Emergent lattices with geometrical frustration in doped extended Hubbard models

Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site $U$ and nearest-neighbor $V$ Coulomb interactions at $3/4$ filling ($n=3/2$) and (ii) the triangular lattice with on-site $U$, nearest-neighbor $V$, and next-nearest-neighbor $V'$ Coulomb interactions at $3/8$ filling ($n=3/4$). We consider various approaches including mean-field approximations, perturbation theory, and variational Monte Carlo. For the honeycomb case (i), charge order induces an effective triangular lattice at large values of $U/t$ and $V/t$, where $t$ is the nearest-neighbor hopping integral. The nearest-neighbor spin exchange interactions on this effective triangular lattice are antiferromagnetic in most of the phase diagram, while they become ferromagnetic when $U$ is much larger than $V$. At $U/t\sim (V/t)^3$, ferromagnetic and antiferromagnetic exchange interactions nearly cancel out, leading to a system with four-spin ring-exchange interactions. On the other hand, for the triangular case (ii) at large $U$ and finite $V'$, we find no charge order for small $V$, an effective kagome lattice for intermediate $V$, and one-dimensional charge order for large $V$. These results indicate that Coulomb interactions induce [case (i)] or enhance [case(ii)] emergent geometrical frustration of the spin degrees of freedom in the system, by forming charge order.Comment: 18 pages, 26 figure

Spontaneous symmetry breaking in correlated wave functions

We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of N\'eel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.Comment: 13 pages, 11 figure

Evaluating thermal expectation values by almost ideal sampling with Trotter gates

We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random product states. We restrict the number of applications of Trotter gates to be proportional to the system size, and thus the preparation would be easily accomplished in fault-tolerant quantum computers. When the Trotter gates are made from a nonintegrable Hamiltonian, we observe that the sampling efficiency increases with system size. This trend means that almost ideal sampling of initial states can be achieved in sufficiently large systems. We also find that the sampling efficiency is almost equal to that of Haar random sampling in some cases.Comment: 6 pages, 5 figure