A. Singhania: Benchmarking METTS for Finite-Temperature Simulations of Z2 Models: Applications to Rydberg atom ladder systems

Understanding the thermodynamic properties of quantum frustrated systems remains a central challenge in condensed matter physics. While quantum Monte Carlo methods have been instrumental in exploring finite-temperature behavior, they encounter severe limitations in frustrated regimes due to the sign problem. Tensor network techniques, particularly the Minimally Entangled Typical Thermal States (METTS) algorithm [1,2], have recently emerged as powerful alternatives, especially for SU(2)-symmetric Hamiltonians [3]. However, in systems lacking such symmetries, METTS suffers from strong autocorrelations that hinder statistical convergence [4]. In this work, we highlight the critical role of basis selection during the state collapse step in mitigating these issues and reducing statistical errors [5,6]. We benchmark an improved METTS algorithm on the transverse-field Ising model and apply it to study the order-by-disorder transition in Rydberg atom ladder systems, demonstrating its effectiveness in capturing key thermodynamic signatures in frustrated quantum models [7]. [1] S. R. White, Phys. Rev. Lett. 102, 190601 (2009). [2] E. M. Stoudenmire and S. R. White, New J. Phys. 12, 055026 (2010). [3] A. Wietek, et. al. Phys. Rev. X 11, 031007 (2021) [4] S. Goto and I. Danshita Phys. Rev. Res. 2, 043236 (2020) [5] I. Chen, et. al. Quantum 8, 1545 (2024). [6] I. Chen, et. al. arXiv:2407.11949 [7] M. Sarkar, et. al. SciPost Phys. 14, 004 (2023)