Quantum Link Model Maintains Symmetry-Protected Topological Phase Despite Disorder, Showing Robustness Beyond Harris Criterion

Understanding how quantum systems maintain their unique properties when faced with imperfections is a central challenge in modern physics, and recent work by Mykhailo V. Rakov, Luca Tagliacozzo, Maciej Lewenstein, and colleagues addresses this question within the context of quantum materials. The researchers investigate a specific model, known as the U(1) quantum link model arranged in a ladder geometry, to determine how easily its ‘symmetry-protected topological phase’, a state of matter with robust quantum properties, breaks down when disorder is introduced. Their findings demonstrate a surprising resilience to imperfections, revealing that this topological phase survives even with a degree of disorder that would typically destroy such fragile quantum states, and challenging conventional expectations based on the Harris criterion. This robustness, explained through theoretical arguments, offers valuable insight into designing more stable and practical quantum technologies. Scientists revisited the U(1) quantum link model using a ladder geometry, discovering that its critical exponent and central charge consistently align with the Ising universality class for all observed configurations. Surprisingly, this criticality persists even when disorder is introduced into the system, defying expectations based on the Harris criterion, which typically predicts the loss of criticality with disorder. This work establishes a clear connection between the quantum link model and established universality classes, providing insights into the nature of phase transitions in this system and contributing to a deeper understanding of quantum field theories and their potential applications in condensed matter physics, particularly concerning systems exhibiting emergent gauge symmetries.

Lattice Gauge Theory and Tensor Networks Research spanning condensed matter physics, quantum field theory, lattice gauge theory, tensor networks, and quantum simulation highlights the increasing use of these techniques to explore complex quantum systems. The core of this research focuses on lattice gauge theory, particularly U(1) and SU(2) gauge theories, employing tensor networks to simulate these systems and explore phenomena like confinement and symmetry breaking. Algorithms like DMRG, MPS, PEPS, and MERA are used to efficiently represent and manipulate the wavefunctions of these systems. Researchers are increasingly using quantum systems, such as ultracold atoms, to simulate lattice gauge theories, aiming to solve problems intractable for classical computers.

This research also investigates fundamental concepts in condensed matter physics, including quantum criticality, entanglement entropy, and topological phases of matter, while exploring the behaviour of interacting spins on lattices and the effects of disorder on quantum systems, such as Anderson localization. Studies connect lattice gauge theory to the continuum limit and apply quantum field theory techniques to condensed matter systems. Specific areas of focus include symmetry-protected topological phases, utilizing the entanglement spectrum to identify topological order, and employing techniques like bosonization and conformal field theory to describe critical phenomena. Researchers are also investigating the effects of randomness and disorder on quantum systems, including the Luttinger liquid model. This body of work demonstrates the intersection of condensed matter physics, quantum information theory, and quantum computing, with a strong emphasis on computational methods and the pursuit of quantum advantage. The frequent references to topological matter highlight the importance of this area of research, with many studies focusing on one-dimensional and two-dimensional systems for tractability.

Disorder Preserves Criticality in Ladder Systems Scientists investigated the U(1) link model on a two-leg ladder, discovering that its critical exponent and central charge align with the Ising universality class for all observed configurations. Contrary to expectations, this criticality persists even with the introduction of disorder. The research demonstrates that disorder affecting only the rung connections of the ladder remains stable until quite strong disorder levels are reached, while disorder in the ladder legs disrupts the nonzero mass criticality, though symmetry-protected topological properties for zero mass remain stable with small disorder.

The team measured the disorder-averaged entanglement entropy and leg magnetization to characterize the system’s phases, finding that the VA and V0 phases remain distinct even with disorder. For a fermion mass of 0. 25 and a weak disorder strength of 0. 1, the structure of the phase diagram remains largely unchanged, with a clear transition between the VA and V0 phases. Data reveals a slight shift in the transition point compared to the clean system, and a small residual magnetization develops in the VA phase attributable to disorder-induced defects. Finite-size scaling analyses confirm the robustness of the Ising universality class, yielding a central charge of 0. 5 and a correlation-length exponent of 1. Further measurements of the disorder-averaged rung magnetization at varying disorder strengths demonstrate that the system maintains a distinct transition up to a disorder strength of approximately 0. 4. Beyond this point, the data show only weak dependence on system size, indicating a loss of a clear phase transition. Specifically, the depth of the minima in the rung magnetization curves flattens out and disappears at a disorder strength of 0. 41, marking the point where the system transitions from a clear phase transition to a crossover behaviour. These results establish that the VA-to-V0 transition remains consistent with the Ising universality class even in the presence of weak disorder, and provide detailed measurements of how disorder impacts the system’s phase diagram and critical properties.

Robust Topological Phase Survives Strong Disorder This work revisits the quantum link model on a two-leg ladder, confirming the existence of a symmetry-protected topological phase when the system has zero mass and identifying potential transitions within the phase diagram as mass or leg tunneling varies. Detailed analysis reveals that the observed phase transitions consistently fall within the Ising universality class, indicating a specific type of critical behaviour. Importantly, researchers demonstrate a surprising robustness of this topological order against disorder, a disruption that typically destroys such phases according to the Harris criterion.

The team found that disorder affecting rung tunneling has a limited impact, with the topological phase persisting until the disorder becomes quite strong. Disorder in leg tunneling, however, does disrupt the criticality for non-zero mass systems. The observed stability is explained, at least phenomenologically, by the preservation of the protecting symmetry of the topological phase. The authors acknowledge that a fully controlled theoretical explanation for the stability of the Ising transitions at zero mass remains elusive. Future work may focus on developing such a description, building on the field-theoretic arguments presented here.

This research demonstrates a subtle interplay between disorder and symmetry in the ladder system, revealing unexpected resilience in the topological phase and challenging conventional expectations regarding the impact of disorder on critical phenomena. 👉 More information 🗞 Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder 🧠 ArXiv: https://arxiv.org/abs/2512.10642 Tags: