Quantum quenches of scar states in the Affleck-Kennedy-Lieb-Tasaki model via Clifford augmented tensor network simulation

In the microscopic world of quantum physics, matter behaves in ways that defy our everyday intuition. At the heart of this strange behavior lies a concept called entanglement, where particles become so deeply linked that the state of one instantly influences the other, regardless of distance. For decades, scientists have used this phenomenon to understand how complex materials form and how they might be used for future technologies. However, there is another, more elusive resource at play in these systems, often described as a form of computational "magic." This magic is not about illusion, but about a specific type of complexity that makes a quantum system difficult to simulate with standard computers. While entanglement tells us how much information is shared between parts of a system, this "magic" measures how far a system is from being simple and predictable. Understanding the balance between these two properties is crucial for figuring out which quantum states are stable enough to be useful and which will quickly fall apart.

A team of researchers at the University of Melbourne and CSIRO has recently explored this balance within a specific model of quantum matter known as the Affleck-Kennedy-Lieb-Tasaki, or AKLT, model. This model describes a chain of atoms with a spin of one, a setup that historically served as a mathematical proof for a special state of matter called the Haldane phase. This phase is unique because it is protected by symmetry, meaning its properties remain robust even when the system is slightly disturbed. Within this model, scientists have discovered special excited states called "scar states." Unlike typical excited states that quickly lose their structure and turn into random thermal noise, these scar states retain a surprising amount of order and low entanglement, almost as if they are immune to the usual chaos of quantum decay. The researchers wanted to know if these scar states also possess the special "magic" that makes them hard to simulate, and whether their unique topological order survives when the system is suddenly changed.

To investigate this, the team employed a powerful new simulation technique called Clifford augmented tensor networks. Imagine trying to map a vast, complex landscape; standard methods might get lost in the details, but this new approach uses a special kind of mathematical shortcut. It identifies parts of the system that are simple and predictable, handling them with efficient rules, while focusing its heavy computational power only on the complex, "magical" parts that break those rules. This allowed the researchers to simulate the behavior of the AKLT model with a level of precision that would have been impossible with older methods. They first examined the ground state, the lowest energy state of the system, and the various scar states sitting above it. They found that, contrary to what one might expect from such orderly states, both the ground state and the scar states are highly "magical." They possess a high degree of non-stabilizerness, a technical term for that specific complexity, which was measured using a metric called Stabilizer Rényi Entropy. This means that even though these states are simple in terms of how much they are entangled, they are incredibly complex in the way they process quantum information.

The researchers then put these states to the test by performing a "quantum quench." This is a process where the rules governing the system are abruptly changed. They started with the AKLT model and suddenly switched the interactions between the atoms to those of a different, well-known model called the anti-ferromagnetic Heisenberg Hamiltonian. Crucially, this change happened entirely within the same topological phase, meaning the fundamental symmetry protecting the system remained intact. The question was whether the special order of the scar states would survive this sudden shift. Using their advanced simulation tools, they tracked how the "string order"—a specific pattern of correlation that acts as a signature of the system's topological nature—evolved over time. They observed that the string order did not remain static. Instead, it began to decay, or "melt," as time passed.

The results revealed a fascinating dependence on the energy of the state. For the lowest energy scar states, the string order decayed slowly, suggesting a degree of resilience. However, for the higher-energy scar states, the decay was much more rapid and pronounced. The researchers found that the more energy the scar state had, the faster its topological signature disappeared. This suggests that while the symmetry of the system was preserved, the specific algebraic structure that supported the existence of these scar states in the first place was broken by the change in the Hamiltonian. The study indicates that the topological protection of these scar states is fragile when the underlying mathematical support is removed, even if the broader phase of matter remains the same.

The team also compared their new simulation method against traditional techniques. They found that their Clifford augmented approach was significantly more accurate, capable of tracking the system's evolution over longer periods with the same amount of computational resources. This efficiency was vital, as it allowed them to observe the decay of the string order without the simulation breaking down due to accumulated errors. While the study confirms that these scar states are highly complex and possess a unique form of order, it also highlights their vulnerability. The rapid decay of the string order in higher-energy states suggests that the topological properties of these states are not as robust as those of the ground state when the system is deformed. The researchers note that while their simulations show this decay clearly, determining whether the order vanishes completely over extremely long timescales would require even more powerful computing resources. For now, the work provides a clear picture of how these exotic quantum states behave under stress, revealing that their special properties are a delicate balance between order and complexity.