# Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons

@article{Hohenadler2005TemperatureAQ, title={Temperature- and quantum phonon effects on Holstein-Hubbard bipolarons}, author={Martin Hohenadler and Wolfgang von der Linden}, journal={Physical Review B}, year={2005}, volume={71}, pages={184309} }

The one-dimensional Holstein-Hubbard model with two electrons of opposite spin is studied using an extension of a recently developed quantum Monte Carlo method, and a very simple yet rewarding variational approach, both based on a canonically transformed Hamiltonian. The quantum Monte Carlo method yields very accurate results in the regime of small but finite phonon frequencies, characteristic of many strongly correlated materials such as, e.g., the cuprates and the manganites. The influence of…

## 21 Citations

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- 2010

Abstract
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- 2010

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## References

SHOWING 1-10 OF 33 REFERENCES

### Single-particle spectral function of the Holstein-Hubbard bipolaron

- Physics
- 2005

The one-electron spectral function of the Holstein-Hubbard bipolaron in one dimension is studied using cluster perturbation theory together with the Lanczos method. In contrast to other approaches,…

### Two-dimensional Hubbard-Holstein bipolaron

- Physics
- 2004

We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion U and with increasing…

### Bipolarons in the extended Holstein Hubbard model

- Physics
- 2001

There is growing evidence that electron-phonon coupling plays an important role in determining exotic properties of novel materials such as colossal magnetoresistance 1 and high-Tc compounds. 2 Since…

### Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

- Physics
- 1999

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay…

### Quantum Monte Carlo and variational approaches to the Holstein model

- Physics
- 2004

Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic…

### Small bipolarons in the 2-dimensional Holstein-Hubbard model. II. Quantum bipolarons

- Physics
- 2000

Abstract:We study the effective mass of the bipolarons and essentially the possibility to get both light and strongly bound bipolarons in the Holstein-Hubbard model and some variations in the…

### Dynamical properties of the one-dimensional Holstein model

- Physics
- 1999

The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron…

### Ferromagnetism and electron-phonon coupling in the manganites

- Physics
- 2002

The physics of ferromagnetic doped manganites, such as La 1-x Ca x MnO 3 with x ≈ 0.2-0.4, is reviewed. The concept of double exchange is discussed within the general framework of itinerant electron…