Dice Question Streamline Icon: https://streamlinehq.com

Validity of the holographic interpretation for nonlinear response in the critical transverse-field Ising chain

Establish whether interpreting nonlinear response effects in the one-dimensional transverse-field Ising model at criticality as corresponding to nonlinear interactions of bulk fields within the anti–de Sitter/conformal field theory (AdS/CFT) framework is valid, given that the model lacks a conventional classical gravitational dual.

Information Square Streamline Icon: https://streamlinehq.com

Background

The paper studies spacetime-localized response phenomena in the transverse-field Ising model (TFIM) at criticality and interprets them via an AdS/CFT-inspired picture, where boundary perturbations map to bulk wavepacket dynamics along null geodesics. In linear response, this interpretation is tied to two-point correlators and causal structure.

When considering stronger perturbations, the authors note that incorporating nonlinear effects on the boundary would correspond, in the holographic language, to nonlinear interactions of bulk fields. However, because the TFIM corresponds to a c=1/2 CFT without a conventional classical gravitational dual, it is uncertain whether such a nonlinear AdS/CFT interpretation is applicable. The authors proceed numerically but explicitly state the theoretical uncertainty as an open issue.

References

In the context of the AdS/CFT correspondence, incorporating nonlinear effects in the response corresponds to taking into account nonlinear interactions of the bulk fields. In the case of the transverse-field Ising model, however, a conventional classical gravitational picture is absent, and it remains unclear whether such an interpretation is valid.

— Operator dependence and robustness of spacetime-localized response in a quantum critical spin chain (2510.04047 - Imagawa et al., 5 Oct 2025) in Section 3: Numerical Analysis—Nonlinear and Multiple Perturbation Effects (opening paragraph)