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Oliver R. Bellwood

Publications and source records attributed to Oliver R. Bellwood.

2 recordsLinked to original sources
arXiv2026

Algebraic Structure 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 twelve sites using the Bethe ansatz. We find that the algebraic degree of the ground state magnon phases and Bethe roots scale with respect to system size at a different rate to the ground-state energy and wavefunction coefficients. The ground-state Bethe roots and energy are found to become Galois unsolvable for ten or more sites, thus demonstrating the lack of a symbolic analytical solution 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↗