The Signal
Yang Team Identifies Quantum Transitions That Require Open Chains
A study describes dynamical quantum phase transitions that occur in open chains but not under periodic boundary conditions. The authors connect the effect to memory, complex momenta and a winding number, and propose a particle-counting test
Quantum.world Team · Written with AI · fact-checked ·
“We identify non-Bloch DQPTs, which occur only in open chains and are determined by complex momenta instead.”
Zhesen Yang, Wei-Wei Yang, Henning Schomerus and Jiangping Hu, the paper’s authors
The four researchers describe a type of dynamical quantum phase transition that depends on whether a chain has open ends. In their paper, “Non-Bloch Dynamical Quantum Phase Transitions with Memory,” submitted to arXiv on October 29, they show that an open chain can have a transition absent under periodic boundary conditions, even in the thermodynamic limit. Their result makes the boundary part of the bulk dynamics rather than a small edge correction.
Why an open chain changes the transition
Dynamical quantum phase transitions, or DQPTs, occur when a quantity called the dynamical free energy becomes nonanalytic at a particular time. In periodic chains, the transitions studied conventionally are set by real-valued Bloch momenta. Yang and colleagues find that open boundaries can instead produce transitions governed by complex momenta, which they call non-Bloch DQPTs.
Their mechanism depends on the winding number, a topological property of the chain’s projected time-evolution operator. When that number is zero, the open and periodic systems have the same dynamical free energy in the thermodynamic limit. When it is nonzero, the open-boundary dynamics can differ: periodic-chain transitions disappear, and a new transition can emerge in the open chain.
A Hermitian chain with memory
The authors study a Su–Schrieffer–Heeger chain with broken time-reversal symmetry, coupled to the edge of a semi-infinite two-dimensional substrate. The full chain-and-substrate system is Hermitian, but particles can leave the chain and later return. That retained memory makes the chain’s effective dynamics non-Markovian and produces non-Hermitian behavior in the projected evolution, without adding engineered gain or loss.
In the model, the chain’s boundary-sensitive transition occurs at dimensionless time g t = 2.83, where g sets the chain-to-substrate coupling scale. The periodic-chain transitions occur at g t = 1.67, 3.80 and 7.05; under open boundaries, those transitions are absent from the chain’s dynamical free energy. The reported values come from the paper’s chosen model parameters, not from a measurement on a physical device.
Complex momentum provides the calculation
To calculate the open-chain result, the researchers analytically continue the periodic-chain propagator from real to complex momentum. In their formulation, the open-chain dynamical free energy follows from the continued periodic result along a path with zero winding number. Finite-size numerical calculations support the relationship.
The boundary effect is not caused simply by the non-Hermitian skin effect, in which states gather near a chain’s ends. The paper finds that this effect alone does not make the dynamical free energies differ; the winding number must also be nonzero. The authors identify memory and broken time-reversal symmetry as necessary ingredients for that winding in their model.
Particle counting offers a test
The team proposes measuring the winding number in a fermionic system by preparing a filled chain above an empty substrate, switching on the coupling and imaging particle occupations. They retain only snapshots in which a selected window around the chain’s midpoint returns to its initial pattern, then count the net particle transfer across a cut. In the model, the average transferred charge approaches the winding number as the window grows.
For one simulated example with 30 chain cells, a window spanning four cells and g t = 2.5, the probability of counting one transferred particle among retained snapshots is 0.991. The paper identifies fermionic simulators with site-resolved imaging as a possible platform for this measurement, and also points to waveguide arrays and other quantum simulators as places to investigate related dynamics. These are proposed tests; the paper reports no experimental observation of the new transition.