The critical phase of a non-Hermitian quasicrystal exhibits stronger transport than its surrounding delocalized phases. A one-dimensional nonreciprocal Aubry, André, Harper model using dynamical quantum phase transitions and wavepacket diffusion analysis reveals this behaviour at Zhejiang Normal University. Nonreciprocity reverses expected hierarchies in how materials conduct, potentially enabling new approaches to control quantum systems. A specific state within structured materials can unexpectedly enhance movement instead of restrict it. Studying non-Hermitian quasicrystals, materials exhibiting unique wave behaviour, the team found that their ‘critical’ condition allows greater transport compared to surrounding material phases.

This discovery challenges established understanding of conduction and introduces new ways to investigate quantum dynamics. Unusual behaviour has been demonstrated within non-Hermitian quasicrystals, materials exhibiting unique wave characteristics, by researchers. Their work centres on a one-dimensional system where movement can be unexpectedly enhanced rather than restricted under specific conditions; this is particularly true during the ‘critical’ phases of these materials.

Rapidly changing the rules governing a game helps understand dynamical quantum phase transitions or DQPTs, which represent sudden shifts in a quantum system’s properties. The team used both analysis of these DQPTs and studies of how quickly energy spreads through the material, measured by the diffusion exponent β, functioning like observing dye spreading in water to indicate spread rate as ballistic (fast), diffusive (moderate) or localized (slow/nonexistent).

Ballistic transport and enhanced dynamical quantum phase transitions in non-Hermitian quasicrystals

A critical phase within non-Hermitian quasicrystals achieves ballistic transport, with the diffusion exponent β reaching one; this contrasts sharply with Hermitian systems where criticality typically exhibits diffusive behaviour (β=0.5). Extended phases are also normally diffusive rather than ballistic, a finding previously unobserved. Self-similar fractal structures present within the energy spectrum of these materials promote particle movement unlike conventional models, causing this reversal. Careful analysis using parity-sorted classification revealed an energy dependence for dynamical quantum phase transitions not observed in standard Hermitian physics.

DQPTs were more pronounced when transitioning between localized or extended states due to even/odd index structuring of eigenstates. The researchers further substantiated their findings by examining quenches, abrupt changes in a system’s parameters, to reveal underlying shifts in behaviour through dynamical quantum phase transitions (DQPTs). Analysis of Loschmidt echoes, measures of initial state deviation over time, showed that such quenches induced stronger DQPTs than expected because of the unique even/odd index structure inherent within the material’s spectrum.

Wavepacket Diffusion and Parity Sorting Reveal Dynamical Phase Transitions in Quasicrystals

Tracking how energy spreads through the material via wavepacket diffusion provided key insights. The team quantified this process with a diffusion exponent β to determine if spreading was rapid (‘ballistic’), moderate or slow. This measurement offered a detailed picture of particle movement within different phases. The team employed parity-sorted energy spectrum classification to fully understand these dynamics, organising energy levels based on mathematical characteristics related to symmetry.

This technique directly encoded information about the system’s unusual PT symmetry and proved essential for analysing sudden shifts in quantum properties known as dynamical quantum phase transitions (DQPTs). Simulations performed using a finite size system containing two hundred and thirty-three lattice points, a Fibonacci number, accurately represented the quasiperiodic potential. This approach allowed detailed analysis of complex systems compared to simpler models lacking nonreciprocity or periodic structures because it provided greater control over parameters influencing particle behaviour.

Enhanced particle transport via critical state manipulation in non-Hermitian quasicrystals

Manipulation of the critical state within non-Hermitian quasicrystals could unlock enhanced particle transport, according to scientists. This challenges established understanding where such points typically hinder movement rather than enable it. However, current investigations remain confined to a specific one-dimensional system, the Aubry, André, Harper model, leaving open whether these surprising findings extend into more complex three-dimensional materials or other systems lacking reciprocity. These results are significant because they demonstrate a principle applicable beyond simple physics despite being limited to this single mathematical model describing electrons moving through an artificially structured material. Careful analysis of energy spectrum classifications can reveal subtle details about transitions within non-Hermitian quasicrystals and highlight that DQPTs aren’t uniform across all energies as seen in standard materials.

Manipulation of the critical state within non-Hermitian quasicrystals enabled stronger particle transport than expected, reversing typical behaviour where such states impede movement. Researchers demonstrated this using simulations on a one-dimensional system with two hundred and thirty-three lattice points, revealing how diffusion exponents vary between phases. They found that unlike conventional systems, the critical phase exhibited ballistic motion, particles travelled without resistance, while the extended phase became diffusive. This work highlights how energy spectrum classifications can reveal detailed information about quantum transitions within these complex materials.

👉 More information
🗞 Quench dynamics in nonreciprocal Aubry-André-Harper model
✍️ Zhiyu Pei, Yongxu Fu and Gao Xianlong
🧠 ArXiv: https://arxiv.org/abs/2609.10342

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