In this work, we describe the simplifications to the Extremely Correlated Fermi Liquid Theory (ECFL) \\cite{ECFL, Monster} which occur in the limit of infinite spatial dimensions. In particular, we show that the single-particle electron Green's function G(k) can be written in terms of two momentum-independent self-energies. Moreover, we elucidate the nature of the ECFL \\lambda expansion in the limit of infinite dimensions and carry out this expansion explicitly to O(\\lambda^2). Additionally, we demonstrate the vanishing of vertex corrections to the optical conductivity in general and to each order in \\lambda in the limit of infinite dimensions. We generalize the ECFL formalism to the infinite-U Anderson impurity model (AIM) , and demonstrate a Dynamical Mean-Field Theory (DMFT) like mapping between the ECFL objects of the infinite-dimensional t-J model and the infinite-U AIM, and show that this mapping holds to each order in \\lambda. We compute the spectral function for the AIM to O (\\lambda^2) and make comparisons with results obtained through Numerical Renormalization Group (NRG) computations. Finally, we develop a novel formalism for the high-temperature expansion of dynamical correlation functions in the infinite-U Hubbard model which is more efficient than any used previously and gives results for an arbitrary number of spin species. We use it to calculate the single-particle Green's function G(k) to fourth order in (\\beta t) for m spin-species on a d-dimensional hypercube.In this work, we describe the simplifications to the Extremely Correlated Fermi Liquid Theory (ECFL) \\cite{ECFL, Monster} which occur in the limit of infinite spatial dimensions. In particular, we show that the single-particle electron Green's function G(k) can be written in terms of two momentum-independent self-energies. Moreover, we elucidate the nature of the ECFL \\lambda expansion in the limit of infinite dimensions and carry out this expansion explicitly to O(\\lambda^2). Additionally, we demonstrate the vanishing of vertex corrections to the optical conductivity in general and to each order in \\lambda in the limit of infinite dimensions. We generalize the ECFL formalism to the infinite-U Anderson impurity model (AIM) , and demonstrate a Dynamical Mean-Field Theory (DMFT) like mapping between the ECFL objects of the infinite-dimensional t-J model and the infinite-U AIM, and show that this mapping holds to each order in \\lambda. We compute the spectral function for the AIM to O (\\lambda^2) and make comparisons with results obtained through Numerical Renormalization Group (NRG) computations. Finally, we develop a novel formalism for the high-temperature expansion of dynamical correlation functions in the infinite-U Hubbard model which is more efficient than any used previously and gives results for an arbitrary number of spin species. We use it to calculate the single-particle Green's function G(k) to fourth order in (\\beta t) for m spin-species on a d-dimensional hypercube.

Jan 1, 20140 citations

Fermi Liquids in Two Dimensions

WORLD SCIENTIFIC eBooksMar 1, 20080 citations

Low-energy physics of the t−J model in d=∞ using extremely correlated Fermi liquid theory: Cutoff second-order equations

B. Sriram Shastry, Edward Perepelitsky

We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with $J=0$ , using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high- $T$ entropy. The resulting quasiparticle weight $Z$ , the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite $T$ rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising $T$ . The present scheme is generalizable to finite dimensions and a nonvanishing $J$ .We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with $J=0$, using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter $1/(2S)$ in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high-$T$ entropy. The resulting quasiparticle weight $Z$, the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite $T$ rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising $T$. The present scheme is generalizable to finite dimensions and a nonvanishing $J$.

arXiv:1605.08213Physical review. B./Physical review. BJul 28, 201618 citations

Diagrammatic λ series for extremely correlated Fermi liquids

Edward Perepelitsky, B. Sriram Shastry

arXiv:1410.5174Annals of PhysicsMar 14, 20158 citations

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

Wenxin Ding, Rok Žitko, B. Sriram Shastry

Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely, the Hall constants ${R}_{H}$ and Hall angles ${\ensuremath{\theta}}_{H}$, and the longitudinal and transverse optical response of the $U=\ensuremath{\infty}$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller-correlated Fermi liquid (GCFL) and the Gutzwiller-correlated strange metal (GCSM). We find that the Hall angle $cot{\ensuremath{\theta}}_{H}$ is proportional to ${T}^{2}$ in the GCFL regime, while upon warming into the GCSM regime it first passes through a downward bend and then continues as ${T}^{2}$ . Equivalently, ${R}_{H}$ is weakly temperature dependent in the GCFL regime, but becomes strongly temperature dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ and the optical Hall angles $tan{\ensuremath{\theta}}_{H}(\ensuremath{\omega})$ below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely, the Hall constants ${R}_{H}$ and Hall angles ${\ensuremath{\theta}}_{H}$, and the longitudinal and transverse optical response of the $U=\ensuremath{\infty}$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller-correlated Fermi liquid (GCFL) and the Gutzwiller-correlated strange metal (GCSM). We find that the Hall angle $cot{\ensuremath{\theta}}_{H}$ is proportional to ${T}^{2}$ in the GCFL regime, while upon warming into the GCSM regime it first passes through a downward bend and then continues as ${T}^{2}$. Equivalently, ${R}_{H}$ is weakly temperature dependent in the GCFL regime, but becomes strongly temperature dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ and the optical Hall angles $tan{\ensuremath{\theta}}_{H}(\ensuremath{\omega})$ below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.

arXiv:1705.01914Physical review. B./Physical review. BSep 25, 20179 citations

We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with

J=0

, using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter

1/(2S)

in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high-

T

entropy. The resulting quasiparticle weight

Z

, the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite

T

rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising

T

. The present scheme is generalizable to finite dimensions and a nonvanishing

J

{R}_{H}

and Hall angles ${\ensuremath{\theta}}_{H}$, and the longitudinal and transverse optical response of the $U=\ensuremath{\infty}$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller-correlated Fermi liquid (GCFL) and the Gutzwiller-correlated strange metal (GCSM). We find that the Hall angle $cot{\ensuremath{\theta}}_{H}$ is proportional to

{T}^{2}

in the GCFL regime, while upon warming into the GCSM regime it first passes through a downward bend and then continues as

{T}^{2}

. Equivalently,

{R}_{H}

is weakly temperature dependent in the GCFL regime, but becomes strongly temperature dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ and the optical Hall angles $tan{\ensuremath{\theta}}_{H}(\ensuremath{\omega})$ below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.