A new preprint reports that a conformal-boundary calculation can organize several kinds of post-quench behavior in interacting non-Hermitian quantum-chain models, including return signals, local measurements and spatial correlations. The calculation was tested against finite-size Yang–Lee and complex five-state Potts models, where parameters fixed from static information were used to predict later dynamics.
The central idea is to treat the right-hand and left-hand preparations of a non-Hermitian system as the two temporal boundaries of a conformal strip — a mathematical description of evolution between boundaries. The construction assumes that both preparations flow to the same conformal boundary condition.
Close matches in the Yang–Lee test
The main benchmark used filtered product preparations in the Yang–Lee spin chain at longitudinal coupling λ = 4, near the critical field hz ≃ 1.55872195, with filter strength β = 1. Across system sizes L = 12, 14, …, 22, independently projected parameters followed the predicted relation between the S and η pairings.
For product Z and product XZ, the predicted and lattice one-point minima were closely aligned. The relative differences were 0.23% and 0.16%, respectively; the matched values were 0.179035 versus 0.179449 for product Z and 0.148718 versus 0.148962 for product XZ. These are finite-size model-comparison discrepancies, not statistical confidence intervals.
The same statically calibrated formulas also described pairing-dependent changes in the magnitude and phase of the return amplitude, the complex signal used to track the system’s return. Product X followed the common trajectory obtained with the two pairings.
A wider test of the same construction
After the local signal was used for normalization, the η-paired spatial data at separations r = 4, 6 and 8 collapsed onto one real function from the boundary calculation. The S-paired data followed that same function through analytic continuation along complex-valued paths.
In a separate direct field-on Yang–Lee quench at λ = 4 and system size L = 22, a strip parameter of about T = 0.4043 was fixed from Euclidean data before the real-time predictions were made. The normalized complex residuals for the spatial signals were 6.01%, 4.42% and 2.44% at separations 4, 6 and 8.
At the complex five-state Potts fixed point, a parameter calibrated from the spin sector reproduced the curvature and relative separation of spin and energy trajectories, with their continuously tracked phases especially well captured. The test used system size L = 10 and a calibrated complex parameter of 1.298266 + 0.261890i.
What the results establish
Taken together, the return, local, spatial, direct-quench and Potts comparisons show predictive agreement within the finite-size regimes tested. They are not a test of arbitrary boundary conditions: the leading construction assumes a shared conformal boundary condition, and distinct boundary fixed points would require additional boundary-changing operators and conformal blocks.
The leading formulas also assume one dominant extrapolation description on each boundary, complete biorthogonal eigenbases in the sectors studied and no Jordan blocks. The Potts calculation was a focused primary-dynamics test because its accessible space-time window was too narrow for a controlled two-point test.
A finite-size theoretical study
The document is an arXiv version-1 preprint dated 20 August 2026. It reports support from the Global Science Graduate Course program of the University of Tokyo and JSPS KAKENHI Grant Number JP23K25791.
Paper data and sources
Original title: Biorthogonal Conformal Dynamics in Non-Hermitian Quantum Quenches
Authors: Yifan Liu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
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