Finite Volume Energy Spectrum Research Articles

Deuteron system in finite volume with particle-dimer picture

This article delves into the application of Dimer images in addressing two-body problems within lattice quantum chromodynamics (LQCD), providing the finite volume energy spectrum of deuterons in the context of S13-D13 coupled-channels. The author commences by introducing the Dimer-particle method and formulating the Lagrangian for the scattering of two fermions. Additionally, the author defines the relativistic high partial zeta-function in a moving reference system and outlines a method for its rapid convergence calculation. The article further scrutinizes zeta-function representations across various momentum shells and discusses issues related to symmetry breakdown in specific momentum configurations. In sum, this work presents innovative methods for incorporating spin and isospin indices into dimer models, thereby establishing closer relevance to LQCD and deuteron studies.

Effects of multiple single-particle basis states in scattering systems

Low-lying baryon resonances have been explored using Hamiltonian Effective Field Theory (HEFT), in a formalism where resonances with a three-quark component are described by both two-particle meson–baryon states and a bare basis state. Here, we investigate the use of multiple bare states in the Hamiltonian, to extend the formalism to higher energy ranges, and represent a larger portion of the low-lying baryon spectrum. Introducing a second bare state into a toy model extension of the low-energy Δ(1232) system, we explore the influence of the second bare state on the position of poles in the infinite-volume T-matrix. Considering the same system in a finite-volume, we analyse the finite-volume energy spectrum in the presence of a second bare state, providing insight into the interplay between two bare basis states, representing quark-model states, and the relationship between infinite-volume poles and finite-volume eigenstates.

Refining the cutoff 3d gravity/ Toverline{T} correspondence

Pure gravity in AdS3 is a theory of boundary excitations, most simply expressed as a constrained free scalar with an improved stress tensor that is needed to match the Brown-Henneaux central charge. Excising a finite part of AdS gives rise to a static gauge Nambu-Goto action for the boundary graviton. We show that this is the Toverline{T} deformation of the infinite volume theory, as the effect of the improvement term on the deformed action can be absorbed into a field redefinition. The classical gravitational stress tensor is reproduced order by order by the Toverline{T} trace equation. We calculate the finite volume energy spectrum in static gauge and find that the trace equation imposes sufficient constraints on the ordering ambiguities to guarantee agreement with the light-cone gauge prediction. The correlation functions, however, are not completely fixed by the trace equation. We show how both the gravitational action and the Toverline{T} deformation allow for finite improvement terms, and we match these to the undetermined total derivative terms in Zamolodchikov’s point splitting definition of the Toverline{T} operator.

Finite-volume energy spectrum, fractionalized strings, and low-energy effective field theory for the quantum dimer model on the square lattice

We present detailed analytic calculations of finite-volume energy spectra, mean field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. The analytic considerations explain why a string connecting two external static charges in the confining columnar phase fractionalizes into eight distinct strands with electric flux $\frac{1}{4}$. An emergent approximate spontaneously broken $SO(2)$ symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phonon-like excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results and Monte Carlo data. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude

In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the spectrum to a non-standard infinite-volume quantity, denoted ${\cal K}_{{\rm df},3}$. Here we present the relation between ${\cal K}_{{\rm df},3}$ and ${\cal M}_3$. We then discuss briefly how our now completed formalism can be practically implemented to extract ${\cal M}_3$ from the finite-volume energy spectrum.

Resonance properties from the finite-volume energy spectrum

A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the Delta-resonance a clear resonance structure emerges in such an analysis. Consequently, measuring the volume-dependence of the energy levels in lattice QCD will allow to determine the mass and the width of the Delta with reasonable accuracy.

Analysis of the Δ -resonance in a finite volume⋆

We discuss Luscher's approach for the extraction of the Δ -resonance parameters from lattice QCD data. Within this approach, we propose a novel strategy to analyze the data corresponding to the finite volume energy spectrum. By using the new method, it is further demonstrated that Luscher's approach allows one to determine the mass and width of the Δ at a reasonable accuracy, despite the fact that the “avoided level crossing” in the energy spectrum has been washed out due to the large width of the resonance.

Comparison of analytic and numerical results in the XY-model

We study the two dimensional XY-model with high precision Monte Carlo techniques and investigate the continuum approach of the step-scaling function of its finite volume mass gap. The continuum extrapolated results are found consistent with analytic predictions for the finite volume energy spectrum based on the equivalence with sine-Gordon theory. To come to this conclusion it was essential to use an also predicted form of logarithmic decay of lattice artifacts for the extrapolation.

Identification of resonance parameters from the finite volume energy spectrum

New finite size formulas are derived which allow the identification of the energy and the width of a resonance from the finite volume energy spectrum. The results are valid in QCD as well as Higgs models. Their applicability in numerical simulations of lattice field theories is discussed in detail.