arXiv subjects

Thomas Luu

Publications and source records attributed to Thomas Luu.

At least 19 recordsLinked to original sources

arXiv2026

The origin of excited states of the $\Lambda$ baryon at the SU(3) point from Lattice QCD

In this work we determine the finite-volume lattice QCD spectrum at the flavor symmetric $\mathrm{SU}(3)$ point in the meson-baryon singlet and octet irreducible representations. We construct the appropriate interpolation operators and perform the calculation on ensembles in quite large volume ($L=48$). We find three below-threshold energy levels, with the singlet having lower energy and the two octets being non-degenerate at one sigma, which for these large volumes ($M_{\pi} L\approx 14.5$) strongly suggests a bound state close to that energy at each of the irreducible representations. We confront this finite-volume spectrum with the prediction from UCHPT through the L\"uscher method finding qualitative agreement. Finally we perform a re-fit of UCHPT free parameters to the available (experimental and lattice) data including the energy levels calculated in this work. This allows us to follow the pole trajectories to the physical point, identifying the $\Lambda(1405)$ as a lower octet, and $\Lambda(1380)$ as a singlet bound state in the $\mathrm{SU(3)}$ limit. Furthermore, $\Lambda(1670)$ is identified on a qualitative level as the heavier octet bound state and its relation to three-body final states is discussed.

hep-lat↗

arXiv2026

The structure of the lightest positive-parity charmed mesons from LQCD

The nature of low-lying scalar and axial-vector charmed mesons has long been debated, specifically whether they are best explained as hadronic molecules or compact tetraquark systems. These two scenarios exhibit quite different features for the accessible $SU(3)$ multiplets in the scalar and axial-vector sectors. To resolve this debate, we performed $N_f=3+1$ lattice simulations and calculated the energy levels of the $SU(3)$ $[6]$ and $[\overline{15}]$ multiplets for both the scalar and axial-vector mesons in an $SU(3)$ flavor-symmetric setting. In both sectors we find attractive states for the [6] and repulsive interactions for the $[\overline{15}]$. This is consistent with the hadronic molecule picture, but not the compact tetraquark picture which predicts a low-lying $[\overline{15}]$ states in the axial-vector sector but not in the scalar sector.

hep-lat↗

arXiv2026

Stable Determinant Monte Carlo Simulations at Large Inverse Temperature $\beta$

At low temperatures $T$ where $1/T=\beta\gg1$ the na\"ive implementation of determinant quantum Monte Carlo (DQMC) methods suffers from loss of precision and numerical instabilities when evaluating the fermion determinant. This instability propagates into the calculation of observables that rely on the evaluation of the inverse of the fermion matrix, or the Greens function. For DQMC methods that rely on the Hamiltonian Monte Carlo (HMC) algorithm, an additional complication comes from evaluating the force terms required for integrating Hamilton's equations of motion, since here loss of precision and numerical instabilities are also prevalent. We show how to address all these issues using various choices of matrix decompositions, allowing us to simulate at $\beta\gtrsim 90$, which corresponds to room temperature for graphene structures. Furthermore, our implementation has numerical costs that scale similarly to the na\"ive implementation, namely as $\mathcal{O}(N_x^3N_t)$, where $N_x$ ($N_t$) is the number of spatial (temporal) sites.

physics.comp-ph↗

arXiv2026

Hamiltonian Monte Carlo enhanced by Exact Diagonalization

Strongly correlated fermionic systems are of great interest in condensed matter physics and numerical methods are indispensable tools for their study. However, existing approaches such as exact diagonalization (ED) and stochastic quantum Monte Carlo methods each suffer from fundamental limitations: ED is hindered by exponential scaling in system size, while Monte Carlo methods are plagued by sign problems and long autocorrelation times. These limitations restrict the accessible parameter space and developing algorithms that efficiently alleviate them remains a central challenge in computational physics. In this work, we propose a hybrid algorithm that combines ED and Hamiltonian Monte Carlo (HMC) to simulate 2D arrays of coupled quantum wires, modeled as interacting fermionic Hubbard chains. We demonstrate how our hybrid implementation of HMC, which we dub H$^2$MC, outperforms either method alone across several key simulation facets. When compared to pure ED, H$^2$MC has a much more favorable computational scaling, which allows us to push simulations to much larger 2D arrays. H$^2$MC also greatly alleviates the sign problem and reduces autocorrelation times when compared to pure HMC formulations utilizing either real or imaginary auxiliary fields. Our formalism demonstrates how complementary strengths of seemingly disparate methods can be leveraged to enable feasible simulations in an extended parameter space.

cond-mat.str-el↗

arXiv2026

Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows

The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.

cond-mat.str-el↗

arXiv2026

The Lambda 1405 at the $SU(3)$ point in lattice QCD

The pole structure of the $\Lambda(1405)$ has been a topic of debate for a long time. Chiral perturbation theory predicts that its experimental spectrum may be explained by a two pole structure originating in the $SU(3)$ chiral dynamics of the baryon-meson interaction. The $SU(3)$-symmetric flavor point is readily accessible in lattice QCD, in this work we study the baryon-meson states directly at this point. We construct interpolation operators that belong to the irreducible representations of $SU(3)$ that are attractive in the channel with the quantum numbers of the (singlet and two octets). The extracted energy levels can be used as input for chiral perturbation theory to find the poles associated with each representation. The relevant correlation functions are computed on $SU(3)$-symmetric ensembles with $M_{\pi}\approx 714$ MeV using the distillation technique.

hep-lat↗

arXiv2026

Toward Scalable Normalizing Flows for the Hubbard Model

Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures, with a focus on enhancing stability and efficiency. Additionally, we present the scaling behavior of stochastic normalizing flows and non-equilibrium Markov chain Monte Carlo methods for this fermionic system.

cond-mat.str-el↗

arXiv2025

Defect engineering spin centers in interacting many-body Su-Schrieffer-Heeger chains

The ability to engineer topologically distinct materials opens the possibility of enabling novel phenomena in low-dimensional nano-systems, as well as manufacturing novel quantum devices. One of the simplest examples, the SSH model with both even and odd number of sites, demonstrates the connection between localized edge states and the topology of the system. We show that the SSH model hosts localized spin centers due to the interplay between the localized edge states and the on-site Hubbard interaction. We further show how one can engineer any number of localized spin centers within the chain by careful addition of defects. These spin centers are paired in spin-singlet or spin-triplet channels within each block separated by the defects, and together they construct an array of spin singlet and/or triplet qubits. As this system is realizable experimentally, our findings describe a novel way for manipulating and engineering spin qubits and therefore provide a platform for performing many-body quantum simulations on spin excitations like magnons and triplons.

cond-mat.str-el↗

arXiv2025

Simulating Correlated Electrons with Symmetry-Enforced Normalizing Flows

We present the first proof of principle that normalizing flows can accurately learn the Boltzmann distribution of the fermionic Hubbard model - a key framework for describing the electronic structure of graphene and related materials. State-of-the-art methods like Hybrid Monte Carlo often suffer from ergodicity issues near the time-continuum limit, leading to biased estimates. Leveraging symmetry-aware architectures as well as independent and identically distributed sampling, our approach resolves these issues and achieves significant speed-ups over traditional methods.

cond-mat.str-el↗

arXiv2025

Fully ergodic simulations using radial updates

A sensible application of the Hybrid Monte Carlo (HMC) method is often hindered by the presence of large - or even infinite - potential barriers. These potential barriers separate the configuration space into distinct sectors and can lead to ergodicity violations that bias measurements. In this work, we address this problem by augmenting HMC with a multiplicative Metropolis-Hastings update in a so-called ''radial direction'' of the fields which enables crossing the potential barriers and ensures ergodicity of the sampling algorithm at comparably low computational cost. We demonstrate the algorithm on a simple toy model and show how it can be applied to the fermionic Hubbard model describing physics ranging from an exactly-solvable two-site system to the $C_{20}H_{12}$ perylene molecule. Our numerical results show that the radial updates successfully remove ergodicity violations, while simultaneously reducing autocorrelation times.

cond-mat.str-el↗

arXiv2025

Exclusion of a diquark-antidiquark structure for the lightest positive-parity charmed mesons

The nature of low-lying scalar and axial-vector charmed mesons has been debated for decades, with hadronic molecular and compact tetraquark models being prominent candidates. These two models predict quite different features for the accessible SU(3) multiplets in the scalar and axial-vector sectors, which can be tested through lattice calculations at SU(3) symmetric points. In this work, we perform lattice calculations for both scalar and axial-vector charmed mesons with an SU(3) symmetric pion mass about 613 MeV for the SU(3) $[6]$ and $[\overline{15}]$ multiplets. We find that the $[6]$ multiplet exhibits attractive interactions in both scalar and axial-vector sectors, while the $[\overline{15}]$ multiplet shows repulsive interactions in both sectors. The energy shifts in the scalar and axial-vector sectors are compatible with each other within uncertainties. These results are fully consistent with the hadronic molecular picture, while challenging the compact tetraquark model, which predicts the existence of low-lying $[\overline{15}]$ states in the axial-vector sector but not in the scalar sector.

hep-lat↗

arXiv2025

Search for Stable States in Two-Body Excitations of the Hubbard Model on the Honeycomb Lattice

We present one- and two-body measurements for the Hubbard model on the honeycomb (graphene) lattice from ab-initio quantum monte carlo simulations. Of particular interest is excitons, which are particle/hole excitations in low-dimensional systems. They are analogous to the pion in QCD, but without confinement, the question of whether they are bound and stable is of great interest in the condensed matter arena. By measuring one- and two-body correlators across various spin and isospin channels we can compute two-body energies relative to their thresholds, ultimately allowing us to check for stable states.

cond-mat.str-el↗

arXiv2025

Exploring Group Convolutional Networks for Sign Problem Mitigation via Contour Deformation

The sign problem that arises in Hybrid Monte Carlo calculations can be mitigated by deforming the integration manifold. While simple transformations are highly efficient for simulation, their efficacy systematically decreases with decreasing temperature and increasing interaction. Machine learning models have demonstrated the ability to push further, but require additional computational effort and upfront training. While neural networks possess the capacity to learn physical symmetries through proper training, there are anticipated advantages associated with encoding them into the network's structure. These include enhanced accuracy, accelerated training, and improved stability. The objective of the present study is twofold. First, we investigate the benefits of group convolutional models in comparison to fully connected networks, with a specific focus on the effects on the sign problem and on computational aspects. Second, we examine their capabilities for transfer learning, demonstrating the ability to further reduce training cost. We perform our investigations on the Hubbard model on select low-dimensional systems.

cond-mat.dis-nn↗

arXiv2025

Simulating the Hubbard Model with Equivariant Normalizing Flows

Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In the context of lattice field theory, normalizing flows have been successfully applied to accurately learn the Boltzmann distribution, enabling a range of tasks such as direct estimation of thermodynamic observables and sampling independent and identically distributed (i.i.d.) configurations. In this work, we present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model. This model is widely employed to study the electronic structure of graphene and other carbon nanomaterials. State-of-the-art numerical simulations of the Hubbard model, such as those based on Hybrid Monte Carlo (HMC) methods, often suffer from ergodicity issues, potentially leading to biased estimates of physical observables. Our numerical experiments demonstrate that leveraging i.i.d.\ sampling from the normalizing flow effectively addresses these issues.

cond-mat.str-el↗

arXiv2024

Quantum sampling on a quantum annealer for large volumes in the strong coupling limit for gauge group U(3)

In our previous studies [1, 2], we confirmed that a quantum annealer can be used for importance sampling of gauge theories. In this paper, we extend the previous results to larger 2-dimensional and 4-dimensional lattices to generate ensembles for U(3) gauge theory in the strong coupling limit. We make use of the D-Wave quantum annealer to generate histograms for sub-lattices, and use the Metropolis-Hastings algorithm to determine thermodynamic observables and their dependence on the physical parameters on large volumes. We benchmark our results to those obtained from classical Monte Carlo simulations.

hep-lat↗

arXiv2024

Hubbard interaction at finite $T$ on a hexagonal lattice

The temporal finite volume induces significant effects in Monte Carlo simulations of systems in low dimensions, such as graphene, a 2-D hexagonal system known for its unique electronic properties and numerous potential applications. In this work, we explore the behavior of fermions on a hexagonal sheet with a Hubbard-type interaction characterized by coupling $U$. This system exhibits zero or near zero-energy excitations that are highly sensitive to finite temperature effects. We compute corrections to the self-energy and the effective mass of low-energy excitations, arriving at a quantization condition that includes the temporal finite volume. These analyses are then conducted for both zero and finite temperatures. Our findings reveal that the first-order $\mathcal{O}(U)$ contributions are absent, leading to non-trivial corrections starting at $\mathcal{O}(U^2)$. We validate our calculations against exact and numerical results obtained from Hybrid Monte Carlo simulations on small lattices.

cond-mat.str-el↗

arXiv2024

Overcoming Ergodicity Problems of the Hybrid Monte Carlo Method using Radial Updates

Despite its many advantages, the sensible application of the Hybrid Monte Carlo (HMC) method is often hindered by the presence of large - or even infinite - potential barriers. These potential barriers partition the configuration space into distinct sectors, which leads to ergodicity violations and biased measurements of observables. In this work, we address this problem by augmenting the HMC method with a multiplicative Metropolis-Hastings update in a so-called "radial direction" of the fields, which enables jumps over the aforementioned potential barriers at comparably low computational cost. The effectiveness of this approach is demonstrated for the Hubbard model, formulated in a non-compact space by means of a continuous Hubbard-Stratonovich transformation. Our numerical results show that the radial updates successfully resolve the ergodicity violation, while simultaneously reducing autocorrelations.

cond-mat.str-el↗

arXiv2024

Reducing the Sign Problem with simple Contour Deformation

We apply constant imaginary offsets to the path integral for a reduction of the sign problem in the Hubbard model. These simple transformations enhance the quality of results from HMC calculations without compromising the speed of the algorithm. This method enables us to efficiently calculate systems that are otherwise inaccessible due to a severe sign problem. To support this claim, we present observables of the C20 and C60 fullerenes. Furthermore, we demonstrate that at a certain offset, the sign problem is completely lifted in the limit of large chemical potential.

cond-mat.str-el↗