20 research outputs found
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 and nearest-neighbor Coulomb interactions at filling
() and (ii) the triangular lattice with on-site , nearest-neighbor
, and next-nearest-neighbor Coulomb interactions at filling
(). 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
and , where 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 is much larger than . At ,
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 and finite , we find no
charge order for small , an effective kagome lattice for intermediate ,
and one-dimensional charge order for large . 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