arXiv subjects

B. Sriram Shastry

Publications and source records attributed to B. Sriram Shastry.

At least 55 records · Page 3Linked to original sources

arXiv2009

Effects of Strong Correlations and Disorder in d-Wave Superconductors

We use exact diagonalization techniques to study the interplay between strong correlations, superconductivity, and disorder in a model system. We study an extension of the t-J model by adding an infinite-range d-wave superconductivity inducing term and disorder. Our work shows that in the clean case the magnitude of the order parameter is surprisingly small for low-hole filling, thus implying that mean-field theories might be least accurate in that important regime. We demonstrate that substantial disorder is required to destroy a d-wave superconducting state for low-hole doping. We provide the first bias free numerical results for the local density of states of a strongly correlated d-wave superconducting model, relevant for STM measurements at various fillings and disorders.

cond-mat.str-el↗

arXiv2008

Drude weight in systems with open boundary conditions

For finite systems, the real part of the conductivity is usually decomposed as the sum of a zero frequency delta peak and a finite frequency regular part. In studies with periodic boundary conditions, the Drude weight, i.e., the weight of the zero frequency delta peak, is found to be nonzero for integrable systems, even at very high temperatures, whereas it vanishes for generic (nonintegrable) systems. Paradoxically, for systems with open boundary conditions, it can be shown that the coefficient of the zero frequency delta peak is identically zero for any finite system, regardless of its integrability. In order for the Drude weight to be a thermodynamically meaningful quantity, both kinds of boundary conditions should produce the same answer in the thermodynamic limit. We shed light on these issues by using analytical and numerical methods.

cond-mat.str-el↗

arXiv2007

The Hall Number, Optical Sum Rule and Carrier Density for the $t$-$t'$-$J$ model

We revisit the relationship between three classical measures of particle number, namely the chemical doping $x$, the Hall number $x_{hall}$ and the particle number inferred from the optical sum rule $x_{opt}$. We study the $t$-$t'$-$J$ model of correlations on a square lattice, as a minimal model for High $T_c$ systems, using numerical methods to evaluate the low temperature Kubo conductivites. These measures disagree significantly in this type of system, owing to Mott Hubbard correlations. The Hall constant has a complex behavior with several changes of sign as a function of filling $x$, depending upon the model parameters. Thus $x_{hall}$ depends sensitively on $t'$ and $J$, due to a kind of quantum interference.

cond-mat.str-el↗

arXiv2007

Dynamical thermal response functions for strongly correlated one-dimensional systems

In this article we study the thermal response functions for two one-dimensional models, namely the Hubbard and spin-less fermion $t$-$V$ models. By exactly diagonalizing finite sized systems we calculate dynamical electrical, thermoelectrical, and thermal conductivities via the Kubo formalism. The thermopower (Seebeck coefficient), Lorenz number, and dimensionless figure of merit are then constructed which are quantities of great interest to the physics community both theoretically and experimentally. We also geometrically frustrate these systems and destroy integrability by the inclusion of a second neighbor hop. These frustrated systems are shown to have enhanced thermopower and Lorenz number at intermediate and low temperatures.

cond-mat.str-el↗

arXiv2007

Thermoelectric effects in a strongly correlated model for Na$_x$CoO$_2$

Thermal response functions of strongly correlated electron systems are of appreciable interest to the larger scientific community both theoretically and technologically. Here we focus on the infinitely correlated t-J model on a geometrically frustrated two-dimensional triangular lattice. Using exact diagonalization on a finite sized system we calculate the dynamical thermal response functions in order to determine the thermopower, Lorenz number, and dimensionless figure of merit. The dynamical thermal response functions is compared to the infinite frequency limit and shown to be very weak functions of frequency, hence, establishing the validity of the high frequency formalism recently proposed by Shastry for the thermopower, Lorenz number, and the dimensionless figure of merit. Further, the thermopower is demonstrated to have a low to mid temperature enhancement when the sign of the hopping parameter $t$ is switched from positive to negative for the geometrically frustrated lattice considered.

cond-mat.str-el↗

arXiv2007

Signatures of integrability in charge and thermal transport in 1D quantum systems

Integrable and non-integrable systems have very different transport properties. In this work, we highlight these differences for specific one dimensional models of interacting lattice fermions using numerical exact diagonalization. We calculate the finite temperature adiabatic stiffness (or Drude weight) and isothermal stiffness (or ``Meissner'' stiffness) in electrical and thermal transport and also compute the complete momentum and frequency dependent dynamical conductivities $σ(q,ω)$ and $κ(q,ω)$. The Meissner stiffness goes to zero rapidly with system size for both integrable and non-integrable systems. The Drude weight shows signs of diffusion in the non-integrable system and ballistic behavior in the integrable system. The dynamical conductivities are also consistent with ballistic and diffusive behavior in the integrable and non-integrable systems respectively.

cond-mat.str-el↗

arXiv2006

Strong Correlations Produce the Curie-Weiss Phase of Na$_{x}$CoO$_2$

Within the t-J model we study several experimentally accessible properties of the 2D-triangular lattice system Na$_x$CoO$_2$, using a numerically exact canonical ensemble study of 12 to 18 site triangular toroidal clusters as well as the icosahedron. Focusing on the doping regime of $x\sim0.7$, we study the temperature dependent chemical potential, specific heat, magnetic susceptibility and the dynamic Hall coefficient $R_H(T,ω)$ as well as the magnetic field dependent thermopower. We find a crossover between two phases near $x \sim 0.75$ in susceptibility and field suppression of the thermopower arising from strong correlations. An interesting connection is found between the temperature dependence of the diamagnetic susceptibility and the Hall-coefficient. We predict a large thermopower enhancement, arising from {\em transport corrections} to the Heikes-Mott formula, in a model situation where the sign of hopping is reversed from that applicable to Na$_x$CoO$_2$.

cond-mat.str-el↗

arXiv2006

Finite temperature properties of the triangular lattice t-J model, applications to Na$_x$CoO$_2$

We present a finite temperature ($T$) study of the t-J model on the two-dimensional triangular lattice for the negative hopping $t$, as relevant for the electron-doped Na$_x$CoO$_2$ (NCO). To understand several aspects of this system, we study the $T$-dependent chemical potential, specific heat, magnetic susceptibility, and the dynamic Hall-coefficient across the entire doping range. We show systematically, how this simplest model for strongly correlated electrons describes a crossover as function of doping ($x$) from a Pauli-like weakly spin-correlated metal close to the band-limit (density $n=2$) to the Curie-Weiss metallic phase ($1.5<n<1.75$) with pronounced anti-ferromagnetic (AFM) correlations at low temperatures and Curie-Weiss type behavior in the high-temperature regime. Upon further reduction of the doping, a new energy scale, dominated by spin-interactions ($J$) emerges (apparent both in specific heat and susceptibility) and we identify an effective interaction $J_{eff}(x)$, valid across the entire doping range. This is distinct from Anderson's formula, as we choose here $t<0$, hence the opposite sign of the usual Nagaoka-ferromagnetic situation. This expression includes the subtle effect of weak kinetic AFM - as encountered in the infinitely correlated situation ($U=\infty$). By explicit computation of the Kubo-formulae, we address the question of practical relevance of the high-frequency expression for the Hall coefficient $R_H^*$. We hope to clarify some open questions concerning the applicability of the t-J model to real experimental situations through this study.

cond-mat.str-el↗

arXiv2004

Spin-s wavefunctions with algebraic order

We generalize the Gutzwiller wavefunction for s = 1/2 spin chains to construct a family of wavefunctions for all s > 1/2. Through numerical simulations, we demonstrate that the spin spin correlation functions for all s decay as a power law with logarithmic corrections. This is done by mapping the model to a classical statistical mechanical model, which has coupled Ising spin chains with long range interactions. The power law exponents are those of the Wess Zumino Witten models with k = 2s. Thus these simple wavefunctions reproduce the spin correlations of the family of Hamiltonians obtained by the Algebraic Bethe Ansatz.

cond-mat.str-el↗

arXiv2004

Field-Driven Transitions in the Dipolar Pyrochlore Antiferromagnet Gd$_2$Ti$_2$O$_7$

We present a mean-field theory for magnetic field driven transitions in dipolar coupled gadolinium titanate Gd$_2$Ti$_2$O$_7$ pyrochlore system. Low temperature neutron scattering yields a phase that can be regarded as a 8 sublattice antiferromagnet, in which long-ranged ordered moments and fluctuating moments coexist. Our theory gives parameter regions where such a phase is realized, and predicts several other phases, with transitions amongst them driven by magnetic field as well as temperature. We find several instances of {\em local} disorder parameters describing the transitions.

cond-mat.str-el↗

arXiv2003

Superconductivity in CoO$_2$ Layers and the Resonating Valence Bond Mean Field Theory of the Triangular Lattice t-J model

Motivated by the recent discovery of superconductivity in two dimensional CoO$_2$ layers, we present some possibly useful results of the RVB mean field theory applied to the triangular lattice. Away from half filling, the order parameter is found to be complex, and yields a fully gapped quasiparticle spectrum. The sign of the hopping plays a crucial role in the analysis, and we find that superconductivity is as fragile for one sign as it is robust for the other. Na$_x$CoO$_2\cdot y$H$_2$O is argued to belong to the robust case, by comparing the LDA Fermi surface with an effective tight binding model. The high frequency Hall constant in this system is potentially interesting, since it is pointed out to increase linearly with temperature without saturation for T $>$ T$_{degeneracy}$.

cond-mat.str-el↗

arXiv2003

Quantum transport using the Ford-Kac-Mazur formalism

The Ford-Kac-Mazur formalism is used to study quantum transport in (1) electronic and (2) harmonic oscillator systems connected to general reservoirs. It is shown that for non-interacting systems the method is easy to implement and is used to obtain many exact results on electrical and thermal transport in one-dimensional disordered wires. Some of these have earlier been obtained using nonequilibrium Green function methods. We examine the role that reservoirs and contacts can have on determining the transport properties of a wire and find several interesting effects.

cond-mat.mes-hall↗

arXiv2003

Extracting Hidden Symmetry from the Energy Spectrum

In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapors. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the Hydrogen atom.

cond-mat↗

arXiv2002

Spin-Ice and Other Frustrated Magnets on the Pyrochlore Lattice

The recent identification of the dysprosium titanate compound $Dy_2 Ti_2 O_7$ as a ``Spin-Ice'', i.e. the spin analog of regular entropic ice of Pauling, has created considerable excitement. The ability to manipulate spins using magnetic fields gives a unique advantage over regular ice in these systems, and has been used to study the recovery of entropy. Predicted magnetization plateaus have been observed, testing the underlying model consisting of a competition between short ranged super exchange, and long ranged dipolar interactions between spins. I discuss other compounds that are possibly spin ice like: $Ho_2 Ti_2 O_7$, and the two stannates $Ho_2 Sn_2 O_7$, $Dy_2 Sn_2 O_7$.

cond-mat.stat-mech↗

arXiv2001

Exact Spectral Functions of a Non Fermi Liquid in 1 Dimension

We study the exact one electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give the spectral functions, which turn out to be computable, interesting and non trivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.

cond-mat.str-el↗

arXiv2001

Solution of a Generalized Stieltjes Problem

We present the exact solution for a set of nonlinear algebraic equations $\frac{1}{z_l}= πd + \frac{2 d}{n} \sum_{m \neq l} \frac{1}{z_l-z_m}$. These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain \cite{dhar}. These equations are low $d$ (density) ``degenerations'' of more complicated transcendental equation of Bethe's Ansatz for a ferromagnet, but are interesting in themselves. They generalize, through a single parameter, the equations of Stieltjes, $x_l = \sum_{m \neq l} 1/(x_l-x_m)$, familiar from Random Matrix theory. It is shown that the solutions of these set of equations is given by the zeros of generalized associated Laguerre polynomials. These zeros are interesting, since they provide one of the few known cases where the location is along a nontrivial curve in the complex plane that is determined in this work. Using a ``Green's function'' and a saddle point technique we determine the asymptotic distribution of zeros.

cond-mat↗

arXiv2000

Equilibrium and dynamical properties of the ANNNI chain at the multiphase point

We study the equilibrium and dynamical properties of the ANNNI (axial next-nearest-neighbor Ising) chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low temperature behaviour of the system with a well defined low temperature peak of the specific heat that carries the thermodynamic ``weight'' of the ground state entropy. In our study of the dynamical properties, the stochastic Kawasaki dynamics is considered. The Fokker-Planck operator for the process corresponds to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with constraints on allowed states. This leads to a number of differences in its properties which are obtained through exact numerical diagonalization, simulations and by obtaining various analytic bounds.

cond-mat.stat-mech↗

arXiv2000

Exact Solution of a Repulsive Fermi Model With Enhanced Superconducting Correlations

We present the exact solution of a model of interacting fermions in any dimension with a pure repulsive interaction projecting out a given Cooper channel. The solution rests upon the infinite ranged character of the interaction in real space, leading to a functional integral that is dominated by a Gaussian term. The solution produces strong superconducting enhancements and quasi long ranged order in a channel that is not present in the Hamiltonian explicitly, but of the form given by arguments from order by projection.

cond-mat.supr-con↗