The 284th R-CCS Cafe (Jan 23, 2026)

Title:
Studying one-dimensional quantum criticality via sine-square deformation

Abstract:
Sine-square deformation (SSD) is a smooth boundary modulation in which the local energy scale of the Hamiltonian is modulated by a site-dependent function, efficiently suppressing boundary effects under open boundary conditions. In this talk, we propose a method to analyze quantum critical phenomena in one-dimensional systems, based on the theoretical expectation that translational invariance of local observables in the ground state of the SSD Hamiltonian is restored at quantum critical points (QCPs). As case studies, we demonstrate our procedure using two models: the antiferromagnetic Ising chain in mixed transverse and longitudinal magnetic fields with nearest-neighbor and long-range interactions. For the nearest-neighbor model, we show that the QCP can be accurately estimated by our procedure with systems of up to 84 sites, or even smaller, in good agreement with results from the literature. For the long-range model, we show that our method also allows us to determine the phase boundary, which is found to be slightly shifted relative to the nearest-neighbor case, leading to a reduced region of antiferromagnetic order. We further examine whether this framework can be extended beyond locating QCPs to characterize critical phenomena. Our results suggest that the SSD-based framework may be useful for extracting critical exponents and analyzing scaling behavior in quantum systems.
Moreover, we propose an experimental scheme to implement the antiferromagnetic $J_1-J_2$ Ising couplings with SSD using Rydberg atom arrays in optical tweezers to a very good approximation.