arXiv subjects

Giovanni Cataldi

Publications and source records attributed to Giovanni Cataldi.

12 recordsLinked to original sources

arXiv2026

Real-Time String Dynamics in $3+1$D Lattice Quantum Electrodynamics

Understanding real-time string dynamics in three spatial dimensions is essential for connecting quantum simulations of lattice gauge theories (LGTs) to the physical dimensionality of QED and QCD, where transverse fluctuations and competing local processes proliferate. We present the first real-time simulations of string breaking in $3+1$D lattice quantum electrodynamics. Using tree tensor networks, we simulate the quench dynamics of electric flux strings in a $3\!+\!1$D U(1) LGT with dynamical matter. At strong coupling, the string breaks resonantly at a sharp resonance condition of mass and gauge couplings, converting electric energy into matter--antimatter pairs that screen the static charges. Off resonance, we classify all competing channels---pair production, string deformations and extensions, and flux loops---whose multiplicity, extensive for pair production and flux loops, depletes the string sector even far from resonance. A channel-resolved perturbation theory quantitatively reproduces these dynamics and their Fourier spectrum. Our results establish diagnostics and benchmarks for upcoming quantum simulators of higher-dimensional LGTs.

hep-lat↗

arXiv2026

Non-Abelian string melting and thermalization in an open lattice gauge theory

Open-system lattice gauge theory (LGT) has so far been developed predominantly in Abelian settings, leaving open how genuinely non-Abelian gauge structure reshapes dissipative real-time dynamics. Here, we study a $1+1$D SU(2) Yang--Mills LGT with dynamical matter coupled to a thermal scalar environment through a gauge-preserving Lindblad evolution, which we solve using tensor networks. Starting from a quark--antiquark pair connected by a chromoelectric flux string, we find that the thermal medium melts the string by delocalizing the color charges and screening the flux; on resonance, this dissipative melting competes with and delays coherent string breaking. The thermalization time is non-monotonic in the environment coupling, decreasing through environment-assisted transport at weak dissipation before increasing in a quantum-Zeno regime. In the strong-dephasing limit, a Schrieffer--Wolff expansion maps the dynamics to a classical exclusion process and yields the Liouvillian thermalization time analytically. Beyond these generic open-system effects, the non-Abelian matter structure produces a systematic mesonic bias in the steady state, while the thermalization time decreases with temperature, in contrast to the Abelian Schwinger model trend and in qualitative agreement with pNRQCD studies of the quark--gluon plasma. These results establish a gauge-preserving framework for thermalization and string dynamics in open non-Abelian lattice gauge theories.

hep-lat↗

arXiv2026

Quantum Resources in Disorder-Free Localization Dynamics of Gauge Theories

Quantum-state complexity diagnostics provide valuable insight into many-body dynamics, information scrambling, and quantum computation. Here, we investigate the real-time dynamics of quantum complexity in $1+1$-dimensional Abelian U(1) and non-Abelian SU(2) lattice gauge theories (LGTs), focusing on the disorder-free localization (DFL) regime. Using stabilizer R\'enyi entropy, participation R\'enyi entropy, and fermionic non-Gaussianity as measures of complexity, we observe, for both theories, two main behaviors as a function of the gauge coupling: at intermediate values, a power-law relaxation towards saturation, consistent with observations in many-body localization, and, at sufficiently large values, an ultraslow double-logarithmic growth, which we substantiate with a configuration-space bound verified by exact counting. Our results not only provide deeper insight into the dynamics of DFL but also highlight the role of gauge invariance in constraining quantum resources and are relevant to recent quantum simulations of LGTs.

quant-ph↗

arXiv2025

Optimal local basis truncation of lattice quantum many-body systems

We show how to optimally reduce the local Hilbert basis of lattice quantum many-body (QMB) Hamiltonians. The basis truncation exploits the most relevant eigenvalues of the estimated single-site reduced density matrix (RDM). It is accurate and numerically stable across different model phases, even close to quantum phase transitions. We apply this procedure to different models, such as the Sine-Gordon model, the $\varphi^{4}$ theory, and lattice gauge theories, namely Abelian $\mathrm{U}(1)$ and non-Abelian $\mathrm{SU}(2)$, in one and two spatial dimensions. Our results reduce state-of-the-art estimates of computational resources for classical and quantum simulations.

cond-mat.str-el↗

arXiv2025

Real-Time String Dynamics in a $2+1$D Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction

Understanding flux string dynamics can provide insight into quark confinement and hadronization. First-principles quantum and numerical simulations have mostly focused on toy-model Abelian lattice gauge theories (LGTs). With the advent of state-of-the-art quantum simulation experiments, it is important to bridge this gap and study string dynamics in non-Abelian LGTs beyond one spatial dimension. Using tensor network methods, we simulate the real-time string dynamics of a $2\!+\!1$D SU$(2)$ Yang--Mills LGT with dynamical matter. In the strong-coupling regime and at resonance, string breaking occurs through sharp Casimir reduction along with meson and baryon-antibaryon formation, a distinctively non-Abelian feature. At finite baryon density, we discover a \textit{baryon blockade} mechanism that delays string breaking. Away from resonance, the magnetic term drives purely non-Abelian fluctuations: glueball loops and self-crossed strings that resolve two SU$(2)$ intertwiners with distinct dynamics. For higher-energy strings, we uncover representation-dependent tension-reduction resonances. Our findings serve as a guide for upcoming quantum simulators of non-Abelian LGTs.

hep-lat↗

arXiv2025

Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory

We investigate how isolated quantum many-body systems dynamically equilibrate under non-Abelian gauge-symmetry constraints. By encoding gauge superselection sectors into static $\mathrm{SU}(2)$ background charges, we map out the dynamical phase diagram of a (1+1)D $\mathrm{SU}(2)$ lattice gauge theory with dynamical matter. We uncover three distinct regimes: (i) an ergodic phase, (ii) a fragmented phase that is nonthermal but delocalized, and (iii) a disorder-free many-body localized regime. In the latter, a superposition of gauge superselection sectors preserves spatial matter inhomogeneities in time, as evidenced by distinct temporal scalings of entropy. We highlight the non-Abelian nature of these phases and argue for potential realizations on qudit processors.

cond-mat.quant-gas↗

arXiv2025

Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods

This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.

hep-lat↗

arXiv2024

Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap

Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories approaching relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. In this work, we review the state-of-the-art of Tensor Network methods and discuss a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories.

hep-lat↗

arXiv2024

Quantum Many-Body Scarring in a Non-Abelian Lattice Gauge Theory

Quantum many-body scarring (QMBS) is an intriguing mechanism of weak ergodicity breaking that has recently spurred significant attention. Particularly prominent in Abelian lattice gauge theories (LGTs), an open question is whether QMBS nontrivially arises in non-Abelian LGTs. Here, we present evidence of robust QMBS in a non-Abelian SU(2) LGT with dynamical matter. Starting in product states that require little experimental overhead, we show that prominent QMBS arises for certain quenches, facilitated through meson and baryon-antibaryon excitations, highlighting its non-Abelian nature. The uncovered scarred dynamics manifests as long-lived coherent oscillations in experimentally accessible local observables as well as prominent revivals in the state fidelity. Our findings bring QMBS to the realm of non-Abelian LGTs, highlighting the intimate connection between scarring and gauge symmetry, and are amenable for observation in a recently proposed trapped-ion qudit quantum computer.

cond-mat.quant-gas↗

arXiv2023

Digital quantum simulation of lattice fermion theories with local encoding

We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and two-qubit gates and is scalable since integrating each Hamiltonian term requires a finite (non-scaling) cost. The exact local fermion encoding we adopt relies on auxiliary $\mathbb{Z}_2$ lattice gauge fields by adding a pure gauge Hamiltonian term akin to the Toric Code. By numerically emulating the quantum simulator real-time dynamics, we observe a timescale separation for spin- and charge-excitations in a spin-$\frac{1}{2}$ Hubbard ladder in the $t-J$ model limit.

quant-ph↗

arXiv2023

Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks

We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes (>30 matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. At intermediate system sizes, we detect a liquid phase of quark-pair bound-state quasiparticles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: For low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order.

hep-lat↗

arXiv2021

Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency

We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to $64\times64$, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.

quant-ph↗