arXiv subjects

B. Sriram Shastry

Publications and source records attributed to B. Sriram Shastry.

At least 37 records · Page 2Linked to original sources

arXiv2014

Linked-cluster expansion for the Green's function of the infinite-U Hubbard model

We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Pade approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the order of, the hopping amplitude. We also discuss several different approaches for obtaining the spectral functions through analytic continuation of the imaginary frequency Green's function, and show results for the system near half filling. We benchmark our results for the equation of state against those obtained from a numerical linked-cluster expansion carried out to the eleventh order.

cond-mat.str-el↗

arXiv2013

Extremely Correlated Fermi Liquids in the limit of infinite dimensions

We study the infinite spatial dimensionality limit of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory for the t-J model. We directly analyze the Schwinger equations of motion for the Gutzwiller projected electron Green's function. From simplifications arising in this limit, we are able to make several exact statements about the theory. The ECFL Green's function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to second order in λ. In a related publication, these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t-J model can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green's function and the caparison factor of the ECFL theory. Additionally, the optical conductivity is shown to be obtainable from the Green's function with negligibly small vertex corrections. These results are shown to hold to each order in λ.

cond-mat.str-el↗

arXiv2013

Extremely Correlated Fermi Liquid study of the U=infinity Anderson Impurity Model

We apply the recently developed extremely correlated Fermi liquid theory to the Anderson impurity model, in the extreme correlation limit. We develop an expansion in a parameter λ, related to n_d, the average occupation of the localized orbital, and find analytic expressions for the Green's functions to O(λ^2). These yield the impurity spectral function and also the self-energy Σ(ω) in terms of the two self energies of the ECFL formalism. The imaginary parts of the latter, have roughly symmetric low energy behaviour (~ ω^2), as predicted by Fermi Liquid theory. However, the inferred impurity self energy Σ"(ω) develops asymmetric corrections near n_d ~ 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an over broadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.

cond-mat.str-el↗

arXiv2013

Electronic spectral properties of the two-dimensional infinite-U Hubbard model

A strong-coupling series expansion for the Green's function and the extremely-correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-U Hubbard model. Results from these two complementary methods agree very well at both, low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the quasiparticle peak location in the strongly-correlated regime. This is examined by the ECFL results at low temperatures, where it is shown that the spectral function is largely skewed towards the occupied states.

cond-mat.str-el↗

arXiv2013

Extremely Correlated Fermi Liquids: Self consistent solution of the second order theory

We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the t-J model in two dimensions. We use typical sets of band parameters relevant to the cuprate superconductors. The second order theory in the parameter λis argued to be quantitatively valid in the overdoped regime for 0 < n < 0.75 (n is the particle density). The calculation involves the self consistent solution of equations for an auxiliary Fermi liquid type Greens function and an adaptive spectral weight, or caparison factor, described in recent papers by Shastry (Refs. (1) and (5)). We present the numerical results at low as well as high T at various low to intermediate densities in the normal phase with emphasis placed on features that are experimentally accessible. We display the momentum space occupation function m(k), various energy dispersions locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions along various directions in the Brillouin zone, and with typical additional elastic scattering. The line-shapes have an asymmetric shape and a broad background that is seen in experiments near and beyond optimal hole doping, and validate approximate recent recent versions of the theory. The results display features such as the high energy kink, and provide an in depth understanding of its origin and dependence on band parameters.

cond-mat.str-el↗

arXiv2013

Extremely Correlated Fermi Liquids: The Formalism

We present the detailed formalism of the extremely correlated Fermi liquid theory, developed for treating the physics of the t-J model. We start from the exact Schwinger equation of motion for the Greens function for projected electrons, and develop a systematic expansion in a parameter λ, relating to the double occupancy. The resulting Greens function has a canonical part arising from an effective Hamiltonian of the auxiliary electrons, and a caparison part, playing the role of a frequency dependent adaptive spectral weight. This adaptive weight balances the requirement at low ω, of the invariance of the Fermi volume, and at high ω, of decaying as c_0/(i ω), with a correlation depleted c_0 <1. The effective Hamiltonian H_{eff} describing the auxiliary Fermions is given a natural interpretation with an effective interaction V_{eff} containing both the exchange J(ij), and the hopping parameters t(ij). It is made Hermitian by adding suitable terms that ultimately vanish, in the symmetrized theory developed in this paper. Simple but important shift invariances of the t-J model are noted with respect to translating its parameters uniformly. These play a crucial role in constraining the form of V_{eff} and also provide checks for further approximations. The auxiliary and physical Greens function satisfy two sum rules, and the Lagrange multipliers for these are identified. A complete set of expressions for the Greens functions to second order in λis given, satisfying various invariances. A systematic iterative procedure for higher order approximations is detailed. A superconducting instability of the theory is noted at the simplest level with a high transition temperature.

cond-mat.str-el↗

arXiv2013

Functionally independent conservations laws in a quantum integrable model

We study a recently proposed quantum integrable model defined on a lattice with N sites, with Fermions or Bosons populating each site, as a close relative of the well known spin-1/2 Gaudin model. This model has 2N arbitrary parameters, a linear dependence on an interaction type parameter x, and can be solved exactly. It has N known constants of motion that are linear in x. We display further constants of motion with higher Fermion content, that are are linearly independent of the known conservation laws. Our main result is that despite the existence of these higher conservation laws, the model has only N functionally independent conservation laws. Therefore we propose that N can be viewed as the number of degrees of freedom, in parallel to the classical definition of integrability.

cond-mat.str-el↗

arXiv2013

Quantum integrability in systems with finite number of levels

We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We argue that if the matrices depend on a (real) parameter, one can define quantum integrability from this feature alone, leading to specific results such as exact solvability, Poissonian energy level statistics and to level crossings.

cond-mat.str-el↗

arXiv2013

DiracQ: A Quantum Many-Body Physics Package

We present a software package DiracQ, for use in quantum many-body Physics. It is designed for helping with typical algebraic manipulations that arise in quantum Condensed Matter Physics and Nuclear Physics problems, and also in some subareas of Chemistry. DiracQ is invoked within a Mathematica session, and extends the symbolic capabilities of Mathematica by building in standard commutation and anticommutation rules for several objects relevant in many-body Physics. It enables the user to carry out computations such as evaluating the commutators of arbitrary combinations of spin, Bose and Fermi operators defined on a discrete lattice, or the position and momentum operators in the continuum. Some examples from popular systems, such as the Hubbard model, are provided to illustrate the capabilities of the package.

cond-mat.str-el↗

arXiv2012

Entropy, frustration and large thermopower of doped Mott insulators on the fcc lattice

Electronic frustration and strong correlations may lead to large Seebeck coefficients. To understand this physics on general grounds, we compute the thermopower of the one-band Hubbard model on the 3-dimensional fcc lattice over the whole range of fillings for intermediate and large interaction strength. Dynamical mean-field theory shows that when the density approaches half-filling, the fcc lattice at strong coupling exhibits a large low temperature Seebeck coefficient $S$. The largest effect occurs as one approaches $n=1$ from dopings where electronic frustration is maximized. The high-frequency limit of the thermopower and the Kelvin limit are both used to provide physical insight as well as practical tools to estimate the thermopower. The high-frequency limit gives a reliable estimate of the DC limit at low temperature when the metal becomes coherent. By contrast, the Kelvin approach is useful in the strongly interacting case at high temperature when transport is incoherent. The latter result shows that in doped Mott insulators at high temperature and strong coupling the thermopower can be understood on entropic grounds.

cond-mat.str-el↗

arXiv2012

Optimal doping and entropic origin of giant thermopower in doped Mott insulators

This paper has been withdrawn by the authors because the results were incorrect due to the use of an impurity solver that fails at large interaction strength and above half-filling. This led, first, to the development of a new impurity solver (arXiv:1202.5814 or Phys.Rev. B 86, 085133 (2012)) and, second, to a complete revision of the thermopower results with different conclusions. Therefore a new paper on thermopower was submitted (arXiv:1209.4349) and the present one withdrawn.

cond-mat.str-el↗

arXiv2011

Anatomy of the Self Energy

The general problem of representing the Greens function $G(k,z)$ in terms of self energy, in field theories lacking Wick's theorem, is considered. A simple construction shows that a Dyson like representation with a self energy $Σ(k,z)$ is always possible, provided we start with a spectral representation for $G(k,z)$ for finite sized systems and take the thermodynamic limit. The self energy itself can then be iteratively expressed in terms of another higher order self energy, capturing the spirit of Mori's formulation. We further discuss alternative and more general forms of $G(k,z)$ that are possible. In particular, a recent theory by the author of extremely correlated Fermi liquids at density "$n$", for Gutzwiller projected non canonical Fermi operators obtains a new form of the Greens function: $$G(k,z)= \frac{\{1- \frac{n}{2}\} + Ψ(k,z)}{z - \hat{E}_k - Φ(k,z)}, $$ with {\em a pair of self energies} $Φ(z)$ and $Ψ(z)$. Its relationship with the Dyson form is explored. A simple version of the two self energy model was shown recently to successfully fit several data sets of photoemission line shapes in cuprates. We provide details of the unusual spectral line shapes that arise in this model, with the characteristic skewed shape depending upon a single parameter. The EDC and MDC line shapes are shown to be skewed in opposite directions, and provide a testable prediction of the theory.

cond-mat.str-el↗

arXiv2011

A Fidelity Study of the Superconducting Phase Diagram in the 2D Single-band Hubbard Model

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the d-wave pair/spin/charge-density matrices. The calculations show a d-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion U and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping t'. We also demonstrate that negative t' plays an important role in facilitating d-wave superconductivity.

cond-mat.supr-con↗

arXiv2011

Extremely Correlated Fermi Liquids

We present the theory of an extremely correlated Fermi liquid (ECFL) with $U\to \infty$. This liquid has an underlying Fermi liquid (FL) Greens function that is further caparisoned. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct $T$ dependent left skew. An important energy scale $Δ(\vec{k},x)$ emerges as the average inelasticity of the FL Greens function, and influences the photoemission spectra profoundly. A duality is identified wherein an apparent loss of coherence of the ECFL results from an excessively sharp FL.

cond-mat.str-el↗

arXiv2011

Universal features of Thermopower in High Tc systems and Quantum Criticality

In high Tc superconductors a wide ranging connection between the doping dependence of the transition temperature Tc and the room temperature thermopower Q has been observed. A "universal correlation" between these two quantities exists with the thermopower vanishing at optimum doping as noted by OCTHH (Obertelli, Cooper, Tallon, Honma and Hor). In this work we provide an interpretation of this OCTHH universality in terms of a possible underlying quantum critical point (QCP) at Tc. Central to our viewpoint is the recently noted Kelvin formula relating the thermopower to the density derivative of the entropy. Perspective on this formula is gained through a model calculation of the various Kubo formulas in an exactly solved 1-dimensional model with various limiting procedures of wave vector and frequency.

cond-mat.supr-con↗

arXiv2010

The Kelvin Formula for Thermopower

Thermoelectrics are important in physics, engineering, and material science due to their useful applications and inherent theoretical difficulty, especially in strongly correlated materials. Here we reexamine the framework for calculating the thermopower, inspired by ideas of Lord Kelvin from 1854. We find an approximate but concise expression, which we term as the Kelvin formula for the the Seebeck coefficient. According to this formula, the Seebeck coefficient is given as the particle number $N$ derivative of the entropy $Σ$, at constant volume $V$ and temperature $T$, $S_{\text{Kelvin}}=\frac{1}{q_e}\{\frac{\partial Σ}{\partial N} \}_{V,T}$. This formula is shown to be competitive compared to other approximations in various contexts including strongly correlated systems. We finally connect to a recent thermopower calculation for non-Abelian fractional quantum Hall states, where we point out that the Kelvin formula is exact.

cond-mat.str-el↗

arXiv2010

Dynamics of Energy Transport in a Toda Ring

We present results on the relationships between persistent currents and the known conservation laws in the classical Toda ring. We also show that perturbing the integrability leads to a decay of the currents at long times, with a time scale that is determined by the perturbing parameter. We summarize several known results concerning the Toda ring in 1-dimension, and present new results relating to the frequency, average kinetic and potential energy, and mean square displacement in the cnoidal waves, as functions of the wave vector and a parameter that determines the non linearity.

cond-mat.stat-mech↗

arXiv2009

Fidelity and superconductivity in two-dimensional t-J models

We compute the ground-state fidelity and various correlations to gauge the competition between different orders in two-dimensional t-J-type models. Using exact numerical diagonalization techniques, these quantities are examined for (i) the plain t-J and t-t'-J models, (ii) for the t-J model perturbed by infinite-range d-wave or extended-s-wave superconductivity inducing terms, and (iii) the t-J model, plain and with a d-wave perturbation, in the presence of non-magnetic quenched disorder. Various properties at low hole doping are contrasted with those at low electron filling. In the clean case, our results are consistent with previous work that concluded that the plain t-J model supports d-wave superconductivity. As a consequence of the strong correlations present in the low hole doping regime, we find that the magnitude of the d-wave condensate occupation is small even in the presence of large d-wave superconductivity inducing terms. In the dirty case, we show the robustness of the ground state in the strongly correlated regime against disorder.

cond-mat.str-el↗