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arXiv:0911.3596 · Physical Review B

Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices

Oleg Derzhko, Johannes Richter, A. Honecker, Mykola Maksymenko, Roderich Moessner

Published Jan 26, 2010• 78 citations
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Abstract

We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices---sawtooth chain and two kagom\'e chains---with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of exact many-electron ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential ${\ensuremath{\mu}}_{0}$. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact-diagonalization data for finite systems.

DOI
10.1103/physrevb.81.014421

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We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices---sawtooth chain and two kagom'e chains---with completely dispersionless (flat) lowest single-electron bands. We construct the complete manifold of exact many-electron ground states at low electron fillings and calculate the degeneracy of these states. As a result, we obtain closed-form expressions for low-temperature thermodynamic quantities around a particular value of the chemical potential \ensuremathμ0{\ensuremath{\mu}}_{0}\ensuremathμ0​. We discuss specific features of thermodynamic quantities of these ground-state ensembles such as residual entropy, an extra low-temperature peak in the specific heat, and the existence of ferromagnetism and paramagnetism. We confirm our analytical results by comparison with exact-diagonalization data for finite systems.
The repulsive Hubbard model on a sawtooth chain exhibits the lowest single-electron band which is completely dispersionless (flat) for a specific choice of the hopping parameters. We construct exact many-electron ground states for electron fillings up to 1/4. We map the low-energy degrees of freedom of the electron model to a model of classical hard dimers on a chain and, as a result, obtain the ground-state degeneracy as well as closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the chemical potential. We compare our analytical findings with complementary numerical data. Although we consider a specific model, we believe that some of our results such as a low-temperature peak in the specific heat are generic for flat-band ferromagnets.
We consider the antiferromagnetic Heisenberg model and the repulsive Hubbard model for a class of frustrated lattices with a completely dispersionless (flat) lowest one-particle (either one-magnon or one-electron) band. We construct exact many-particle ground states for a wide range of particle densities, calculate their degeneracy, and, as a result, obtain closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the magnetic field h sat or the chemical potential μ 0 . We confirm our analytic findings by numerical data for finite lattices.
We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain relation of the exchange (hopping) integrals. Although these eigenstates differ in details for the two models because of the different statistics, they share some characteristic features. The localized eigenstates are highly degenerate and become ground states in high magnetic fields (Heisenberg model) or at certain electron fillings (Hubbard model), respectively. They may dominate the low-temperature thermodynamics and lead to an extra low-temperature maximum in the specific heat. The ground-state degeneracy can be calculated exactly by a mapping of the manifold of localized ground states onto a classical hard-dimer problem, and explicit expressions for thermodynamic quantities can be derived which are valid at low temperatures near the saturation field for the Heisenberg model or around a certain value of the chemical potential for the Hubbard model, respectively.
Spinless fermions on highly frustrated lattices are characterized by the lowest single-particle band which is completely flat.Concrete realizations are provided by the sawtooth chain and the kagom é lattice.For these models a real-space picture is given in terms of localized states.Furthermore, we find a finite zero-temperature entropy for a suitable choice of the chemical potential.The entropy is computed numerically at finite temperature and one observes a strong cooling effect during adiabatic changes of the chemical potential.We argue that the localized states, the associated zerotemperature entropy as well as the large temperature variations carry over to the repulsive Hubbard model.The relation to flat-band ferromagnetism is also discussed briefly.
We study the repulsive Hubbard model both analytically and numerically on a family of highly frustrated lattices which have one-electron states localized on isolated trapping cells. We construct and count exact many-electron ground states for a wide range of electron densities and obtain closed-form expressions for the low-temperature thermodynamic quantities which are universal for all lattices of the family. Furthermore, we find that saturated ferromagnetism is obtained only for sufficiently high electron densities and large Hubbard repulsion UUU while there is no finite average moment in the ground states at lower densities.
We consider the one-orbital N -site repulsive Hubbard model on two kagome like chains, both of which yield a completely dispersionless (flat) one-electron band.Using exact many-electron ground states in the subspaces with n ≤ nmax (nmax ∝ N ) electrons, we calculate the square of the total spin in the ground state to discuss magnetic properties of the models.We have found that although for n < nmax the ground states contain fully polarized states, there is no finite region of electron densities n/N < 1 (N = N/3 or N = N/5) where ground-state ferromagnetism survives for N → ∞.