-mat.str-el↗

arXiv2026

Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice

We study the Heisenberg antiferromagnet on the maple-leaf lattice using several numerical approaches, focusing on the numerical linked-cluster expansion (NLCE), which exhibits an unconventional convergence extending to low and even zero temperatures. We evaluate thermodynamic properties as well as spin-spin correlations through the equal-time structure factor. Within NLCE the specific heat capacity reveals a two-peak structure at $T_1 \approx 0.479\,J$ and $T_2 \approx 0.131\,J$, reminiscent of the corresponding result for the triangular lattice. At intermediate temperatures, the spin-spin structure factor develops features that reflect the absence of reflection symmetry in the lattice. The zero-temperature convergence of NLCE enables reliable estimates of the ground-state energy and points to a short-range correlated paramagnetic ground state composed of resonating hexagonal motifs. The NLCE results are benchmarked against Pseudo-Majorana Functional Renormalization Group, finite-temperature Lanczos, and classical Monte Carlo simulations.

cond-mat.str-el↗

arXiv2026

XDiag: Exact Diagonalization for Quantum Many-Body Systems

Exact diagonalization (ED) is a cornerstone technique in quantum many-body physics, enabling precise solutions to the Schrödinger equation for interacting quantum systems. Despite its utility in studying ground states, excited states, and dynamical behaviors, the exponential growth of the Hilbert space with system size presents significant computational challenges. We introduce XDiag, an open-source software package designed to combine advanced and efficient algorithms for ED with and without symmetry-adapted bases with user-friendly interfaces. Implemented in C++ for computational efficiency and wrapped in Julia for ease of use, XDiag provides a comprehensive toolkit for ED calculations. Key features of XDiag include the first publicly accessible implementation of sublattice coding algorithms for large-scale spin system diagonalizations, efficient Lin table algorithms for symmetry lookups, and random-hashing techniques for distributed memory parallelization. The library supports various Hilbert space types (e.g., spin-1/2, electron, and t-J models), facilitates symmetry-adapted block calculations, and automates symmetry considerations. The package is complemented by extensive documentation, a user guide, reproducible benchmarks demonstrating near-linear scaling on thousands of CPU cores, and over 20 examples covering ground-state calculations, spectral functions, time evolution, and thermal states. By integrating high-performance computing with accessible scripting capabilities, XDiag allows researchers to perform state-of-the-art ED simulations and explore quantum many-body phenomena with unprecedented flexibility and efficiency.

cond-mat.str-el↗

arXiv2026

Competing Paramagnetic Phases in the Maple-Leaf Heisenberg Antiferromagnet

We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin-$1/2$ Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to $N=36$ sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted) $120^\circ$ magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear Néel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped $\mathbb{Z}_{2}$ spin liquid Ansatz is in astonishing agreement with the exact $N=36$ ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.

cond-mat.str-el↗

arXiv2024

Shedding Light on Evanescent Shadows -- Exploration of non-anticommuting $γ_5$ in Dimensional Regularisation

The mathematical consistency of the BMHV scheme of dimensional regularisation (DReg) comes at the cost of requiring symmetry-restoring counterterms to cancel the regularisation-induced breaking of gauge and BRST invariance. There is no unique way to extend a 4-dimensional theory to $D$ dimensions, and different choices can be made for the dimensionally regularised fermions, evanescent parts of their kinetic terms and evanescent gauge interactions. Here we present a detailed study of the impact of changing such evanescent details. We leverage this freedom to identify a particularly convenient formulation that simplifies practical calculations. In order to thoroughly study the available options, we focus on a general abelian chiral gauge theory including scalar fields and adopt a general approach to the BMHV implementation. This allows for specialisation to various models and different approaches, including those from the literature. Importantly, our model can be specialised to the abelian sector of the Standard Model (SM). Consequently, this article also serves as a roadmap for upcoming applications to the full SM.

hep-ph↗

arXiv2022

Weighted averages in population annealing: analysis and general framework

Population annealing is a powerful sequential Monte Carlo algorithm designed to study the equilibrium behavior of general systems in statistical physics through massive parallelism. In addition to the remarkable scaling capabilities of the method, it allows for measurements to be enhanced by weighted averaging, admitting to reduce both systematic and statistical errors based on independently repeated simulations. We give a self-contained introduction to population annealing with weighted averaging, generalize the method to a wide range of observables such as the specific heat and magnetic susceptibility and rigorously prove that the resulting estimators for finite systems are asymptotically unbiased for essentially arbitrary target distributions. Numerical results based on more than $10^7$ independent population annealing runs of the two-dimensional Ising ferromagnet and the Edwards-Anderson Ising spin glass are presented in depth. In the latter case, we also discuss efficient ways of measuring spin overlaps in population annealing simulations.

cond-mat.stat-mech↗