Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states

Abstract:We investigate the imaginary-time relaxation critical dynamics of the two-dimensional transverse-field Ising model using infinite projected entangled pair states (iPEPS) with the full-update strategy. Simulating directly in the thermodynamic limit, we explore the relaxation process near the critical point with two types of initial states: a fully polarized state and a product state with a small magnetization. For the fully polarized state, the magnetization shows a power law scaling $M\propto \tau^{-\beta/(\nu z)}$ in the imaginary-time evolution, from which both the critical point and critical exponent can be determined with high accuracy. For the nearly paramagnetic state, the relaxation process exhibits a behavior of $M\propto \tau^\theta$ with $\theta=0.1958$ being the critical initial-slip exponent, which is in good agreement with that obtained from the dynamic scaling of the self-correlation in quantum Monte Carlo method. These universal features emerge well before the system converges to the ground state, demonstrating the efficiency of imaginary-time evolution for probing quantum criticality. Our results demonstrate that iPEPS can serve as a robust and scalable method for studying dynamical critical phenomena in two-dimensional quantum many-body systems.

Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2511.10934 [cond-mat.str-el]

(or arXiv:2511.10934v2 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2511.10934 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. B 113, 245108 (2026)

https://doi.org/10.1103/h9rl-gpxr Focus to learn more DOI(s) linking to related resources

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