Ultracold-atom simulators have provided important insights into charge and spin transport in the two-dimensional Hubbard model [1, 2]. However, theoretical tools to compute quantities directly measured in experiments, such as space- and time-resolved charge/spin densities following a quench of an external density-modulating field, are still scarce. Here, we devise the alternating-basis quantum Monte Carlo (ABQMC) method for interacting electrons on a lattice, which is uniquely suited to compute such quantities. Apart from out-of-equilibrium setups, the formalism is equally applicable in thermal equilibrium described by either canonical or grand-canonical ensemble. The method relies on the Suzuki–Trotter decomposition (STD) and owes flexibility to the representation of the kinetic and interaction terms in the many-body bases in which they are diagonal. We formulate a Monte Carlo update scheme that respects both the momentum and particle-number conservation laws, to restrict the configuration space. The sampling efficiency is further enhanced by ensuring that the ABQMC algorithm manifestly respects several symmetries of the Hubbard model [3, 4]. We find that the method's performance is heavily plagued by the fermionic sign problem, whose extent is primarly related to the number of time-slices in the STD. Nevertheless, the ABQMC equation of state (density vs. chemical potential curve) computed on square-lattice clusters containing up to 48 sites agrees remarkably well with reference methods. We also discuss how the (real-time) dynamics of the survival probability of pure density-wave-like states on 4x4 clusters depends on the filling and the initial density pattern.
Acknowledgement: The authors acknowledge funding provided by the Institute of Physics Belgrade, through the grant by the Ministry of Education, Science, and Technological Development of the Republic of Serbia, as well as by the Science Fund of the Republic of Serbia, under the Key2SM project (PROMIS program, Grant No. 6066160).
1. P. T. Brown et al., Science 363, 379 (2019).
2. M. A. Nichols et al., Science 363, 383 (2019).
3. J. Yu et al., Phys. Rev. Lett. 119, 225302 (2017).
4. H. Zhai et al., New J. Phys. 21, 015003 (2019).