References

Burgelman, L.; Francuz, A.; Brehmer, P.; Devos, L.; Haegeman, J.; Verstraete, F. and Vanhecke, B. (2026). Implicit differentiation of tensor network algorithms, arXiv:2607.15030 [quant-ph]. ↩¹

Corboz, P. (2016). Variational optimization with infinite projected entangled-pair states. Phys. Rev. B 94, 035133. ↩¹

Evenbly, G. (2018). Gauge fixing, canonical forms, and optimal truncations in tensor networks with closed loops. Phys. Rev. B 98, 085155. ↩¹ ↩²

Francuz, A.; Schuch, N. and Vanhecke, B. (2025). Stable and Efficient Differentiation of Tensor Network Algorithms. Physical Review Research 7, 013237.

Haegeman, J. and Verstraete, F. (2017). Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods. Annual Review of Condensed Matter Physics 8, 355–406. ↩¹ ↩²

Hasenbusch, M. (2001). Monte Carlo Studies of the Three-Dimensional Ising Model in Equilibrium. International Journal of Modern Physics C 12, 911–1009. ↩¹

Liu, W.-Y.; Gong, S.-S.; Li, Y.-B.; Poilblanc, D.; Chen, W.-Q. and Gu, Z.-C. (2022). Gapless quantum spin liquid and global phase diagram of the spin-1/2 J1-J2 square antiferromagnetic Heisenberg model. Science Bulletin 67, 1034–1041. ↩¹

Qin, M.; Shi, H. and Zhang, S. (2016). Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method. Phys. Rev. B 94, 085103. ↩¹ ↩²

Sandvik, A. W. (2010). Computational Studies of Quantum Spin Systems. AIP Conference Proceedings 1297, 135–338. ↩¹ ↩²

Vanderstraeten, L.; Burgelman, L.; Ponsioen, B.; Van Damme, M.; Vanhecke, B.; Corboz, P.; Haegeman, J. and Verstraete, F. (2022). Variational Methods for Contracting Projected Entangled-Pair States. Physical Review B 105, 195140. ↩¹

Vanderstraeten, L.; Haegeman, J. and Verstraete, F. (2019). Tangent-Space Methods for Uniform Matrix Product States. SciPost Physics Lecture Notes, 007. ↩¹ ↩²

Vanderstraeten, L.; Vanhecke, B. and Verstraete, F. (2018). Residual entropies for three-dimensional frustrated spin systems with tensor networks. Phys. Rev. E 98, 042145. ↩¹ ↩²

Zhang, X.-Y.; Yang, Q.; Corboz, P.; Haegeman, J. and Tang, W. (2026). Accelerating two-dimensional tensor network optimization by preconditioning. Phys. Rev. B 113, 125111. ↩¹

Zhang, Y.; Yang, Q. and Corboz, P. (2025). Accelerating two-dimensional tensor network contractions using QR-decompositions, arXiv:2505.00494 [cond-mat.str-el]. ↩¹