arXiv:2203.01338 · Physical review. B./Physical review. B

Disorder-free localization with Stark gauge protection

Haifeng Lang, Philipp Hauke, Johannes Knolle, Fabian Grusdt, Jad C. Halimeh

Published Nov 18, 2022• 18 citations

Abstract

A paradigm of strong ergodicity breaking -- disorder-free localization (DFL) -- offers a fundamental probe of out-of-equilibrium quantum many-body physics and also promises potential applications in quantum information technology. As such, stabilizing DFL against errors on modern quantum simulators becomes of paramount importance. Here, the authors introduce the concept of Stark gauge protection, which comprises an experimentally friendly sum of local symmetry generators each weighted by its spatial location. This stabilizes DFL up to all investigated evolution times.

DOI: 10.1103/physrevb.106.174305

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arXiv:2203.01338 · Physical review. B./Physical review. B

Disorder-free localization with Stark gauge protection

Haifeng Lang, Philipp Hauke, Johannes Knolle, Fabian Grusdt, Jad C. Halimeh

Published Nov 18, 2022• 18 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.106.174305

Related papers

Stabilizing Disorder-Free Localization

Jad C. Halimeh, Hongzheng Zhao, Philipp Hauke +1 more

Disorder-free localization is a paradigm of nonergodicity in translation-invariant quantum many-body systems hosting gauge symmetries. The quench dynamics starting from simple initial states, which correspond to extensive superpositions of gauge superselection sectors, exhibits many-body localization with the system dynamically inducing its own disorder. An open question concerns the stability of disorder-free localization in the presence of gauge-breaking errors, and whether processes due to the latter can be controllably suppressed. Here, we show that translation-invariant \textit{single-body gauge terms} induce a quantum Zeno effect that reliably protects disorder-free localization against errors up to times at least polynomial in the protection strength. Our experimentally feasible scheme not only shows that disorder-free localization can be reliably stabilized, but also opens promising prospects for its observation in quantum simulators.Disorder-free localization is a paradigm of nonergodicity in translation-invariant quantum many-body systems hosting gauge symmetries. The quench dynamics starting from simple initial states, which correspond to extensive superpositions of gauge superselection sectors, exhibits many-body localization with the system dynamically inducing its own disorder. An open question concerns the stability of disorder-free localization in the presence of gauge-breaking errors, and whether processes due to the latter can be controllably suppressed. Here, we show that translation-invariant \textit{single-body gauge terms} induce a quantum Zeno effect that reliably protects disorder-free localization against errors up to times at least polynomial in the protection strength. Our experimentally feasible scheme not only shows that disorder-free localization can be reliably stabilized, but also opens promising prospects for its observation in quantum simulators.

arXiv:2111.02427Nov 3, 20211 citation

Disorder-free localization as a purely classical effect

Pablo Sala, Giuliano Giudici, Jad C. Halimeh

Disorder-free localization (DFL) is an ergodicity-breaking mechanism that has been shown to occur in lattice gauge theories in the quench dynamics of initial states spanning an extensive number of gauge superselection sectors. Whether this type of DFL is intrinsically a quantum interference effect or can arise classically has hitherto remained an open question whose resolution is pertinent to further understanding the far-from-equilibrium dynamics of gauge theories. In this work, we utilize cellular automaton circuits to model the quench dynamics of large-scale quantum link model (QLM) formulations of $(1+1)\mathrm{D}$ quantum electrodynamics, showing excellent agreement with the exact quantum case for small system sizes. Our results demonstrate that DFL persists in the thermodynamic limit as a purely classical effect arising from the finite-size regularization of the gauge-field operator in the QLM formulation, and that quantum interference, though not a necessary condition, may be employed to enhance DFL.Disorder-free localization (DFL) is an ergodicity-breaking mechanism that has been shown to occur in lattice gauge theories in the quench dynamics of initial states spanning an extensive number of gauge superselection sectors. Whether this type of DFL is intrinsically a quantum interference effect or can arise classically has hitherto remained an open question whose resolution is pertinent to further understanding the far-from-equilibrium dynamics of gauge theories. In this work, we utilize cellular automaton circuits to model the quench dynamics of large-scale quantum link model (QLM) formulations of $(1+1)\mathrm{D}$ quantum electrodynamics, showing excellent agreement with the exact quantum case for small system sizes. Our results demonstrate that DFL persists in the thermodynamic limit as a purely classical effect arising from the finite-size regularization of the gauge-field operator in the QLM formulation, and that quantum interference, though not a necessary condition, may be employed to enhance DFL.

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Disorder-free quantum many-body localization can strongly suppress transport while still enabling the dynamical buildup of computationally costly non-Clifford resources. In a tilted transverse-field Ising chain realizing disorder-free Stark many-body localization, we use the stabilizer Rényi entropy to quantify quantum magic (nonstabilizerness) and find that it remains finite and grows anomalously slowly over extended time windows before saturating to a size-dependent plateau deep in the strong-tilt regime, with pronounced initial-state selectivity. Upon increasing the Stark gradient, the long-time magic and half-chain entanglement exhibit consistent finite-size crossing behavior, indicating a crossover from ergodic dynamics to constrained localization. These results establish stabilizer-based magic as a practical complexity diagnostic of disorder-free ergodicity breaking and constrained dynamics, and provide an experimentally accessible route to benchmarking and designing near-term quantum simulators.Disorder-free quantum many-body localization can strongly suppress transport while still enabling the dynamical buildup of computationally costly non-Clifford resources. In a tilted transverse-field Ising chain realizing disorder-free Stark many-body localization, we use the stabilizer Rényi entropy to quantify quantum magic (nonstabilizerness) and find that it remains finite and grows anomalously slowly over extended time windows before saturating to a size-dependent plateau deep in the strong-tilt regime, with pronounced initial-state selectivity. Upon increasing the Stark gradient, the long-time magic and half-chain entanglement exhibit consistent finite-size crossing behavior, indicating a crossover from ergodic dynamics to constrained localization. These results establish stabilizer-based magic as a practical complexity diagnostic of disorder-free ergodicity breaking and constrained dynamics, and provide an experimentally accessible route to benchmarking and designing near-term quantum simulators.

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

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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.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.

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Disorder-Free Localization from Gauss's Law in 2+1D Lattice Gauge Theories — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Disorder-free localization (DFL) in 2+1D lattice gauge theories arises from local gauge constraints (Gauss's law) and global symmetries, not random disorder, producing ergodicity breaking in translation-invariant systems. | MATH: Hamiltonian constraint: $G_i |\psi\rangle = 0$ for all sites $i$ , where $G_i = \sum_{\text{links}} E_i^a - \rho_i$ (Gauss law). Symmetry sectors labeled by eigenvalues of $G_i$ . Localization length $\xi \sim 1/\ln(\Delta E)$ from energy gaps between superselection sectors. No explicit disorder term $\sum_i h_i \sigma_i^z$ needed. | CONNECTION: Gauge invariance imposes a local constraint algebra isomorphic to a root system of type $A_{N-1}$ (SU(N) gauge group). The Hilbert space fragmentation mirrors the decomposition into weight spaces of the Lie algebra. The ratio of sector sizes follows combinatorial patterns (e.g., Catalan numbers for 1+1D U(1) gauge theory). No direct golden ratio or base-60 link. | DEPTH: 8 — DFL is a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Disorder-free localization (DFL) in 2+1D lattice gauge theories arises from local gauge constraints (Gauss's law) and global symmetries, not random disorder, producing ergodicity breaking in translation-invariant systems. | MATH: Hamiltonian constraint: $ G_i |\psi\rangle = 0 $ for all sites $ i $, where $ G_i = \sum_{\text{links}} E_i^a - \rho_i $ (Gauss law). Symmetry sectors labeled by eigenvalues of $ G_i $. Localization length $ \xi \sim 1/\ln(\Delta E) $ from energy gaps between superselection sectors. No explicit disorder term $ \sum_i h_i \sigma_i^z $ needed. | CONNECTION: Gauge invariance imposes a local constraint algebra isomorphic to a root system of type $ A_{N-1} $ (SU(N) gauge group). The Hilbert space fragmentation mirrors the decomposition into weight spaces of the Lie algebra. The ratio of sector sizes follows combinatorial patterns (e.g., Catalan numbers for 1+1D U(1) gauge theory). No direct golden ratio or base-60 link. | DEPTH: 8 — DFL is a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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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.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:2607.28730Aug 3, 20260 citations

(1+1)\mathrm{D}

quantum electrodynamics, showing excellent agreement with the exact quantum case for small system sizes. Our results demonstrate that DFL persists in the thermodynamic limit as a purely classical effect arising from the finite-size regularization of the gauge-field operator in the QLM formulation, and that quantum interference, though not a necessary condition, may be employed to enhance DFL.

Disorder-Free Localization in

2+1

D Lattice Gauge Theories with Dynamical Matter

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.

G_i |\psi\rangle = 0

for all sites

i

, where

G_i = \sum_{\text{links}} E_i^a - \rho_i

(Gauss law). Symmetry sectors labeled by eigenvalues of

G_i

. Localization length

\xi \sim 1/\ln(\Delta E)

from energy gaps between superselection sectors. No explicit disorder term

\sum_i h_i \sigma_i^z

needed. | CONNECTION: Gauge invariance imposes a local constraint algebra isomorphic to a root system of type

A_{N-1}

(SU(N) gauge group). The Hilbert space fragmentation mirrors the decomposition into weight spaces of the Lie algebra. The ratio of sector sizes follows combinatorial patterns (e.g., Catalan numbers for 1+1D U(1) gauge theory). No direct golden ratio or base-60 link. | DEPTH: 8 — DFL is a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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.