# 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)

- 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. https://doi.org/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. https://doi.org/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. https://doi.org/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}

}

https://doi.org/10.1088/1367-2630/aa9b74

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Theory of Raman scattering in Mott-Hubbard systems

journal, August 1990

- Shastry, B. Sriram; Shraiman, Boris I.
- Physical Review Letters, Vol. 65, Issue 8

##
Diagrammatic $\lambda $ series for extremely correlated Fermi liquids

journal, June 2015

- Perepelitsky, Edward; Sriram Shastry, B.
- Annals of Physics, Vol. 357

##
Extremely correlated Fermi liquid theory meets dynamical mean-field theory: Analytical insights into the doping-driven Mott transition

journal, December 2013

- Žitko, R.; Hansen, D.; Perepelitsky, E.
- Physical Review B, Vol. 88, Issue 23

##
Comment on “Anomalous Hall Effect in YB ${\mathrm{a}}_{2}$ C ${\mathrm{u}}_{3}$ ${\mathrm{O}}_{7}$ ”

journal, February 1997

- Ong, N. P.; Anderson, P. W.
- Physical Review Letters, Vol. 78, Issue 5

##
Transport studies of La1.92Sr0.08Cu1-xMxO4 (M=Ni and Zn) and Nd2-yCeyCuO4 up to about 900 K

journal, October 1994

- Takeda, J.; Nishikawa, T.; Sato, M.
- Physica C: Superconductivity, Vol. 231, Issue 3-4

##
Extremely Correlated Fermi Liquids

journal, July 2011

- Shastry, B. Sriram
- Physical Review Letters, Vol. 107, Issue 5

##
Low-energy physics of the $t\text{\u2212}J$ model in $d=\infty $ using extremely correlated Fermi liquid theory: Cutoff second-order equations

journal, July 2016

- Shastry, B. Sriram; Perepelitsky, Edward
- Physical Review B, Vol. 94, Issue 4

##
Electronic Phase Diagram of High- ${T}_{c}$ Cuprate Superconductors from a Mapping of the In-Plane Resistivity Curvature

journal, December 2004

- Ando, Yoichi; Komiya, Seiki; Segawa, Kouji
- Physical Review Letters, Vol. 93, Issue 26

##
Quantum Phase Transition in the Magnetic-Field-Induced Normal State of Optimum-Doped High- ${T}_{c}$ Cuprate Superconductors at Low Temperatures

journal, January 2009

- Balakirev, F. F.; Betts, J. B.; Migliori, A.
- Physical Review Letters, Vol. 102, Issue 1

##
Extremely correlated Fermi liquids: Self-consistent solution of the second-order theory

journal, June 2013

- Hansen, Daniel; Shastry, B. Sriram
- Physical Review B, Vol. 87, Issue 24

##
Scaling of the temperature dependent Hall effect in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4}$

journal, April 1994

- Hwang, H. Y.; Batlogg, B.; Takagi, H.
- Physical Review Letters, Vol. 72, Issue 16

##
Transport functions for hypercubic and Bethe lattices

journal, November 2013

- Arsenault, Louis-François; Tremblay, A. -M. S.
- Physical Review B, Vol. 88, Issue 20

##
One-band tight-binding model parametrization of the high- ${T}_{c}$ cuprates including the effect of ${k}_{z}$ dispersion

journal, August 2005

- Markiewicz, R. S.; Sahrakorpi, S.; Lindroos, M.
- Physical Review B, Vol. 72, Issue 5

##
A General Expression for Hall Coefficient Based on Fermi Liquid Theory

journal, October 1988

- Kohno, H.; Yamada, K.
- Progress of Theoretical Physics, Vol. 80, Issue 4

##
Extremely correlated Fermi liquid study of the $U=\infty $ Anderson impurity model

journal, November 2013

- Shastry, B. Sriram; Perepelitsky, Edward; Hewson, Alex C.
- Physical Review B, Vol. 88, Issue 20

##
Effect of Zn impurities on the normal-state Hall angle in single-crystal YBa_{2}Cu_{3-x}Zn_{x}O_{7-δ}

journal, October 1991

- Chien, T.; Wang, Z.; Ong, N.
- Physical Review Letters, Vol. 67, Issue 15

##
Extremely correlated Fermi liquids: The formalism

journal, March 2013

- Shastry, B. Sriram
- Physical Review B, Vol. 87, Issue 12

##
How Bad Metals Turn Good: Spectroscopic Signatures of Resilient Quasiparticles

journal, February 2013

- Deng, Xiaoyu; Mravlje, Jernej; Žitko, Rok
- Physical Review Letters, Vol. 110, Issue 8

##
Hidden Fermi-liquid Charge Transport in the Antiferromagnetic Phase of the Electron-Doped Cuprate Superconductors

journal, November 2016

- Li, Yangmu; Tabis, W.; Yu, G.
- Physical Review Letters, Vol. 117, Issue 19

##
Superconductivity in Bad Metals

journal, April 1995

- Emery, V. J.; Kivelson, S. A.
- Physical Review Letters, Vol. 74, Issue 16

##
Strange metal from Gutzwiller correlations in infinite dimensions: Transverse transport, optical response, and rise of two relaxation rates

journal, September 2017

- Ding, Wenxin; Žitko, Rok; Shastry, B. Sriram
- Physical Review B, Vol. 96, Issue 11

##
Theory of Hall Effect. I: Nearly Free Electron

journal, September 1969

- Fukuyama, Hidetoshi; Ebisawa, Hiromichi; Wada, Yasushi
- Progress of Theoretical Physics, Vol. 42, Issue 3

##
Evolution of the Hall Coefficient and the Peculiar Electronic Structure of the Cuprate Superconductors

journal, May 2004

- Ando, Yoichi; Kurita, Y.; Komiya, Seiki
- Physical Review Letters, Vol. 92, Issue 19

##
The Resonating Valence Bond State in La2CuO4 and Superconductivity

journal, March 1987

- Anderson, P. W.
- Science, Vol. 235, Issue 4793

##
Theory of extreme correlations using canonical Fermions and path integrals

journal, April 2014

- Shastry, B. Sriram
- Annals of Physics, Vol. 343

##
Hidden Fermi Liquid, Scattering Rate Saturation, and Nernst Effect: A Dynamical Mean-Field Theory Perspective

journal, July 2013

- Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel
- Physical Review Letters, Vol. 111, Issue 3

##
Erratum to: “Theory of extreme correlations using canonical Fermions and path integrals” [Ann. Phys. 343 (2014) 164–199]

journal, October 2016

- Shastry, B. Sriram
- Annals of Physics, Vol. 373

##
Charge dynamics in underdoped ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}:$ Pseudogap and related phenomena

journal, January 2004

- Onose, Y.; Taguchi, Y.; Ishizaka, K.
- Physical Review B, Vol. 69, Issue 2

##
The *t* – *J* model for the oxide high- *T* _{c} superconductors

journal, February 2008

- Ogata, Masao; Fukuyama, Hidetoshi
- Reports on Progress in Physics, Vol. 71, Issue 3

##
Conductivity and Hall effect in the two-dimensional Hubbard model

journal, June 1992

- Voruganti, Puru; Golubentsev, Andrey; John, Sajeev
- Physical Review B, Vol. 45, Issue 24

##
Superconductor-to-nonsuperconductor transition in ( ${\mathrm{La}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${)}_{2}$ ${\mathrm{CuO}}_{4}$ as investigated by transport and magnetic measurements

journal, August 1989

- Takagi, H.; Ido, T.; Ishibashi, S.
- Physical Review B, Vol. 40, Issue 4

##
XSEDE: Accelerating Scientific Discovery

journal, September 2014

- Towns, John; Cockerill, Timothy; Dahan, Maytal
- Computing in Science & Engineering, Vol. 16, Issue 5

##
Extremely Correlated Fermi Liquids

journal, July 2011

- Shastry, B. Sriram
- Physical Review Letters, Vol. 107, Issue 5

##
Low-energy physics of the $t\text{\u2212}J$ model in $d=\infty $ using extremely correlated Fermi liquid theory: Cutoff second-order equations

journal, July 2016

- Shastry, B. Sriram; Perepelitsky, Edward
- Physical Review B, Vol. 94, Issue 4

##
Extremely correlated Fermi liquid theory meets dynamical mean-field theory: Analytical insights into the doping-driven Mott transition

journal, December 2013

- Žitko, R.; Hansen, D.; Perepelitsky, E.
- Physical Review B, Vol. 88, Issue 23

##
Extremely correlated Fermi liquid study of the $U=\infty $ Anderson impurity model

journal, November 2013

- Shastry, B. Sriram; Perepelitsky, Edward; Hewson, Alex C.
- Physical Review B, Vol. 88, Issue 20

##
How Bad Metals Turn Good: Spectroscopic Signatures of Resilient Quasiparticles

journal, February 2013

- Deng, Xiaoyu; Mravlje, Jernej; Žitko, Rok
- Physical Review Letters, Vol. 110, Issue 8

##
Hidden Fermi Liquid, Scattering Rate Saturation, and Nernst Effect: A Dynamical Mean-Field Theory Perspective

journal, July 2013

- Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel
- Physical Review Letters, Vol. 111, Issue 3

##
Extremely correlated Fermi liquids: The formalism

journal, March 2013

- Shastry, B. Sriram
- Physical Review B, Vol. 87, Issue 12

##
One-band tight-binding model parametrization of the high- ${T}_{c}$ cuprates including the effect of ${k}_{z}$ dispersion

journal, August 2005

- Markiewicz, R. S.; Sahrakorpi, S.; Lindroos, M.
- Physical Review B, Vol. 72, Issue 5

##
Theory of Raman scattering in Mott-Hubbard systems

journal, August 1990

- Shastry, B. Sriram; Shraiman, Boris I.
- Physical Review Letters, Vol. 65, Issue 8

##
Superconductivity in Bad Metals

journal, April 1995

- Emery, V. J.; Kivelson, S. A.
- Physical Review Letters, Vol. 74, Issue 16

##
Electronic Phase Diagram of High- ${T}_{c}$ Cuprate Superconductors from a Mapping of the In-Plane Resistivity Curvature

journal, December 2004

- Ando, Yoichi; Komiya, Seiki; Segawa, Kouji
- Physical Review Letters, Vol. 93, Issue 26

##
Superconductor-to-nonsuperconductor transition in ( ${\mathrm{La}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${)}_{2}$ ${\mathrm{CuO}}_{4}$ as investigated by transport and magnetic measurements

journal, August 1989

- Takagi, H.; Ido, T.; Ishibashi, S.
- Physical Review B, Vol. 40, Issue 4

##
Charge dynamics in underdoped ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}:$ Pseudogap and related phenomena

journal, January 2004

- Onose, Y.; Taguchi, Y.; Ishizaka, K.
- Physical Review B, Vol. 69, Issue 2

##
Hidden Fermi-liquid Charge Transport in the Antiferromagnetic Phase of the Electron-Doped Cuprate Superconductors

journal, November 2016

- Li, Yangmu; Tabis, W.; Yu, G.
- Physical Review Letters, Vol. 117, Issue 19

##
Conductivity and Hall effect in the two-dimensional Hubbard model

journal, June 1992

- Voruganti, Puru; Golubentsev, Andrey; John, Sajeev
- Physical Review B, Vol. 45, Issue 24

##
Theory of Hall Effect. I: Nearly Free Electron

journal, September 1969

- Fukuyama, Hidetoshi; Ebisawa, Hiromichi; Wada, Yasushi
- Progress of Theoretical Physics, Vol. 42, Issue 3

##
A General Expression for Hall Coefficient Based on Fermi Liquid Theory

journal, October 1988

- Kohno, H.; Yamada, K.
- Progress of Theoretical Physics, Vol. 80, Issue 4

##
Transport functions for hypercubic and Bethe lattices

journal, November 2013

- Arsenault, Louis-François; Tremblay, A. -M. S.
- Physical Review B, Vol. 88, Issue 20

##
Effect of Zn impurities on the normal-state Hall angle in single-crystal YBa_{2}Cu_{3-x}Zn_{x}O_{7-δ}

journal, October 1991

- Chien, T.; Wang, Z.; Ong, N.
- Physical Review Letters, Vol. 67, Issue 15

##
Comment on “Anomalous Hall Effect in YB ${\mathrm{a}}_{2}$ C ${\mathrm{u}}_{3}$ ${\mathrm{O}}_{7}$ ”

journal, February 1997

- Ong, N. P.; Anderson, P. W.
- Physical Review Letters, Vol. 78, Issue 5

##
Strange metal from Gutzwiller correlations in infinite dimensions: Transverse transport, optical response, and rise of two relaxation rates

journal, September 2017

- Ding, Wenxin; Žitko, Rok; Shastry, B. Sriram
- Physical Review B, Vol. 96, Issue 11

##
Evolution of the Hall Coefficient and the Peculiar Electronic Structure of the Cuprate Superconductors

journal, May 2004

- Ando, Yoichi; Kurita, Y.; Komiya, Seiki
- Physical Review Letters, Vol. 92, Issue 19

##
Scaling of the temperature dependent Hall effect in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4}$

journal, April 1994

- Hwang, H. Y.; Batlogg, B.; Takagi, H.
- Physical Review Letters, Vol. 72, Issue 16

##
Quantum Phase Transition in the Magnetic-Field-Induced Normal State of Optimum-Doped High- ${T}_{c}$ Cuprate Superconductors at Low Temperatures

journal, January 2009

- Balakirev, F. F.; Betts, J. B.; Migliori, A.
- Physical Review Letters, Vol. 102, Issue 1

##
XSEDE: Accelerating Scientific Discovery

journal, September 2014

- Towns, John; Cockerill, Timothy; Dahan, Maytal
- Computing in Science & Engineering, Vol. 16, Issue 5

##
Extremely correlated Fermi liquids: Self-consistent solution of the second-order theory

journal, June 2013

- Hansen, Daniel; Shastry, B. Sriram
- Physical Review B, Vol. 87, Issue 24

Works referencing / citing this record:

##
Influence of magnetism and correlation on the spectral properties of doped Mott insulators

journal, March 2018

- Wang, Yao; Moritz, Brian; Chen, Cheng-Chien
- Physical Review B, Vol. 97, Issue 11

##
$t-{t}^{\prime}-J$ model in one dimension using extremely correlated Fermi-liquid theory and time-dependent density matrix renormalization group

journal, July 2018

- Mai, Peizhi; White, Steven R.; Shastry, B. Sriram
- Physical Review B, Vol. 98, Issue 3

##
Nonresonant Raman scattering in extremely correlated Fermi liquids

journal, September 2018

- Mai, Peizhi; Shastry, B. Sriram
- Physical Review B, Vol. 98, Issue 11

##
Extremely correlated Fermi liquid of the $t-J$ model in two dimensions

journal, November 2018

- Mai, Peizhi; Shastry, B. Sriram
- Physical Review B, Vol. 98, Issue 20