# Extremely correlated Fermi liquid theory of the *t-J* model in 2 dimensions: low energy properties

## Abstract

Low energy properties of the metallic state of the two-dimensional *t-J* model are presented for second neighbor hopping with hole-doping ($$t^{\prime} \leqslant 0$$) and electron-doping ($$t^{\prime} \gt 0$$), with various superexchange energy *J*. We use a closed set of equations for the Greens functions obtained from the *extremely correlated Fermi liquid theory*. These equations reproduce the known low energies features of the large *U* Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest *T* for density $$n\gtrsim 0.8$$, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a *T*^{2} behavior at low *T*, followed by an interesting kink at higher *T*. The Hall number exhibits strong renormalization due to correlations. Flipping the sign of $$t^{\prime} $$ changes the curvature of the resistivity versus *T* curves between convex and concave. Furthermore our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of California, Santa Cruz, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1437768

- Alternate Identifier(s):
- OSTI ID: 1500089

- Grant/Contract Number:
- FG02-06ER46319.; FG02-06ER46319

- Resource Type:
- Published Article

- Journal Name:
- New Journal of Physics

- Additional Journal Information:
- Journal Name: New Journal of Physics Journal Volume: 20 Journal Issue: 1; Journal ID: ISSN 1367-2630

- Publisher:
- IOP Publishing

- Country of Publication:
- United Kingdom

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; strong correlations; 2-dimensional t-J model; temperature dependent resistivity; cotangent Hall angle; extremely correlated Fermi liquid

### Citation Formats

```
Shastry, B. Sriram, and Mai, Peizhi. Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties. United Kingdom: N. p., 2018.
Web. doi:10.1088/1367-2630/aa9b74.
```

```
Shastry, B. Sriram, & Mai, Peizhi. Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties. United Kingdom. doi:10.1088/1367-2630/aa9b74.
```

```
Shastry, B. Sriram, and Mai, Peizhi. Mon .
"Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties". United Kingdom. doi:10.1088/1367-2630/aa9b74.
```

```
@article{osti_1437768,
```

title = {Extremely correlated Fermi liquid theory of the t-J model in 2 dimensions: low energy properties},

author = {Shastry, B. Sriram and Mai, Peizhi},

abstractNote = {Low energy properties of the metallic state of the two-dimensional t-J model are presented for second neighbor hopping with hole-doping ($t^{\prime} \leqslant 0$) and electron-doping ($t^{\prime} \gt 0$), with various superexchange energy J. We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density $n\gtrsim 0.8$, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T2 behavior at low T, followed by an interesting kink at higher T. The Hall number exhibits strong renormalization due to correlations. Flipping the sign of $t^{\prime} $ changes the curvature of the resistivity versus T curves between convex and concave. Furthermore our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.},

doi = {10.1088/1367-2630/aa9b74},

journal = {New Journal of Physics},

number = 1,

volume = 20,

place = {United Kingdom},

year = {2018},

month = {1}

}

DOI: 10.1088/1367-2630/aa9b74

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