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arXiv:2111.08715 · PRX Quantum

Enhancing Disorder-Free Localization through Dynamically Emergent Local Symmetries

Jad C. Halimeh, Lukas Homeier, Hongzheng Zhao, Annabelle Bohrdt, Fabian Grusdt, Philipp Hauke, Johannes Knolle

Published May 31, 2022• 32 citations
arXivHTMLPDF

Abstract

Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors.Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation invariant.In a recent work [Halimeh et al., arXiv:2111.02427(2021)], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in U(1) gauge theories against gauge errors that couple different superselection sectors.Here, we show in the case of Z 2 gauge theories that disorder-free localization can not only be stabilized, but also enhanced by the addition of translation-invariant terms linear in a local Z 2 pseudogenerator that acts identically to the full generator in a single superselection sector, but not necessarily outside of it.We show analytically and numerically how this leads through the quantum Zeno effect to the dynamical emergence of a renormalized gauge theory with an enhanced local symmetry, which contains the Z 2 gauge symmetry of the ideal model, associated with the Z 2 pseudogenerator.The resulting proliferation of superselection sectors due to this dynamically emergent gauge theory creates an effective disorder greater than that in the original model, thereby enhancing disorder-free localization.We demonstrate the experimental feasibility of the Z 2 pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup.

DOI
10.1103/prxquantum.3.020345

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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
Disorder-free localization is a recently discovered phenomenon of nonergodicity that can emerge in quantum many-body systems hosting gauge symmetries when the initial state is prepared in a superposition of gauge superselection sectors.Thermalization is then prevented up to all accessible evolution times despite the model being nonintegrable and translation invariant.In a recent work [Halimeh et al., arXiv:2111.02427(2021)], it has been shown that terms linear in the gauge-symmetry generator stabilize disorder-free localization in U(1) gauge theories against gauge errors that couple different superselection sectors.Here, we show in the case of Z 2 gauge theories that disorder-free localization can not only be stabilized, but also enhanced by the addition of translation-invariant terms linear in a local Z 2 pseudogenerator that acts identically to the full generator in a single superselection sector, but not necessarily outside of it.We show analytically and numerically how this leads through the quantum Zeno effect to the dynamical emergence of a renormalized gauge theory with an enhanced local symmetry, which contains the Z 2 gauge symmetry of the ideal model, associated with the Z 2 pseudogenerator.The resulting proliferation of superselection sectors due to this dynamically emergent gauge theory creates an effective disorder greater than that in the original model, thereby enhancing disorder-free localization.We demonstrate the experimental feasibility of the Z 2 pseudogenerator by providing a detailed readily implementable experimental proposal for the observation of disorder-free localization in a Rydberg setup.
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 strong ergodicity breaking that has been shown to occur in global quenches of lattice gauge theories when the system is initialized in a superposition over an extensive number of gauge sectors. Here, we show that preparing the system in a thermal Gibbs ensemble without any coherences between different gauge sectors also gives rise to disorder-free localization, with temperature acting as a disorder strength. We demonstrate our findings by calculating the quench dynamics of the imbalance of thermal ensembles in both U(1)\mathrm{U}(1)U(1) and Z2\mathbb{Z}_2Z2​ lattice gauge theories through exact diagonalization, showing greater localization with increasing ensemble temperature. Furthermore, we show how adding terms linear in local pseudogenerators can enhance temperature-induced disorder-free localization due to the dynamical emergence of an enriched local symmetry. Our work expands the realm of disorder-free localization into finite-temperature physics, and shows counterintuitively that certain quantum nonergodic phenomena can become more prominent at high temperature. We discuss the accessibility of our conclusions in current quantum simulation and computing platforms.
Localization due to the presence of disorder has proven crucial for our current understanding of relaxation in isolated quantum systems. The many-body localized phase constitutes a robust alternative to the thermalization of complex interacting systems, but recently the importance of disorder has been brought into question. A number of disorder-free localization mechanisms have been put forward connected to local symmetries of lattice gauge theories. Here, starting from translationally invariant (1+1)(1+1)(1+1)-dimensional quantum electrodynamics, we modify the dynamics of the gauge field which allows us to construct a lattice model with a UUU(1) local gauge symmetry revealing a mechanism of disorder-free localization. We consider two different discretizations of the continuum model resulting in a free-fermion soluble model in one case and an interacting model in the other. We diagnose the localization of our translationally invariant model in the far-from-equilibrium dynamics following a global quantum quench.
The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified local pseudogenerators designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to time scales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multibody full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the Z2{\mathbb{Z}}_{2}Z2​ lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.
Disorder-induced phenomena in quantum many-body systems pose a challenge for analytical and numerical approaches at relevant time and system scales. To reduce the cost of disorder sampling, we investigated quantum circuits initialized in states that form tunable superpositions over all disorder configurations, which in lattice gauge theories can be interpreted as superpositions over gauge sectors. On the experimentally accessible timescales, we observed localization in the absence of disorder in one and two dimensions: Perturbations failed to diffuse despite fully disorder-free evolution and initial states. However, entropy measurements revealed that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a long-standing challenge in many-body localization studies.
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