Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
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2016
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| _version_ | 1866909990482083840 |
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| author | Perepelitsky, Edward Galatas, Andrew Mravlje, Jernej Žitko, Rok Khatami, Ehsan Shastry, B Sriram Georges, Antoine |
| author_facet | Perepelitsky, Edward Galatas, Andrew Mravlje, Jernej Žitko, Rok Khatami, Ehsan Shastry, B Sriram Georges, Antoine |
| contents | We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary electron density $n$, and both finite and infinite repulsion $U$. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high-temperature and, at large-$U$, they are featureless with characteristic widths of order the lattice hopping parameter $t$. In the infinite-$d$ limit we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte-Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale. The resistivity increases linearly in $T$ at high-temperature without saturation. This results from the $1/T$ behaviour of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturate at high-$T$. We find that $σ(n,T) \approx (1-n)σ(n=0,T)$ to a very good approximation for all $n$, with $σ(n=0,T)\propto t/T$ at high temperatures. The saturation at small $n$ occurs due to a compensation between the density-dependence of the effective number of carriers and that of the scattering time. The $T$-dependence of the resistivity displays a knee-like feature which signals a cross-over to the intermediate-temperature regime where the diffusion constant (or scattering time) start increasing with decreasing $T$. At high-temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1608_01600 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective Perepelitsky, Edward Galatas, Andrew Mravlje, Jernej Žitko, Rok Khatami, Ehsan Shastry, B Sriram Georges, Antoine Strongly Correlated Electrons We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit, arbitrary electron density $n$, and both finite and infinite repulsion $U$. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high-temperature and, at large-$U$, they are featureless with characteristic widths of order the lattice hopping parameter $t$. In the infinite-$d$ limit we compare the series expansion results with accurate numerical renormalization group and interaction expansion quantum Monte-Carlo results. We find excellent agreement down to surprisingly low temperatures, throughout most of the bad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale. The resistivity increases linearly in $T$ at high-temperature without saturation. This results from the $1/T$ behaviour of the compressibility or kinetic energy, which play the role of the effective carrier number. In contrast, the scattering time (or diffusion constant) saturate at high-$T$. We find that $σ(n,T) \approx (1-n)σ(n=0,T)$ to a very good approximation for all $n$, with $σ(n=0,T)\propto t/T$ at high temperatures. The saturation at small $n$ occurs due to a compensation between the density-dependence of the effective number of carriers and that of the scattering time. The $T$-dependence of the resistivity displays a knee-like feature which signals a cross-over to the intermediate-temperature regime where the diffusion constant (or scattering time) start increasing with decreasing $T$. At high-temperatures, the thermopower obeys the Heikes formula, while the Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$. |
| title | Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/1608.01600 |