Lattice Gauge Theories Demonstrate Anomalously Fast Transport, Defying Kinetic Constraints

The seemingly universal expectation that kinetic constraints slow down the movement of energy and other conserved quantities receives a surprising challenge from new research into gauge theories, complex systems that underpin much of particle physics. Devendra Singh Bhakuni, Roberto Verdel, and Jean-Yves Desaules, working with colleagues at the Abdus Salam International Centre for Theoretical Physics and the Institute of Science and Technology Austria, demonstrate that certain gauge theories actually exhibit faster than expected dynamics. The team reveals that, after a mathematical transformation, simplified models of these theories behave in ways that defy conventional understanding of constrained systems, bridging the gap between free-flowing energy and heavily restricted movement. This work not only uncovers superdiffusive energy transport over a wide range of conditions, but also reveals ballistic spin transport, a remarkably efficient form of movement, with implications for simulating complex physical systems and understanding the behaviour of matter in extreme conditions.

The research investigates how gauge theories can overcome kinetic constraints typically slowing dynamics in many-body systems, potentially enabling faster-than-diffusive dynamics. Researchers demonstrate that integrating out the gauge fields in one-dimensional U(1) lattice gauge theories results in an exact mapping onto XX models featuring non-local constraints, establishing a new class of kinetically constrained models which smoothly transitions between free theories and highly constrained fermionic systems. The findings reveal that these models exhibit dynamics that defy the expectation of slowed transport of conserved charges, offering a pathway to understanding systems with unexpectedly rapid behaviour.

Constrained Quantum Models and Transport Properties

This work details a comprehensive analysis of transport properties, specifically how energy and spin move, within two related quantum models: the Quantum Link Model and a variation of the PXP model extended to higher spins. The researchers investigate whether transport is diffusive, ballistic, or something in between, focusing on the influence of constraints on these properties. Calculations reveal that the Quantum Link Model possesses a conserved quantity related to magnetization, consistent between the constrained model and a related free model. Extending the analysis to the spin-S PXP model, the researchers find that the constraints are stronger than in the Quantum Link Model.

As the spin increases, the Quantum Link Model approaches a free system, while the PXP model remains constrained. Analysis using exact diagonalization and tensor network methods reveals that energy transport in the spin-S PXP model is diffusive, while spin transport exhibits ballistic behaviour, with persistent oscillations in the spin-spin correlation function. These findings demonstrate that the Quantum Link Model and the spin-S PXP model exhibit different transport properties. The Quantum Link Model shows both diffusive energy and ballistic spin transport, while the spin-S PXP model shows diffusive energy transport and ballistic spin transport with different characteristics. The strength of the constraint plays a crucial role in determining the transport behaviour, and the non-extensive conservation of magnetization is a unique feature of the constrained model.

Ballistic Transport in Constrained Gauge Theories

This work demonstrates that gauge theories can exhibit faster-than-diffusive dynamics, defying expectations that kinetic constraints typically slow down transport. Researchers established an exact mapping between one-dimensional U(1) lattice gauge theories and XX models with non-local constraints, revealing a new class of kinetically constrained models bridging free theories and highly constrained fermionic systems. Experiments utilizing exact diagonalization revealed surprisingly ballistic energy transport, characterized by a dynamical exponent of z = 1, across a broad range of constraint radii. Further tensor network simulations, performed on a system of size 256, confirmed these findings and allowed probing beyond the timescales accessible with exact diagonalization.

Analysis of the energy-energy autocorrelation function revealed that the system maintains superdiffusive scaling, with the inverse dynamical exponent initially remaining close to 1 for times less than 25. Measurements of particle number fluctuations showed linear growth similar to the unconstrained system, though with differing saturation values. Investigations into spin transport revealed robust ballistic spreading, as demonstrated by the infinite-temperature connected spin-spin correlation function. The space-time profile showed a linear light-cone with fronts moving ballistically in opposite directions, indicating that spin excitations maintain ballistic behaviour even at larger system sizes, unlike energy transport which shows some deviation. These results suggest that gauge-invariance constraints can give rise to faster-than-diffusive transport, a surprising outcome given the typical effects of kinetic constraints.

Gauge Invariance Enables Ballistic and Superdiffusive Transport

The research demonstrates that certain quantum systems, specifically those governed by gauge theories, can exhibit surprisingly efficient transport of energy and spin, defying expectations based on kinetic constraints. By mapping a one-dimensional gauge theory onto a constrained quantum model, the researchers found that energy transport is superdiffusive, while spin transport achieves ballistic behaviour, over extended timescales. This finding is significant because it challenges conventional understanding of how constraints affect dynamics in quantum systems and has implications for simulating complex physical phenomena. The team acknowledges that the observed superdiffusion is specific to the model studied. Future research could explore the extent to which these findings apply to other quantum models and investigate their relevance to analogue and digital quantum simulators, potentially enabling the efficient simulation of gauge theories on next-generation platforms. The authors also note that the robust ballistic spreading of spin excitations remains consistent even with larger system sizes.