Understanding quantum many-body states of correlated electrons is one main theme in modern condensed-matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, was recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Chen et al., Phys. Rev. X 8, 031082 (2018)], complemented by independent determinant quantum Monte Carlo, offers a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to an unprecedented low temperature of a few percent of the tunneling energy. We observe excellent agreement with ultracold fermion measurements at both half filling and finite doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behaviors of the antimoments.

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition has long been sought yet undiscovered directly in magnetic materials. Here, the authors identify two phase transitions with BKT fluctuations detected by NMR and critical scaling behavior in magnetic susceptibility expected for the BKT transition in a frustrated magnet TmMgGaO4.

With recently developed exponential tensor-network approach, the authors perform accurate finite-temperature simulations of the extended Kitaev model with additional interactions common in Kitaev materials. At intermediate temperature, they find an emergent Curie law of magnetic susceptibility and a stripy spin-structure factor characterizing the robust Kitaev fractional liquid.

TmMgGaO4 is one of a number of recently-synthesized quantum magnets that are proposed to realize important theoretical models. Here the authors demonstrate the agreement between detailed experimental measurements and state-of-the-art predictions based on the 2D transverse field triangular lattice Ising model.

The anomalous thermodynamic properties of the paradigmatic frustrated spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLH) has remained an open topic of research over decades, both experimentally and theoretically. Here, we further the theoretical understanding based on the recently developed, powerful exponential tensor renormalization group method on cylinders and stripes in a quasi-one-dimensional (1D) setup, as well as a tensor product operator approach directly in 2D. The observed thermal properties of the TLH are in excellent agreement with two recent experimental measurements on the virtually ideal TLH material Ba8CoNb6O24.

We speed up thermal simulations of quantum many-body systems in both one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix $\rho=e^{-\beta H}$ onto itself. We refer to this scheme of doubling $\beta$ in each step of the imaginary time evolution as the exponential tensor renormalization group (XTRG). This approach is in stark contrast to conventional Trotter-Suzuki-type methods which evolve $\rho$ on a linear quasicontinuous grid in inverse temperature $\beta\equiv1/T$.