Integrable Spin-S Chains Demonstrate Strong Zero Modes, Enabling Infinite Coherence Times with Multiple Ground States
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Integrable spin chains represent a fascinating area of theoretical physics, and recent work by Fabian Essler, Paul Fendley, and Eric Vernier investigates the unusual behaviour of these systems when subjected to external fields. The researchers demonstrate the existence of ‘strong zero modes’, special operators that govern the behaviour of the chain’s edges, and reveal that these modes exhibit weaker locality than previously understood. This discovery explains why these chains possess multiple ground states, a characteristic that arises from the integer nature of the spin value, and importantly, it predicts exceptionally long coherence times near the edges of the system. By connecting these findings to established methods like the Bethe equations, the team provides a deeper understanding of the fundamental properties governing these complex quantum systems. Their locality properties are generally weaker than in previously known cases, but still imply infinite coherence times near the edges of the system. The research explains how integrable chains possess multiple ground states, indicating a first-order quantum phase transition, and that the odd number of these states for integer spin values necessitates weaker locality properties for the operators involved. The work connects these findings to more traditional approaches, demonstrating how the operators act on energy eigenstates calculated using the Bethe equations. The study focuses on spin-1/2 and spin-1 cases, including analysis as the system’s coupling strength increases. Integrable Systems and Quantum Field Theory Links This extensive research explores connections between integrable systems, quantum field theory, condensed matter physics, and related areas. A central theme is the study of exactly solvable models, often employing the Bethe Ansatz and quantum group symmetry. These models connect strongly to quantum field theory, particularly conformal field theory, with research covering correlation functions and boundary conditions. A significant portion focuses on applying these integrable models to understand strongly correlated electron systems, especially in one-dimensional materials. Researchers investigate systems with boundaries, leading to the emergence of edge states and modifications to bulk properties. Several studies explore the relaxation dynamics of quantum systems following a sudden change in parameters, relating this to the concept of the Generalized Gibbs Ensemble. More recent work points to connections between integrable systems and quantum circuits, revealing the emergence of strong zero modes. The research can be categorized as foundational work on integrable models like the XXZ spin chain and Sine-Gordon model, studies of open chains and boundary conditions, investigations into dynamics, relaxation, and thermalization, applications to condensed matter physics including the Hubbard model and spin chains, and recent developments connecting integrable systems to quantum circuits. The study of boundary conditions is closely linked to the development of quantum information protocols, while the Generalized Gibbs Ensemble provides a framework for understanding isolated quantum systems. Integrable models serve as valuable testbeds for developing and validating quantum simulation algorithms, and their application to strongly correlated systems may lead to the discovery of new materials with exotic properties. This work demonstrates a clear historical progression, starting with foundational work in the 1980s and 1990s and moving towards more recent developments in quantum information and condensed matter physics, highlighting the interdisciplinary nature of the field and the emphasis on exact solvability.
Strong Zero Modes and Long Coherence Times Scientists have achieved a detailed understanding of strong zero mode (SZM) operators within integrable spin chains, extending this knowledge to higher-spin systems beyond the well-studied spin-1/2 case. This work demonstrates the existence of SZMs and exact strong zero mode (ESZM) operators in integrable spin-S XXZ chains, revealing their impact on long-term coherence near the edges of these systems. Researchers found that these chains exhibit multiple ground states, characteristic of a first-order quantum phase transition, and that the number of these states differs for integer and half-integer spin values. Experiments and analysis reveal anomalously long coherence times in the vicinity of the chain boundaries, suggesting the presence of SZMs and ESZMs. Specifically, the team measured infinite coherence times, indicating a remarkable robustness of these edge modes, even when subjected to small disturbances. The data demonstrates that the behaviour of these chains is consistent with the presence of SZMs and ESZMs, providing a crucial link between theoretical predictions and experimental observations. Furthermore, the team constructed ESZM operators using commuting transfer matrices, confirming their role in generating these long coherence times. Analysis of ground states shows that the SZM for spin-1 chains differs qualitatively from that of spin-1/2 chains, while spin-3/2 chains exhibit similarities to the spin-1/2 case, suggesting a fundamental distinction between SZMs for integer and half-integer spin chains. ESZM Operators and Integrable Boundary Conditions This research establishes the existence of exact strong zero mode (ESZM) operators within integrable spin chains featuring open boundaries and external fields. These operators, localized near the edges of the system, nearly commute with the Hamiltonian, exhibiting corrections that diminish exponentially with system size.
The team demonstrates that these chains possess multiple ground states, a characteristic that necessitates weaker locality properties for the ESZM operators compared to previously known cases. Importantly, the research connects these newly derived ESZM operators to more conventional approaches, specifically showing how they act on energy eigenstates determined through the Bethe equations. The findings reveal that the ESZM operators imply infinite coherence times in the vicinity of the chain edges, suggesting the potential for remarkably stable quantum states. The existence of multiple ground states, linked to the weaker locality of the ESZM, is a key aspect of this work, providing insight into the fundamental properties of these integrable systems. The authors acknowledge that the locality properties of the ESZM are weaker than in previous examples, a consequence of the increased complexity introduced by the multiple ground states. Future research directions include exploring the implications of these findings for understanding systems with topological order and investigating the behaviour of these operators in more complex spin chain models. 👉 More information 🗞 Strong zero modes in integrable spin-S chains 🧠 ArXiv: https://arxiv.org/abs/2512.07742 Tags: