Quantum Chaos Reveals Hidden Phase Transitions

A new discovery about how information spreads in quantum systems could revolutionize how scientists detect fundamental changes in matter. Researchers have found that chaotic quantum systems obey universal scaling laws near critical points, allowing them to locate phase transitions and extract key properties using short-time measurements rather than requiring long observation periods that challenge current experimental capabilities.

The key finding reveals that out-of-time-ordered correlators (OTOCs)—mathematical quantities that measure how information spreads through quantum systems—follow predictable patterns governed by just a few critical exponents when systems approach quantum phase transitions. This means the behavior of information scrambling becomes universal across different quantum systems belonging to the same class, much like how water and certain metals follow the same scaling laws near their critical points despite being fundamentally different materials.

The researchers employed numerical simulations using the time-dependent density matrix renormalization group (t-DMRG) approach to study two paradigmatic models: the transverse axial next-nearest-neighbor Ising (ANNNI) model and the Lipkin-Meshkov-Glick (LMG) model. They examined how OTOCs behave when systems are close to their quantum critical points, analyzing the scaling properties of these correlators under transformations that group multiple lattice sites together. This approach allowed them to derive universal forms for information scrambling that depend only on the system's critical exponents.

Results from the ANNNI model show clear evidence of universal scaling. When researchers plotted OTOC data for different system sizes (16, 24, and 32 lattice sites) using properly rescaled variables, all points collapsed onto a single curve, confirming the predicted scaling behavior. The analysis also revealed a 'butterfly velocity'—the speed at which information spreads—that follows universal temperature dependence near critical points. For the ANNNI model at criticality, this velocity becomes temperature-independent, while for systems like the Bose-Hubbard model, it increases with the square root of temperature.

Perhaps most significantly, the team demonstrated how these scaling laws can be used to detect quantum phase transitions in practical settings. By analyzing the first minimum of normalized OTOCs across different system sizes, they could locate critical points and extract critical exponents without requiring long-time measurements. In the LMG model, this approach yielded a critical exponent of ν = 0.330 ± 0.001, matching the theoretical value exactly. This represents a major advancement over previous methods that relied on long-time averages, which demand extended coherence times that are challenging to maintain in many quantum systems.

The real-world implications are substantial for quantum computing and materials science. Since OTOCs have already been measured experimentally in various physical systems including trapped ions and nuclear magnetic resonance setups, these scaling laws can be immediately tested and applied. Researchers could use short, transient dynamics to characterize quantum materials and identify phase transitions, potentially accelerating the development of quantum technologies and our understanding of complex quantum matter.

However, the approach has limitations. The derived scaling laws and velocity predictions are valid only when the dynamical critical exponent z satisfies z < 2, as causality requires the butterfly velocity to remain bounded. Additionally, while the method works for second-order quantum phase transitions, its applicability to other types of transitions remains unexplored. The researchers also note that their numerical verification was limited to specific models, though the theoretical framework suggests broader applicability across quantum many-body systems undergoing similar transitions.