arXiv subjects

B. Sriram Shastry

Publications and source records attributed to B. Sriram Shastry.

65 records · Page 4Linked to original sources

arXiv1999

A Solvable Model of Interacting Fermions in Two Dimensions

We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an unitary transformation, the model reduces to one in which each particle sees a magnetic field which depends on the total numbers of particles of all the other species; this may be viewed as the mean-field model for a class of anyonic theories. Our model is invariant under charge conjugation C and the product PT (parity and time reversal). For the special case of two species, we examine various properties of this system, such as the Hall conductivity, the wave function overlap arising from the transfer of one particle from one species to another, and the one-particle off-diagonal density matrix. Our model is a generalization of a recently introduced solvable model in one dimension.

cond-mat.str-el↗

arXiv1997

A Majorana Fermion t-J Model in One Dimension

We study a rotation invariant Majorana fermion model in one dimension using diagrammatic perturbation theory and numerical diagonalization of small systems. The model is inspired by a Majorana representation of the antiferromagnetic spin-1/2 chain, and it is similar in form to the t-J model of electrons, except that the Majorana fermions carry spin-1 and Z_2 charge. We discuss the implications of our results for the low-energy excitations of the spin-1/2 chain. We also discuss a generalization of our model from 3 species of Majorana fermions to N species; the SO(4) symmetric model is particularly interesting.

cond-mat.str-el↗

arXiv1997

The Quantum Toda Lattice Revisited

In this work we study the quantum Toda lattice, developing the asymptotic Bethe ansatz method first used by Sutherland. Despite its known limitations we find, on comparing with Gutzwiller's exact method, that it works well in this particular problem and in fact becomes exact as $\hbar$ grows large. We calculate ground state and excitation energies for finite sized lattices, identify excitations as phonons and solitons on the basis of their quantum numbers, and find their dispersions. These are similar to the classical dispersions for small $\hbar$, and remain similar all the way up to $\hbar=1$, but then deviate substantially as we go further into the quantum regime. On comparing the sound velocities for various $\hbar$ obtained thus with that predicted by conformal theory we conclude that the Bethe ansatz gives the energies per particle accurate to O($1/N^2$). On that assumption we can find correlation functions. Thus the Bethe ansatz method can be used to yield much more than the thermodynamic properties which previous authors have calculated.

cond-mat.stat-mech↗

arXiv1996

Uncertainty Principle Enhanced Pairing Correlations in Projected Fermi Systems Near Half Filling

We point out the curious phenomenon of order by projection in a class of lattice Fermi systems near half filling. Enhanced pairing correlations of extended s-wave Cooper pairs result from the process of projecting out s-wave Cooper pairs, with negligible effect on the ground state energy. The Hubbard model is a particularly nice example of the above phenomenon, which is revealed with the use of rigorous inequalities including the Uncertainty Principle Inequality. In addition, we present numerical evidence that at half filling, a related but simplified model shows ODLRO of extended s-wave Cooper pairs.

cond-mat.str-el↗

arXiv1996

Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain

We study the 1-dimensional Heisenberg antiferromagnet with s=1/2 using a Majorana representation of the s=1/2 spins. A simple Hartree-Fock approximation of the resulting model gives a bilinear fermionic description of the model. This description is rotationally invariant and gives power-law correlations in the ``ground state'' in a natural fashion. The excitations are a two-parameter family of particles, which are spin-1 objects. These are contrasted to the ``spinon'' spectrum, and the technical aspects of the representation are discussed, including the problem of redundant states.

cond-mat↗

arXiv1995

Conservation laws in the continuum $1/r^2$ systems

We study the conservation laws of both the classical and the quantum mechanical continuum $1/r^2$ type systems. For the classical case, we introduce new integrals of motion along the recent ideas of Shastry and Sutherland (SS), supplementing the usual integrals of motion constructed much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The difference of these two sets of integrals then gives rise to yet another complete set of integrals of motion. For the quantum case, we first need to resum the integrals proposed by Calogero, Marchioro and Ragnisco. We give a diagrammatic construction scheme for these new integrals, which are the quantum analogues of the classical traces. Again we show that there is a relationship between these new integrals and the quantum integrals of SS by explicit construction.

cond-mat↗

arXiv1995

On Quantum Solitons in the Sawtooth Lattice

We study the sawtooth lattice of a coupled spin $1/2$ Heisenberg system, a variant of the railroad trestle lattice. The ground state of this system is two-fold degenerate with periodic boundary conditions and supports kink antikink excitations, which are distinct in this case, unlike the railroad trestle lattice. The resulting low temperature thermodynamics is compared with the recently discovered Delafossites $Y Cu O_{2.5} ~$.

cond-mat↗

arXiv1994

Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.

cond-mat↗

arXiv1993

Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.

cond-mat↗

arXiv1992

Solution of Some Integrable One-Dimensional Quantum Systems

In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics. The periodic inverse square case is worked out explicitly. Next, we show that in the limit of strong interaction the "spin" degrees of freedom decouple. Taking this limit for our example, we obtain a complete solution to a lattice system introduced recently by Shastry, and Haldane; our solution reproduces the numerical results. Finally, we emphasize the simple explanation for the high multiplicities found in this model.

cond-mat↗

arXiv1992

Mott Transition in the Hubbard model

In this article, I discuss W.Kohn's criterion for a metal insulator transition, within the framework of a one band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some intersting miscellaneous results discussed. The Jordan Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the ``extra phases'' arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e. diamagnetism), and the corresponding ``happy fluxes'' for the fermions identified. A curious result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A ``spin-statistics'' like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out.

cond-mat↗