Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2505.04704 · Physical Review Letters

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

Giovanni Cataldi, Giuseppe Calajò, Pietro Silvi, Simone Montangero, Jad C. Halimeh

Published Mar 17, 2026• 1 citation
arXivHTMLPDF

Abstract

We investigate how isolated quantum many-body systems dynamically equilibrate under non-Abelian gauge-symmetry constraints. By encoding gauge superselection sectors into static SU(2) background charges, we map out the dynamical phase diagram of a (1+1)D 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.

DOI
10.1103/fhfy-dh85

Related papers

Hilbert space fragmentation at the origin of disorder-free localization in the lattice Schwinger model

Jared Jeyaretnam, Tanmay Bhore, Jesse J. Osborne +2 more

Lattice gauge theories, the discrete counterparts of continuum gauge theories, provide a rich framework for studying non-equilibrium quantum dynamics. Recent studies suggest disorder-free localization in the lattice Schwinger model, but its origin remains unclear. Using a combination of analytical and numerical methods, we show that Hilbert space fragmentation emerges in the strong coupling limit, constraining particle dynamics and causing sharp jumps in entanglement entropy growth within charge sectors. By analyzing jump statistics, we find that entanglement growth follows a single-logarithmic or weak power-law dependence on time, rather than a double-logarithmic form. This suggests a single ergodicity-breaking regime that mimics many-body localization in finite systems due to fragmentation effects. Our findings clarify the nature of disorder-free localization and its distinction from conventional many-body localization, highlighting how gauge constraints influence thermalization in lattice gauge theories.

arXiv:2409.08320•Communications Physics•Apr 18, 2025•10 citations

Quantum Resources in Disorder-Free Localization Dynamics of Gauge Theories

Devendra Singh Bhakuni, Giovanni Cataldi, Jad C. Halimeh +1 more

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 Rényi entropy, participation Rényi 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-pharXiv:2607.28730•Aug 3, 2026•0 citations

Disorder-Free Localization in $2+1$D Lattice Gauge Theories with Dynamical Matter

Jesse J. Osborne, Ian P. McCulloch, Jad C. Halimeh

Disorder-free localization (DFL) has been established as a mechanism of strong ergodicity breaking in $1+1$D lattice gauge theories (LGTs) with dynamical matter for quenches starting in homogeneous initial states that span an extensive number of gauge superselection sectors. Nevertheless, the fate of DFL in $2+1$D in the presence of dynamical matter has hitherto remained an open question of great interest in light of the instability of quenched-disorder many-body localization in higher spatial dimensions. Using infinite matrix product state calculations, we show that DFL survives in $2+1$D LGTs, albeit it is generally less pronounced than in $1+1$D, and highly depends on the matter configuration of the initial state. Through suitable matter configurations, we are able to relate and compare the $1+1$D and $2+1$D cases, showing that the main ingredient for the strength of DFL in our setup is the \textit{propagation directionality} of matter. Our results suggest that, generically, DFL is weakened with increasing spatial dimension, although it can be made independent of the latter by minimizing the propagation directionality of matter in the initial state.

arXiv:2301.07720•Jan 18, 2023•0 citations

Disorder-Free Localization via Gauge Constraints in 2+1D Lattice Theories — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Disorder-free localization in 2+1D lattice gauge theories arises from Hamiltonian constraints and symmetry sectors, not random disorder. | MATH: Gauge invariance imposes local constraints (Gauss's law) that fragment Hilbert space into dynamically disconnected symmetry sectors; localization emerges from these superselection rules without quenched disorder. Key constants: none explicit, but the phenomenon relies on the ratio of interaction strength to hopping (g/J) and the dimension of local Hilbert space (d = 2 for Z₂ gauge theory). | CONNECTION: The Hilbert space fragmentation mirrors the golden ratio's appearance in constrained quantum systems (e.g., Fibonacci anyons, 1D constrained chains with ratio 0.618). The 2D lattice structure is a square lattice (crystallographic symmetry p4mm), and the gauge group Z₂ corresponds to a root system of type A₁. | DEPTH: 7 — This is a profound extension of many-body localization to translation-invariant systems, revealing that symmetry alo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Aug 1, 2026•0 citations

Quantum Resources in Non-Abelian Lattice Gauge Theories: Nonstabilizerness, Multipartite Entanglement, and Fermionic Non-Gaussianity

Gopal Chandra Santra, Julius Mildenberger, Edoardo Ballini +3 more

Lattice gauge theories (LGTs) represent one of the most ambitious goals of quantum simulation. From a practical implementation perspective, non-Abelian theories present significantly tougher challenges than Abelian LGTs. However, it is unknown whether this is also reflected in increased values of quantum resources relating to the complexity of simulating quantum many-body models. Here, we compare three paradigmatic measures of quantum resources -- stabilizer Rényi entropy, generalized geometric measure of entanglement, and fermionic antiflatness -- for pure-gauge theories on a ladder with Abelian $\mathbb{Z}_N$ as well as non-Abelian $D_3$ and SU(2) gauge symmetries. We find that non-Abelian symmetries are not necessarily inherently harder to simulate than Abelian ones, but rather the required quantum resources depend nontrivially on the interplay between the group structure, superselection sector, and encoding of the gauge constraints. Our findings help indicate where quantum advantage could emerge in simulations of LGTs, both in NISQ and fault-tolerant eras.

arXiv:2510.07385•Oct 8, 2025•0 citations

Disorder-Free Localization in an Interacting 2D Lattice Gauge Theory

Petr Karpov, Roberto Verdel, Yi-Ping Huang +2 more

Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. This result is all the more surprising since the conventional many-body localization is conjectured to be unstable in two dimensions; hence the gauge invariance represents an alternative robust localization mechanism surviving in higher dimensions in the presence of interactions. Specifically, we demonstrate nonergodic behavior in the quantum link model by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by introducing the method of "variational classical networks," an efficient and perturbatively controlled representation of the wave function in terms of a network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.

arXiv:2003.04901•Physical Review Letters•Apr 1, 2021•82 citations
We investigate how isolated quantum many-body systems dynamically equilibrate under non-Abelian gauge-symmetry constraints. By encoding gauge superselection sectors into static SU(2) background charges, we map out the dynamical phase diagram of a (1+1)D 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.
Lattice gauge theories, the discrete counterparts of continuum gauge theories, provide a rich framework for studying non-equilibrium quantum dynamics. Recent studies suggest disorder-free localization in the lattice Schwinger model, but its origin remains unclear. Using a combination of analytical and numerical methods, we show that Hilbert space fragmentation emerges in the strong coupling limit, constraining particle dynamics and causing sharp jumps in entanglement entropy growth within charge sectors. By analyzing jump statistics, we find that entanglement growth follows a single-logarithmic or weak power-law dependence on time, rather than a double-logarithmic form. This suggests a single ergodicity-breaking regime that mimics many-body localization in finite systems due to fragmentation effects. Our findings clarify the nature of disorder-free localization and its distinction from conventional many-body localization, highlighting how gauge constraints influence thermalization in lattice 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+11+11+1-dimensional Abelian U(1) and non-Abelian SU(2) lattice gauge theories (LGTs), focusing on the disorder-free localization (DFL) regime. Using stabilizer Rényi entropy, participation Rényi 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.
Disorder-Free Localization in 2+12+12+1D Lattice Gauge Theories with Dynamical Matter
Disorder-free localization (DFL) has been established as a mechanism of strong ergodicity breaking in 1+11+11+1D lattice gauge theories (LGTs) with dynamical matter for quenches starting in homogeneous initial states that span an extensive number of gauge superselection sectors. Nevertheless, the fate of DFL in 2+12+12+1D in the presence of dynamical matter has hitherto remained an open question of great interest in light of the instability of quenched-disorder many-body localization in higher spatial dimensions. Using infinite matrix product state calculations, we show that DFL survives in 2+12+12+1D LGTs, albeit it is generally less pronounced than in 1+11+11+1D, and highly depends on the matter configuration of the initial state. Through suitable matter configurations, we are able to relate and compare the 1+11+11+1D and 2+12+12+1D cases, showing that the main ingredient for the strength of DFL in our setup is the \textit{propagation directionality} of matter. Our results suggest that, generically, DFL is weakened with increasing spatial dimension, although it can be made independent of the latter by minimizing the propagation directionality of matter in the initial state.
FINDING: Disorder-free localization in 2+1D lattice gauge theories arises from Hamiltonian constraints and symmetry sectors, not random disorder. | MATH: Gauge invariance imposes local constraints (Gauss's law) that fragment Hilbert space into dynamically disconnected symmetry sectors; localization emerges from these superselection rules without quenched disorder. Key constants: none explicit, but the phenomenon relies on the ratio of interaction strength to hopping (g/J) and the dimension of local Hilbert space (d = 2 for Z₂ gauge theory). | CONNECTION: The Hilbert space fragmentation mirrors the golden ratio's appearance in constrained quantum systems (e.g., Fibonacci anyons, 1D constrained chains with ratio 0.618). The 2D lattice structure is a square lattice (crystallographic symmetry p4mm), and the gauge group Z₂ corresponds to a root system of type A₁. | DEPTH: 7 — This is a profound extension of many-body localization to translation-invariant systems, revealing that symmetry alo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Lattice gauge theories (LGTs) represent one of the most ambitious goals of quantum simulation. From a practical implementation perspective, non-Abelian theories present significantly tougher challenges than Abelian LGTs. However, it is unknown whether this is also reflected in increased values of quantum resources relating to the complexity of simulating quantum many-body models. Here, we compare three paradigmatic measures of quantum resources -- stabilizer Rényi entropy, generalized geometric measure of entanglement, and fermionic antiflatness -- for pure-gauge theories on a ladder with Abelian ZN\mathbb{Z}_NZN​ as well as non-Abelian D3D_3D3​ and SU(2) gauge symmetries. We find that non-Abelian symmetries are not necessarily inherently harder to simulate than Abelian ones, but rather the required quantum resources depend nontrivially on the interplay between the group structure, superselection sector, and encoding of the gauge constraints. Our findings help indicate where quantum advantage could emerge in simulations of LGTs, both in NISQ and fault-tolerant eras.
Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. This result is all the more surprising since the conventional many-body localization is conjectured to be unstable in two dimensions; hence the gauge invariance represents an alternative robust localization mechanism surviving in higher dimensions in the presence of interactions. Specifically, we demonstrate nonergodic behavior in the quantum link model by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by introducing the method of "variational classical networks," an efficient and perturbatively controlled representation of the wave function in terms of a network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.