arXiv subjects

Oliver R. Bellwood

Publications and source records attributed to Oliver R. Bellwood.

2 recordsLinked to original sources

arXiv2026

Galois Solvability of Finite-Size Bethe Solutions in the Heisenberg Chain

The spin-1/2 Heisenberg antiferromagnetic chain is the canonical example of an integrable quantum many-body model. Despite its exact solvability, explicit finite-size solutions are typically only accessible via numerical evaluation of the Bethe ansatz equations. Here, we analyse the algebraic structure of the exact, symbolic ground states for chains up to ten sites using the coordinate Bethe ansatz. We show that both the ground state wavefunction and the Bethe-roots rapidly develop algebraic complexity with respect to system size, but at different rates. The Bethe-roots appear to become Galois unsolvable for chains of eight or more sites, whereas the ground state wavefunction coefficients and energy appear to become unsolvable for ten or more sites. This demonstrates a lack of explicit analytic tractability in a quantum integrable model due to algebraic complexity.

cond-mat.str-el↗

arXiv2025

Fractal Path Strategies for Efficient 2D DMRG Simulations

Numerical simulations of quantum magnetism in two spatial dimensions are often constrained by the area law of entanglement entropy, which heavily limits the accessible system sizes in tensor network methods. In this work, we investigate how the choice of mapping from a two-dimensional lattice to a one-dimensional path affects the accuracy of the two-dimensional Density Matrix Renormalization Group algorithm. We systematically evaluate all mappings corresponding to a subset of the Hamiltonian paths of the $N \cross N$ grid graphs up to $N=8$ and demonstrate that the fractal space-filling curves generally lead to faster convergence in ground state searches compared to the commonly used ``snake" path. To explain this performance gain, we analyze various locality metrics and propose a scalable method for constructing high-performing paths on larger lattices by tiling smaller optimal paths. Our results show that such paths consistently improve simulation convergence, with the advantage increasing with system size.

cond-mat.str-el↗