Magnetism and Phase Separation in Polymeric Hubbard Chains

Abstract

We study a class of one-dimensional chains whose topology leads to flatbands in the electronic spectrum. Using the Hubbard model, we find that these materials should exhibit femmagnetic ordering for a half-filled band, in agreement with a theorem by Lieb. Away from half filling the system displays a very rich magnetic phase diagram. Possible experimental realizations are suggested.

Low-energy structure of the homometallic intertwining double-chain ferrimagnetsA3Cu3(PO4)4Yamamoto1, Ohara2 2007Phys. Rev. B176160View full textAdd to dashboardCite

“…While there exist a macroscopic number of flatbands 50 in the excitation spectrum at ␦ = 1 and ␦ = 0, which signify uncorrelated excitations of local spin-2S multiplets in any case, they become dispersive as soon as ␦ moves away from these particular points. Pair excitations of corner spins S n:3 and S n+1:1 are elementary in plaquette chains of ␦ = 1, while those of S n:1 and S n:3 are elementary in decoupled trimers of ␦ = 0, both of which are completely immobile without any mediation of joint spins S n:2 .…”

How the site degree influences quantum probability on inhomogeneous substrates

“…This provides very simple exact results for the dependency between ψ E ( r) and P k (E), supporting our results for the Apollonian network and percolation clusters. Figure 1(a) and (b) (see, for instance, [16]) present two examples of networks of class A. Indeed, if in Fig.…”

“…We restrict our study to purely geometrical features, and consider clusters on the square lattice obtained by usual bond percolation [12,13], Gaussian percolation [14], as well as on the deterministic Apollonian network [30], and some linear, periodic, inhomogeneous chains [16]. We carry out a numerical investigation of the local properties of the wave function of a system described by a nearest neighbor tight-binding Hamiltonian.…”

Ferrimagnetism in the Hubbard, dimmer-connector frustrated chain

“…Extending this argument to the whole lattice we conclude that each sublattice has an internal ferromagnetic order, while the magnetic moment of the A and B sublattices disposes antiparallel one another, thus yielding a ferrimagnetic (instead of ferromagnetic) order. This argument can be applied even to one-dimensional topologies; that is the case of the "lozenge lattice" for example [6][7][8], where the Hubbard GS is ferrimagnetic in the half-filled band case.…”

“…In this case, Lieb's theorem [4] ensures that the net spin of the chain is S = The AB 2 chain has been studied in the context of Heisenberg [9][10][11] and half-filled band Hubbard [6][7][8] models. While [9][10][11] include two antiferromagnetic exchanges, J (connecting A-B sites) and J 0 (connecting both B sites on the same dimmer), [6][7][8] only consider a non-vanishing electronic hopping between A and B sites (say, a "lozenge" Hubbard lattice), in order to satisfy Lieb's hypothesis of a bipartite lattice [4]. Lieb's results were generalized, showing that the ferrimagnetic order persists in the "lozenge" and in other one-dimensional lattices, when site dependent Hubbard parameters are considered [7].…”