The entanglement phases of gauge-Higgs models on hyperbolic lattices are studied using measurement-only dynamics. The research centres around understanding how non-equilibrium measurements impact these structures. Entanglement transitions between non-equilibrium phases, including topological phases, occur through competition of non-commutating measurements. We chart two-dimensional phase diagrams employing topological entanglement entropy and introducing a generalised measurement-induced entanglement tailored for hyperbolic Higgs phases. Using duality, we identify a new phase absent in Euclidean space where the bulk lattice hosts separated clusters of symmetry-protected topological order. Charting transitions between this “archipelago” phase and neighboring topologies also represents a key finding.

Hyperbolic Lattices Uncover Novel Entanglement Phase and Mean-Field Criticality

Entanglement measures now reveal an “archipelago” phase within gauge-Higgs models on hyperbolic lattices, previously unseen in Euclidean spaces. We characterise it by separated regions of symmetry-protected topological order, with critical exponent δ values consistently falling into a mean-field universality class across transitions involving this new phase. Existing methods failed to resolve the unique properties arising from hyperbolic geometry, limiting prior identification of such distinct entanglement structures beyond established theoretical frameworks.

These newly discovered states exhibit behaviour consistent with well understood physics despite their novel spatial arrangement and opens avenues for exploring more complex phases of matter inaccessible through traditional flat space simulations. Topological entanglement entropy alongside Symmetry Protected Topological (SPT) entanglement detected separated regions within quantum states, revealing an “archipelago” phase absent from flat Euclidean spaces; visualizes these distinct clusters of SPT entanglement. Transitions into or out of this archipelago phase consistently yield a critical exponent δ that falls squarely within mean-field theory, mirroring behaviour seen elsewhere.

Analytical arguments link the system to classical percolation models via stochastic measurements on higher-dimensional cluster states, supporting these numerical findings. A measurement-based approach simulates spacetime evolution using a three-dimensional resource state and allows analysis of ‘entanglement sponges’, mapping directly onto established percolation theories which enabled inference of precise boundary values for their observed phases.

Finite System Sizes Constrain Extrapolations to Macroscopic Material Properties

The discovery of an “archipelago” phase, a novel arrangement of symmetry-protected order within hyperbolic lattices, offers compelling insights into non-equilibrium quantum behaviour, yet translating these findings to real materials presents considerable hurdles. Expanding beyond this may reveal unforeseen complexities or even invalidate aspects of this new topology.

This limitation is particularly acute given existing work on percolation theory suggests that behaviours observed in finite systems don’t always scale predictably when extrapolated to infinite sizes. Despite acknowledged limitations regarding lattice size and extrapolation to infinite systems, a common challenge when studying complex behaviours like those predicted by percolation theory, this work remains important. Establishing the existence of such an arrangement fundamentally alters understanding of how complex quantum states organise themselves under non-equilibrium conditions. The discovery moves beyond simply identifying new phases, demonstrating geometry itself can dictate novel forms of entangled matter and their associated properties. Analysis showed transitions involving this archipelago phase consistently adhere to mean-field universality, a well understood behaviour despite the unusual spatial configuration, confirming its distinct characterisation; future work will explore if these findings translate to materials, potentially unlocking new avenues for quantum technologies.

This research identified a previously unknown “archipelago” phase within gauge-Higgs models on hyperbolic lattices, a unique organization of symmetry-protected topological order. This finding demonstrates that the underlying geometry of space influences how complex quantum states arrange themselves and impacts entanglement structures. By employing measurement-only dynamics and analyzing “entanglement sponges,” researchers charted two-dimensional phase diagrams and determined transitions between phases adhere to mean-field universality with a critical exponent δ. The authors intend to investigate whether these results extend to physical materials in future studies.

👉 More information
🗞 Measurement-induced entanglement phases in hyperbolic gauge-Higgs models
✍️ Cole Kelson-Packer, Hiroki Sukeno and Akimasa Miyake (University of New Mexico)
🧠 ArXiv: https://arxiv.org/abs/2610.36528

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