arXiv subjects

Paul Ludwig

Publications and source records attributed to Paul Ludwig.

3 recordsLinked to original sources

arXiv2026

A Finite-Volume Scheme for the Continuum Extrapolation of Lattice Step-Scaling in (2+1)D Hamiltonian U(1) Gauge Theory

We propose a finite-volume scheme to perform controlled continuum extrapolations of the lattice step-scaling function, a key ingredient for determining the running coupling in a Hamiltonian lattice gauge theory in small volumes. As a testbed, we employ a dual Hamiltonian formulation of pure U(1) gauge theory in (2+1) dimensions and an operator basis that remains efficient toward weak coupling. We describe the implementation of static external charges on the spatial lattice and study, using matrix product states, the resulting confining string, from which we extract the static potential and a force-based renormalized coupling. Using the proposed finite-volume scheme, we demonstrate a stable continuum limit of the step-scaling function on the lattice sizes accessible to present Hamiltonian simulations. The method is readily extendable to other gauge groups and dimensions, providing a pathway toward Hamiltonian step-scaling studies in other theories.

hep-lat↗

arXiv2026

Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model

We investigate a non-Abelian SU$(2)$ quantum link model in $2+1$ dimensions on a hexagonal lattice using tensor network methods. We determine the static quark potential for a wide range of bare coupling values and find that the theory is confining. We also probe the existence of a L\"uscher term and find a clear signal with a $g^2$ dependent coefficient, in qualitative agreement with a strong coupling expansion. Correspondingly, the width of the strings scales logarithmically with the string length again for all $g^2$-values, providing evidence for a rough string, with no indication for a roughening transition.

hep-lat↗

arXiv2025

A Comprehensive Stress Test of Truncated Hilbert Space Bases against Green's function Monte Carlo in U(1) Lattice Gauge Theory

A representation of Lattice Gauge Theories (LGT) suitable for simulations with tensor network state methods or with quantum computers requires a truncation of the Hilbert space to a finite dimensional approximation. In particular for U(1) LGTs, several such truncation schemes are known, which we compare with each other using tensor network states. We show that a functional basis obtained from single plaquette Hamiltonians -- which we call plaquette state basis -- outperforms the other schemes in two spatial dimensions for plaquette, ground state energy and mass gap, as it is delivering accurate results for a wide range of coupling strengths with a minimal number of basis states. We also show that this functional basis can be efficiently used in three spatial dimensions. Green's function Monte Carlo appears to be a highly useful tool to verify tensor network states results, which deserves further investigation in the future.

hep-lat↗