A new type of dynamical quantum phase transition, non-Bloch DQPTs, alters both the speed of changes and overall energy in systems when specific topological conditions are met, even at infinite chain length. Zhesen Yang, Wei-Wei Yang, Henning Schomerus, and Jiangping Hu detailed these transitions which occur only in open chains; they arise from complex momenta than those typically seen in periodic structures. These “non-Bloch DQPTs” represent a novel quantum transition occurring at material edges that differs from typical transitions happening throughout a substance.

This boundary effect persists even in infinitely large materials, indicating boundaries fundamentally change how quantum systems evolve over time. The findings reveal an interplay between internal and external properties, a “bulk-boundary correspondence”, potentially enabling control of quantum behaviour through careful design of material surfaces and their surrounding environment.

Consider charting a course on a map: real momentum is like travelling directly north or east, while complex momentum allows for diagonal paths combining directions simultaneously. This work focuses on understanding how interactions with an external environment, the “memory” of surrounding materials, influences this behaviour and creates unique topological properties within the system; Affiliation: Asia Pacific Centre for Theoretical Physics, Lancaster University, Chinese Academy of Sciences, Xiamen University, New Cornerstone Science Laboratory, China 3Beijing National Laboratory for Condensed Matter Physics and Institute of Physics.

Open Boundaries Reveal Non-Bloch Phase Transitions Driven by Complex Momenta and Topological

A key number, 2.83, marks the threshold where an open boundary condition (OBC) slope jump occurs near the non-Bloch DQPT; detecting this is impossible using traditional methods focused on periodic systems with real momentum values because these new transitions are determined by complex momenta instead. For point-gap winding numbers differing from zero, a topological invariant indicating twisting energy levels within the system’s spectrum, open boundaries fundamentally alter both dynamical free energy and critical times even as chain length approaches infinity. This contrasts sharply with typical equilibrium phase changes, which depend only on bulk properties, revealing a surprising connection between material edges and internal dynamics.

Particle counting techniques directly measure these winding numbers to confirm their influence on boundary behaviour. Momentum can be analytically continued along paths with zero winding number, in particular contrasting previous observations where edges simply mirrored changes happening inside the material. However, it remains unclear if practical quantum devices could reliably maintain the necessary broken time reversal symmetry or precise control over substrate interactions required for observation. The persistence of altered energy levels and timing, even in infinitely long chains, highlights that boundaries actively shape how quantum systems evolve over time.

Unveiling Dynamical Phase Transitions via Complex Momentum Analysis

Analytic continuation into complex momenta unlocked the behaviour of these non-Bloch DQPTs; imagine charting a course on a map where real momentum represents direct travel north or east, while this method allows for diagonal paths combining directions simultaneously. This process mathematically extends calculations beyond standard “real” values of momentum, those describing particles moving predictably through space, into the realm of “complex” numbers which represent combinations of movement and decay.

Calculations were performed on periodic chains defined by parameters including hopping terms *t* 1 and *t* 2, coupling strength *g*, and exchange interactions −*J* x and −*J* y, all treated as real numbers within the model. A Schur complement method was employed to eliminate substrate columns during analysis, simplifying their approach compared to directly solving larger systems.

Non-Bloch Dynamical Phase Transitions Challenge Conventional Material Constraints

This work offers a new perspective for viewing dynamical quantum phase transitions, shifts in how systems evolve, by extending these concepts beyond traditional materials with predictable particle behaviour. Measuring this point-gap winding number demands perfect particle tracking on a flawless substrate; however, acknowledging this challenge does not diminish the significance of these findings. This broadens the scope of DQPTs and introduces new possibilities in understanding complex systems exhibiting memory effects, opening doors for exploring topological phenomena arising from seemingly ordinary dynamics.

The Asia Pacific Centre for Theoretical Physics team revealed a novel type of dynamical quantum phase transition: non-Bloch DQPTs occurring specifically within open chains rather than traditional periodic systems. These transitions arise from complex momenta, differing fundamentally from those governed by real momentum in standard materials and indicating an interaction with the surrounding environment. The implications extend to potentially designing devices that use boundary effects for controlling quantum evolution; realising this requires overcoming practical limitations related to substrate quality and symmetry control.

This research demonstrated non-Bloch dynamical quantum phase transitions (DQPTs) which occur in open chains and are determined by complex momenta, a departure from conventional DQPTs reliant on predictable particle behaviour. This finding expands understanding of how these dynamic shifts happen, revealing they can be influenced by a system’s boundaries and its interactions with external environments like substrates.

Researchers found the point-gap winding number could be measured through precise particle counting, establishing a connection between bulk dynamics and boundary properties within Hermitian systems possessing memory effects. The study provides an analytic continuation to complex momenta for further investigation into this phenomenon.

👉 More information
🗞 Non-Bloch Dynamical Quantum Phase Transitions with Memory
✍️ Zhesen Yang and Wei-Wei Yang (Affiliation: Asia Pacific Center for Theoretical Physics); Henning Schomerus (Lancaster University); Jiangping Hu (Chinese Academy of Sciences)
🧠 ArXiv: https://arxiv.org/abs/2610.39994

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