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B Sriram Shastry

Publications and source records attributed to B Sriram Shastry.

At least 19 recordsLinked to original sources
arXiv2026

Overview of the Theory of Extremely Correlated Fermi Liquids

The Extremely Correlated Fermi Liquids (ECFL) theory is reviewed as a framework for understanding the $t$-$J$ model in metallic systems close to the Mott insulating limit. This overview presents the underlying ideas and the resulting equations in a form accessible to nonexperts. We compare theoretical results with all available resistivity data for single-layer High-T$_{c}$ systems, and with some spectral data. The highlighted results include a density dependent quasilinear T-dependence in resistivity, an unusually small quasiparticle weight, and distinct low-temperature emergent scales that dominate transport, thermodynamics and spectral properties of single-layer High T$_c$ systems. Suggestions are made for further experiments to probe the physics of these challenging quantum many-body systems.

cond-mat.str-el↗
arXiv2026

Partition function zeros of quantum many-body systems: perturbative results

A systematic method to find the Yang-Lee partition function zeros of quantum many-body systems based on perturbation theory at finite temperatures was recently introduced in arXiv:2504.01880. This method identifies wave-vector and temperature-dependent complex virtual energies obtainable from the thermal electronic Greens function. The collection of virtual energies over all $\vec{k}$ yield the Yang-Lee zeroes. We apply this approach to the one-dimensional Hubbard model for different boundary conditions. We compare the results obtained by this method up to second-order in perturbation theory with the results found by exact diagonalization. We also propose a quantity that could be used for experimental detection of these zeros of a Hubbard ring. An example of the detection method is presented using exact diagonalization of the 8-site Hubbard ring.

cond-mat.str-el↗
arXiv2026

Aspects of the normal state resistivity of cuprate superconductors Bi2201, Tl2201 and Hg1201

Planar normal state resistivity data from two families of hole doped single layer cuprate superconductors $Bi2201$ (Bi$_2$Sr$_2$CuO$_{6+x}$) and $Tl2201$ (Tl$_2$Ba$_2$CuO$_{6+x}$) are calculated using the extremely correlated Fermi liquid theory (ECFL). This theory was recently employed for understanding the three families of single layer cuprate superconductors LSCO, BSLCO and NCCO. Adding these two systems accounts for essentially all single layer compounds where data is available for a range of densities and temperatures. The added case of $Bi2201$ is of particular interest since it was the original system where the almost linear in temperature resistivity was reported in 1990, and has been followed up by a systematic doping analysis only recently in 2022. The $Tl2201$ system has two distinct set of band parameters that fit the same Fermi surface, providing new challenges and insights into the ECFL theory.

cond-mat.str-el↗
arXiv2025

Partition function zeros of quantum many-body systems

We present a new method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the single electron self-energy $Σ_σ(k, i ω_n)$ in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wavevector and spin labeled virtual energies $ξ_{k σ}$. These, thermodynamically derived virtual energies, are solutions of equations involving the self-energy at corresponding $kσ$'s. Examples of the method in simplified situations are provided.

cond-mat.stat-mech↗
arXiv2024

Method for reconstructing the self-energy from the spectral function

A fundamental question about the nature of quantum materials such as High-T$_c$ systems remain open to date -- it is unclear whether they are (some variety of) Fermi liquids, or (some variety of) non Fermi liquids. A direct avenue to determine their nature is to study the (imaginary part of the) self-energy at low energies. Here we present a novel method to extract this low $ω$ self-energy from experimentally derived spectral functions. The method seems suited for implementation with high quality angle resolved photoemission data. It is based on a helpful Theorem proposed here, which assures us that the method has minimal (or vanishing) error at the lowest energies. We provide numerical examples showing that a few popular model systems yield distinguishably different low energy self-energies.

cond-mat.str-el↗
arXiv2023

Yang-Lee Zeros of Certain Antiferromagnetic Models

We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice, and the more tractable mean-field model corresponding to infinite-ranged coupling between all sites. In the high-temperature limit, we show that the logarithm of the Yang-Lee zeros can be written as a series in half odd integer powers of the inverse temperature, $k$, with the leading term $\sim k^{1/2}$. This result is true in any dimension and for arbitrary lattices. We also show that the coefficients of the expansion satisfy simple identities (akin to sum rules) for the nearest-neighbor case. These new identities are verified numerically by computing the exact partition function for a 2D square lattice of size $16\times16$. For the mean-field model, we write down the partition function (termed the mean-field polynomials) for the ferromagnetic (FM) and antiferromagnetic (AFM) cases, and derive from them the mean-field equations. We analytically show that at high temperatures the zeros of the AFM mean-field polynomial scale as $\sim k^{1/2}$ as well. Using a simple numerical method, we find the roots lie on certain curves (the root curves), in the thermodynamic limit for the mean-field polynomials for the AFM case as well as for the FM one. Our results show a new root curve, that was not found earlier. Our results also clearly illustrate the phase transition expected for the FM and AFM cases, in the language of Yang-Lee zeros. Moreover, for the AFM case, we observe that the root curves separate two distinct phases of zero and non-zero complex staggered magnetization, and thus depict a complex phase boundary.

cond-mat.stat-mech↗
arXiv2022

Dielectric response of electrons with strong local correlations and long-ranged Coulomb interactions

Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting $t$-$J$-$V_C$ model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard-Gutzwiller-Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the $ \{\vec{q},ω\}$ dependent charge density fluctuations in this model using the extremely correlated fermi liquid theory, characterized by quasiparticles with very small weight $Z$. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system valid for arbitrary $\vec{q}$. Combining these ingredients, we present results for the dynamical charge susceptibility $\widetildeχ_{ρρ}(\vec{q},ω)$, (longitudinal) dielectric function $\varepsilon(\vec{q},ω)$, current susceptibility $\widetildeχ_{J J}(\vec{q},ω)$, conductivity $σ(\vec{q},ω)$, and the plasma frequency for any $\vec{q}$. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale $Ω_p(\vec{q})$, which locates a peak in $\Im m \, \widetildeχ_{ρρ}(\vec{q},ω)$.

cond-mat.str-el↗
arXiv2021

Extremely Correlated Superconductors

Superconductivity in the t-J model is studied by extending the recently introduced extremely correlated fermi liquid theory. Exact equations for the Greens functions are obtained by generalizing Gor'kov's equations to include extremely strong local repulsion between electrons of opposite spin. These equation are expanded in a parameter $λ$ representing the fraction of double occupancy, and the lowest order equations are further simplified near $T_c$, resulting in an approximate integral equation for the superconducting gap. The condition for $T_c$ is studied using a model spectral function embodying a reduced quasiparticle weight $Z$ near half-filling, yielding an approximate analytical formula for $T_c$. This formula is evaluated using parameters representative of single layer High-$T_c$ systems. In a narrow range of electron densities that is necessarily separated from the Mott-Hubbard insulator at half filling, we find superconductivity with a typical $T_c$$\sim$$10^2$K.

cond-mat.supr-con↗
arXiv2020

The Toeplitz matrix $e^{- κ|i-j|}$ and its application to a layered electron gas

We present an explicit solution of the eigen-spectrum Toeplitz matrix $C_{ij}= e^{- κ|i-j|}$ with $0\leq i,j \leq N$ and apply it to find analytically the plasma modes of a layered assembly of 2-dimensional electron gas. The solution is found by elementary means that bypass the Wiener-Hopf technique usually used for this class of problems. It rests on the observation that the inverse of $C_{ij}$ is effectively a nearest neighbor hopping model with a specific onsite energies which can in turn be diagonalized easily. Extensions to a combination of a Toeplitz and Hankel matrix, and to a generalization of $C_{ij}$, are discussed at the end of the paper.

math-ph↗
arXiv2020

Theory of anisotropic elastoresistivity of two-dimensional extremely strongly correlated metals

There is considerable recent interest in the phenomenon of anisotropic electroresistivity of correlated metals. While some interesting work has been done on the iron-based superconducting systems, not much is known for the cuprate materials. Here we study the anisotropy of elastoresistivity for cuprates in the normal state. We present theoretical results for the effect of strain on resistivity, and additionally on the optical weight and local density of states. We use the recently developed extremely strongly correlated Fermi liquid theory in two dimensions, which accounts quantitatively for the unstrained resistivities for three families of single-layer cuprates. The strained hoppings of a tight-binding model are roughly modeled analogously to strained transition metals. The strained resistivity for a two-dimensional $t$-$t'$-$J$ model are then obtained, using the equations developed in recent work. Our quantitative predictions for these quantities have the prospect of experimental tests in the near future, for strongly correlated materials such as the hole-doped and electron-doped high-$T_c$ materials.

cond-mat.str-el↗
arXiv2020

Aspects of the Normal State Resistivity of Cuprate Superconductors

Planar normal state resistivity data taken from three families of cuprate superconductors are compared with theoretical calculations from the recent extremely correlated Fermi liquid theory (ECFL). The two hole doped cuprate materials $LSCO$ and $BSLCO$ and the electron doped material $LCCO$ have yielded rich data sets at several densities $δ$ and temperatures T, thereby enabling a systematic comparison with theory. The recent ECFL resistivity calculations for the highly correlated $t$-$t'$-$J$ model by us give the resistivity for a wide set of model parameters. After using X-ray diffraction and angle resolved photoemission data to fix parameters appearing in the theoretical resistivity, only one parameter, the magnitude of the hopping $t$, remains undetermined. For each data set, the slope of the experimental resistivity at a single temperature-density point is sufficient to determine $t$, and hence the resistivity on absolute scale at all remaining densities and temperatures. This procedure is shown to give a fair account of the entire data.

cond-mat.str-el↗
arXiv2019

Fermi Surface Volume of Interacting Systems

Three Fermion sumrules for interacting systems are derived at T=0, involving the number expectation $\bar{N}(μ)$, canonical chemical potentials $μ(m)$, a logarithmic time derivative of the Greens function $γ_{\vec{k} σ}$ and the static Greens function. In essence we establish at zero temperature the sumrules linking: $$ \bar{N}(μ) \leftrightarrow \sum_{m} Θ(μ- μ(m)) \leftrightarrow \sum_{\vec{k},σ} Θ\left(γ_{\vec{k} σ}\right) \leftrightarrow \sum_{\vec{k},σ} Θ\left(G_σ(\vec{k},0)\right). $$ Connecting them across leads to the Luttinger and Ward sumrule, originally proved perturbatively for Fermi liquids. Our sumrules are nonperturbative in character and valid in a considerably broader setting that additionally includes non-canonical Fermions and Tomonaga-Luttinger models. Generalizations are given for singlet-paired superconductors, where one of the sumrules requires a testable assumption of particle-hole symmetry at all couplings. The sumrules are found by requiring a continuous evolution from the Fermi gas, and by assuming a monotonic increase of $μ(m)$ with particle number m. At finite T a pseudo-Fermi surface, accessible to angle resolved photoemission, is defined using the zero crossings of the first frequency moment of a weighted spectral function.

cond-mat.str-el↗
arXiv2017

A Strange Metal from Gutzwiller correlations in infinite dimensions

Recent progress in extremely correlated Fermi liquid theory (ECFL) and dynamical mean field theory (DMFT) enables us to compute in the $d \to \infty$ limit the resistivity of the $t-J$ model after setting $J\to0$. This is also the $U=\infty$ Hubbard model. We study three densities $n=.75,.8,.85$ that correspond to a range between the overdoped and optimally doped Mott insulating state. We delineate four distinct regimes characterized by different behaviors of the resistivity $ρ$. We find at the lowest $T$ a Gutzwiller Correlated Fermi Liquid regime with $ρ\propto T^2$ extending up to an effective Fermi temperature that is dramatically suppressed from the non-interacting value. This is followed by a Gutzwiller Correlated Strange Metal regime with $ρ\propto (T-T_0)$, i.e. a linear resistivity extrapolating back to $ρ=0$ at a positive $T_0$. At a higher $T$ scale, this crosses over into the Bad Metal regime with $ρ\propto (T+T_1)$ extrapolating back to a finite resistivity at $T=0$, and passing through the Ioffe-Regel-Mott value where the mean free path is a few lattice constants. This regime finally gives way to the High $T$ Metal regime, where we find $ρ\propto T$. The present work emphasizes the first two, where the availability of an analytical ECFL theory is of help in identifying the changes in related variables entering the resistivity formula that accompany the onset of linear resistivity, and the numerically exact DMFT helps to validate the results. We also examine thermodynamic variables such as the magnetic susceptibility, compressibility, heat capacity and entropy, and correlate changes in these with the change in resistivity. This exercise casts valuable light on the nature of charge and spin correlations in the strange metal regime, which has features in common with the physically relevant strange metal phase seen in strongly correlated matters.

cond-mat.str-el↗
arXiv2017

A Strange Metal from Gutzwiller correlations in infinite dimensions II: Transverse Transport, Optical Response and Rise of Two Relaxation Rates

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 $θ_H$, and also the longitudinal and transverse optical response of the $U=\infty$ 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 angles $\cot θ_H \propto T^2$ in the GCFL regime, on warming into the strange metal regime, it passes through a downward bend and continues as $T^2$. Equivalently, $R_H$ is weakly temperature dependent in the GCFL regime, and becomes strongly $T$-dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity $σ_{xx}(ω)$ and the optical Hall angles $\tan θ_H(ω)$ 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 independent 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.

cond-mat.str-el↗
arXiv2017

Kondo-Ising and Tight-Binding Models for TmB4

In $TmB_4$, localized electrons with a large magnetic moment interact with metallic electrons in boron-derived bands. We examine the nature of $TmB_4$ using full-relativistic ab-initio density functional theory calculations, approximate tight-binding Hamiltonian results, and the development of an effective Kondo-Ising model for this system. Features of the Fermi surface relating to the anisotropic conduction of charge are discussed. The observed magnetic moment $\sim 6 \, μ_B$ is argued to require a subtle crystal field effect in metallic systems, involving a flipped sign of the effective charges surrounding a Tm ion. The role of on-site quantum dynamics in the resulting Kondo-Ising type "impurity" model are highlighted. From this model, elimination of the conduction electrons will lead to spin-spin (RKKY-type) interaction of Ising character required to understand the observed fractional magnetization plateaus in $TmB_4$.

cond-mat.str-el↗
arXiv2016

Origin of Kinks in Energy Dispersion of Strongly Correlated Matter

We investigate the origin of ubiquitous low energy kinks found in Angle Resolved Photoemission (ARPES) experiments in a variety of correlated matter. Such kinks are unexpected from weakly interacting electrons and hence identifying their origin should lead to fundamental insights in strongly correlated matter. We devise a protocol for extracting the kink momentum and energy from the experimental data which relies solely on the two asymptotic tangents of each dispersion curve, away from the feature itself. It is thereby insensitive to the different shapes of the kinks as seen in experiments. The body of available data is then analyzed using this method. We proceed to discuss two alternate theoretical explanations of the origin of the kinks. Some theoretical proposals invoke local Bosonic excitations (Einstein phonons or other modes with spin or charge character), located exactly at the energy of observed kinks, leading to a momentum independent self energy of the electrons. A recent alternate is the theory of extremely correlated Fermi liquids (ECFL). This theory predicts kinks in the dispersion arising from a momentum dependent self energy of correlated electrons. We present the essential results from both classes of theories, and identify experimental features that can help distinguish between the two mechanisms. The ECFL theory is found to be consistent with currently available data on kinks in the nodal direction of cuprate superconductors, but conclusive tests require higher resolution energy distribution curve data.

cond-mat.str-el↗
arXiv2016

Transport and Optical Conductivity in the Hubbard Model: A High-Temperature Expansion Perspective

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 $1/T^2$.

cond-mat.str-el↗