arXiv subjects

Simon Hands

Publications and source records attributed to Simon Hands.

At least 19 recordsLinked to original sources

arXiv2026

Lattice Field Theory Analysis of the Chiral Heisenberg Model

Motivated by ongoing interest in the universal behaviour of the Hubbard model of spinning electrons on honeycomb and $\pi$-flux lattices at the semi-metal -- Mott insulator phase transition, we formulate the 3D chiral Heisenberg model, a theory of relativistic fermions in three spacetime dimensions, as a lattice field theory using domain wall fermions. The contact interaction term preserves an SU(2) global symmetry. We perform numerical simulations using the Rational Hybrid Monte Carlo algorithm on system sizes $L^3\times L_s$ with $L\in\{8,\ldots,24\}$ and domain wall separation $L_s\in\{8,16,24\}$. We locate the phase transition corresponding to spontaneous SU(2)$\to$U(1) breaking, yielding critical exponent estimates $\nu^{-1}=0.63(3)$, $\eta_\Phi=1.42(8)$. These values are considerably removed from estimates obtained from simulations performed in (2+1)D, ie. with the time and spatial directions treated differently, but align more closely with analytic estimates obtained using 3D covariant field theory. We also present first results for the fermion correlator, ultimately needed for the determination of the exponent $\eta_\Psi$, highlighting the need to rotate the fermion source to a common reference direction in isospace in order to obtain a signal.

hep-lat↗

arXiv2026

Critical scaling in the $N=1$ Thirring Model in $(2+1)d$

The Thirring model in 2+1$d$ with $N$ Dirac flavors can exhibit spontaneous U($2N)\to$U($N)\otimes$U($N$) breaking through fermion - antifermion condensation in the limit $m\to0$. With no small parameter in play the symmetry-breaking dynamics is strongly-interacting and quantitative work requires a fermion formulation accurately capturing global symmetries. We present simulation results for $N=1$ obtained with Wilson kernel domain wall fermions on $16^3\times L_s$, with $L_s=24,\ldots,120$. The $L_s\to\infty$ extrapolation of the bilinear condensate $\langle\bar\psi\psi\rangle$ as a function of coupling and bare mass is fitted to an empirical equation of state; the resulting critical exponents are significantly altered from previously obtained values, and for the first time resemble those emerging from analytic predictions based on approximate solutions to Schwinger-Dyson equations, consistent with a putative UV-stable renormalisation group fixed point. To address the non-perturbative issue of the value $N_c$ below which such a fixed point exists we present preliminary results obtained with $N=2$.

hep-lat↗

arXiv2025

Approaching the continuum with anisotropic lattice thermodynamics

The FASTSUM collaboration has a long-standing programme of using anisotropic lattice QCD to investigate strong interaction thermodynamics, and in particular spectral quantities. Here we present first results from our new ensemble which has a temporal lattice spacing a_t=15am and anisotropy xi=a_s/a_t=7, giving unprecedented resolution in the temporal direction. We show results for the chiral transition, vector-axial-vector degeneracy, and heavy quarkonium, and compare them with earlier results with coarser time resolution.

hep-lat↗

arXiv2025

Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation

We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localized charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centers. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density $k = 2{\pi}{\rho}$, providing non-perturbative evidence for chiral spirals beyond the large-N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.

hep-lat↗

arXiv2025

Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions

We present results of a lattice field theory simulation of the 2+1$d$ Thirring model with $N=1$ fermion flavors, using domain wall fermions. The model exhibits a U(2) symmetry-breaking phase transition with the potential to define a UV-stable renormalisation group fixed point. The novelty is the replacement of the Shamir kernel used in all previous work with the Wilson kernel, improving the action particularly with respect to the $L_s\to\infty$ limit needed to recover U(2), now under much better control. Auxiliary field ensembles generated on $16^3\times24$ with varying self-interaction strength $g^2$ and bare mass $m$ are used to measure the bilinear condensate order parameter $\langle\bar\psi i\gamma_3\psi\rangle$ with domain wall separations as large as $L_s=120$. The resulting $L_s\to\infty$ extrapolation is used to fit an empirical equation of state modelling spontaneous symmetry breaking as $m\to0$. The fit is remarkably stable and compelling, with the fitted critical exponents $\beta_m\simeq2.4$, $\delta\simeq1.3$ differing markedly from previous estimates. The associated susceptibility exhibits a mass hierarchy in line with physical expectations, again unlike previous estimates. Schwinger-Dyson equation (SDE) solutions of the Thirring model exploiting a hidden local symmetry in the action are reviewed, and analytic predictions presented for the exponents. In contrast to all previous lattice studies, the universal characteristics of the critical point revealed qualitatively resemble the SDE predictions.

hep-lat↗

arXiv2024

Dense QC$_2$D. What's up with that?!?

We present recent updates and results from QC$_2$D (Two Colour QCD) simulations at non-zero baryon density, including progress toward determining the speed of sound.

hep-lat↗

arXiv2024

Thermal lattice QCD results from the FASTSUM collaboration

The FASTSUM Collaboration has developed a comprehensive research programme in thermal lattice QCD using 2+1 flavour ensembles. We review our recent hadron spectrum analyses of open charm mesons and charm baryons at non-zero temperature. We also detail our determination of the interquark potential in the bottomonium system using NRQCD quarks. All of our work uses anisotropic lattices where the temporal lattice spacing is considerably finer than the spatial one allowing better resolution of temporal correlation functions.

hep-lat↗

arXiv2024

Prediction of Multiscale Features Using Deep Learning-based Preconditioner-Solver Architecture for Darcy Equation in High-Contrast Media

Modeling subsurface fluid flow in porous media is crucial for applications such as oil and gas exploration. However, the inherent heterogeneity and multi-scale characteristics of these systems pose significant challenges in accurately reconstructing fluid flow behaviors. To address this issue, we proposed Fourier Preconditioner-based Hierarchical Multiscale Net (FP-HMsNet), an efficient hierarchical preconditioner-learner architecture that combines Fourier Neural Operators (FNO) with multi-scale neural networks to reconstruct multi-scale basis functions of high-dimensional subsurface fluid flow. Using a dataset comprising 102,757 training samples, 34,252 validation samples, and 34,254 test samples, we ensured the reliability and generalization capability of the model. Experimental results showed that FP-HMsNet achieved an MSE of 0.0036, an MAE of 0.0375, and an R2 of 0.9716 on the testing set, significantly outperforming existing models and demonstrating exceptional accuracy and generalization ability. Additionally, robustness tests revealed that the model maintained stability under various levels of noise interference. Ablation studies confirmed the critical contribution of the preconditioner and multi-scale pathways to the model's performance. Compared to current models, FP-HMsNet not only achieved lower errors and higher accuracy but also demonstrated faster convergence and improved computational efficiency, establishing itself as the state-of-the-art (SOTA) approach. This model offers a novel method for efficient and accurate subsurface fluid flow modeling, with promising potential for more complex real-world applications.

physics.flu-dyn↗

arXiv2024

Evaluation of the Bilinear Condensate of the Planar Thirring Model in the Strongly Coupled Region

The planar Thirring model is thought to have a strongly coupled critical point for a single flavour of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterisation via an equation of state. Since the computation is numerically challenging we investigate improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte Carlo scheme, and calculations of the bilinear condensate, an equation of state, and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered.

hep-lat↗

arXiv2023

The Thirring Model in 2+1$d$ with Optimised Domain Wall Fermions

After briefly reviewing the potential for the $N$-flavor Thirring model, formulated with reducible fermions in 2+1$d$, to exhibit a strongly-coupled UV-stable fixed point where U($2N$) symmetry is spontaneously broken by a fermion bilinear condensate, we present recent lattice studies using the Domain Wall Fermion formulation. In particular, we focus on possible improved methods for extracting the necessary $L_s\to\infty$ limit, where $L_s$ is the wall separation, through a combination of partial quenching (ie. $L_s({\rm valence})>L_s({\rm sea})$), replacing the Shamir kernel with the Wilson kernel in the definition of the overlap operator, and improved estimation of the signum function using the Zolotarev approximation. Equation of state fits for critical exponents on $12^3$ systems yield encouraging agreement between distinct approaches, consistent with universal scaling, while contradicting earlier fits based on a naive extrapolation. The new results are also in tension with old results obtained with staggered fermions.

hep-lat↗

arXiv2023

Recent Results from the FASTSUM Collaboration

The FASTSUM Collaboration has developed a comprehensive research programme in thermal QCD using 2+1 flavour, anisotropic ensembles. In this talk, we summarise some of our recent results including thermal hadron spectrum calculations using our ``Generation 2L'' ensembles which have pion masses of 239(1) MeV. These include open charm mesons and charm baryons. We also summarise our work using the Backus Gilbert approach to determining the spectral function of the NRQCD bottomonium system. Finally, we review our determination of the interquark potential in the same system, but using our ``Generation 2'' ensembles which have heavier pion masses of 384(4) MeV.

hep-lat↗

arXiv2022

Hadrons at high temperature: an update from the FASTSUM collaboration

We present the most recent results from the FASTSUM collaboration for hadron properties at high temperature. This includes the temperature dependence of the light and charmed meson and baryon spectrum, as well as properties of heavy quarkonia. The results are obtained using anisotropic lattices with a fixed scale approach. We also present the status of our next generation gauge ensembles.

hep-lat↗

arXiv2022

Thermal Transitions in Dense Two-Colour QCD

The infamous sign problem makes it impossible to probe dense (baryon density $\mu_B>0$) QCD at temperatures near or below the deconfinement threshold. As a workaround, one can explore QCD-like theories such as two-colour QCD (QC2D) which don't suffer from this sign problem but are qualitively similar to real QCD. Previous studies on smaller lattice volumes have investigated deconfinement and colour superfluid to normal matter transitions. In this study we look at a larger lattice volume $N_s=24$ in an attempt to disentangle finite volume and finite temperature effects. We also fit to a larger number of diquark sources to better allow for extrapolation to zero diquark source.

hep-lat↗

arXiv2022

Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions

We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in 2+1+1 dimensions and perform $N=1$ flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous $\mathrm{U}(2)\rightarrow\mathrm{U}(1)\otimes \mathrm{U}(1)$ symmetry breaking; we analyse the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension $\eta_\psi\approx 3$ at the critical point, in stark contrast with the Gross-Neveu model in 3$d$ and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalisable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions.

hep-lat↗

arXiv2022

Open charm mesons at nonzero temperature: results in the hadronic phase from lattice QCD

We study what happens to D and D_s mesons as the temperature increases, using lattice QCD simulations with N_f=2+1 dynamical flavours on anistropic lattices. We have access to five temperatures in the hadronic phase. Using the determined groundstate mass at the lowest temperature, we investigate the effect of rising temperature by analysing ratios of mesonic correlators, without the need for further fitting or spectral reconstruction. In the pseudoscalar and vector channels, we demonstrate that temperature effects are at the percent level and can be captured by a reduction of the groundstate mass as the thermal crossover is approached. In the axial-vector and scalar channels on the other hand, temperature effects are prominent throughout the hadronic phase.

hep-lat↗

arXiv2021

Properties of Overlap and Domain Wall Fermions in the 2+1D Thirring Model

We present some results pertaining to partially quenched formulations of the overlap/domain wall operator with the Thirring model in 2+1D. Auxiliary fields are generated with a Shamir domain wall approach and measurements of eigenvalues and condensates are contrasted with different overlap operators. The numerical challenge posed by a non-compact formulation is highlighted, and the effective use of lower accuracy sea fermions is demonstrated.

hep-lat↗

arXiv2021

Meson thermal masses at different temperatures

We determine the ground state meson masses at low temperature using simulations with $2+1$ flavours of improved Wilson-clover fermions. Subsequently we study the effect of increasing the temperature of the hadron gas, including the transition to the quark-gluon plasma, as well as the restoration of $SU(2)_A$ chiral symmetry. We use the FASTSUM anisotropic, fixed-scale Generation2L ensembles and consider mesons with light, strange and charm content.

hep-lat↗

arXiv2021

Critical Behaviour in the Single Flavor Planar Thirring Model

We report results of simulations of the $2+1d$ Thirring model with $N$ fermion flavors, defined on a lattice using domain wall fermions. This approach is devised to respect as far as possible the underlying U($2N$) symmetry of the continuum model, expected to be recovered in the limit wall separation $L_s\to\infty$. For $N=1$ there is a symmetry-breaking phase transition associated with bilinear condensation at strong fermion self-interaction, which is a plausible location for a quantum critical point. Fits to a renormalisation group-inspired equation of state yield critical exponents distinct from those obtained using a version of the model defined using staggered fermions.

hep-lat↗