Kharkiv Quantum Seminar

 I will make a brief introduction to tensor network (TN) states and algorithms that became a method of choice for strongly correlated quantum many body systems on a lattice in one and two dimensions. I will emphasize the 2D TN known as PEPS (pair-entangled projected state) and its two applications to unitary time evolution and thermal Gibbs states. One is the recent quantum computational advantage demonstration with the coherent D-Wave quantum annealer [1], where TN served, on the one hand, as a benchmark for the quantum simulator and, on the other hand, as the most competitive classical method that, nevertheless, in the end failed the competition with the quantum hardware. The other is tensor network simulation of finite temperature states in the Hubbard and t − J models – the two paradigmatic models of high-Tc superconductivity – that proved notoriously hard to solve analytically/numerically and, therefore, are subject to intensive experimental effort in the ultracold atoms community aiming at their quantum simulation. I will present some PEPS results [2,3] down to temperatures of one tenth of the hopping rate, in the pseudogap regime. These results, obtained directly in the thermodynamic limit, can serve as a guide/benchmark for the current experimental efforts. 

References 

[1] A.D. King, A. Nocera, M.M. Rams, J. Dziarmaga, R. Wiersema, W. Bernoudy,..., Science 388, 199 (2025). 

[2] A. Sinha, M.M. Rams, P. Czarnik, and J. Dziarmaga, Phys. Rev. B 106, 195105 (2022). 

[3] Y. Zhang, A. Sinha, M.M. Rams, J. Dziarmaga, arXiv:2510.04756.

[4] Y. Zhang, F. Bayocboc, J. Dziarmaga, Phys. Rev. B 112, 134420 (2025).