Pinaki Majumdar

Research Summary:

The work over the last academic year continues our studies on magnetism and transport in correlated and disordered electron systems. We have formulated a new approach for lattice fermions strongly coupled to classical degrees of freedom, which allows a breakthrough in the simulation of these complex systems. We call this the `travelling cluster approximation' (TCA). This paper, as well as several studies on electron-phonon systems and magnetism using TCA, are listed below.

• The Travelling Cluster Approximation for Strong Correlation Models of Lattice Fermions Coupled to Classical Fields : We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time &tau_N ∝ N⁴. This limits achievable sizes to N &sim 100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size N_c, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method &tau_N, N_c is proportional to NN_c³. Our results are obviously exact when N_c=N, and converge quickly to this asymptote with increasing N_c. The accuracy improves in systems where the effective disorder seen by the fermions is large. We provided results of preliminary calculations on the Holstein model and the Double Exchange model. The `locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control.

• The Many Electron Ground State of the Adiabatic Holstein Model in Two and Three Dimensions : We present the complete ground state phase diagram of the Holstein model in two and three dimension considering the phonon variables to be classical. We first establish the overall structure of the phase diagram by using exact diagonalisation based Monte Carlo (ED-MC) on small lattices and then use the TCA for annealing the phonon degrees of freedom on large lattices. The phases that emerge include a Fermi liquid (FL), with no lattice distortions, an insulating polaron liquid (PL) at strong coupling, and a charge ordered insulating (COI) phase around half- filling. The COI phase is separated from the Fermi liquid by a regime of phase coexistence whose width grows with increasing electron-phonon coupling. We provide results on the electronic density of states, the COI order parameter, and the spatial organisation of polaronic states, for arbitrary density and electron-phonon coupling. The results highlight the crucial role of spatial correlations in this strong coupling problem.

• The Interplay of Disorder and Thermal Fluctuations in Strongly Coupled Electron-Phonon Systems : We solve the disordered Holstein model in three dimension considering the phonon degrees of freedom to be classical. We map out the various phases of the `clean' strong coupling problem, study the formation and `melting' of the charge ordered (CO) state with temperature (T) and electron density, and uncover a wide regime of phase separation between the CO state and the Fermi liquid. We then quantify the effect of moderate disorder at strong coupling. In the metallic regime, the interplay of disorder and electron-phonon coupling (i) enormously enhances the resistivity (&rho) at T=0, (ii) suppresses the temperature dependent increase of &rho, and (iii) leads to a regime with dρ/dT < 0. Close to half-filling, the CO phase is rapidly suppressed with increasing disorder. These effects underlie phenomena in materials ranging from the A-15 compounds to transition metal oxides.

• Metal-Insulator Transitions in the Disordered Holstein-Double Exchange Model in Three Dimension : We study a three dimensional model of electrons strongly coupled to classical phonons and core spins in the presence of substitutional disorder. We establish the phase diagram using a Monte Carlo technique on large lattices and present results on transport using exact linear response theory. We demonstrate how thermally driven metal-insulator transitions arise in this model from the interplay of lattice polaron effects, spin fluctuations, and extrinsic disorder. We also map out the dependence of the ferromagnetic T_c, the residual resistivity, and the optical spectral weight, on electron-phonon (EP) coupling and disorder. The results highlight the crucial role of both EP coupling and disorder, in addition to double exchange, for even a qualitative understanding of the metallic manganites, and help organise a wide variety of experimental results.

Publications:

• Inhomogeneous Ferromagnetism and Unconventional Charge Dynamics in Disordered Double Exchange Magnets,
  Sanjeev Kumar and Pinaki Majumdar,
  Phys. Rev. Lett. 91, 246602-1 (2003).

• Nanoscale Phase Coexistence and Percolative Quantum Transport,
  Sanjeev Kumar and Pinaki Majumdar,
  Phys. Rev. Lett. 92, 126602 (2004).

• Anti-localisation to Strong Localisation: the Interplay of Magnetic Scattering and Structural Disorder,
  Sanjeev Kumar and Pinaki Majumdar,
  Europhys. Lett. 65, 75 (2004).

Preprints:

• The Travelling Cluster Approximation for Strong Correlation Models of Lattice Fermions Coupled to Classical Fields, Sanjeev Kumar and Pinaki Majumdar, cond-mat 0406082.

• The Many Electron Ground State of the Adiabatic Holstein Model in Two and Three Dimensions, B. Poornachandra Sekhar, Sanjeev Kumar and Pinaki Majumdar, cond-mat 0406083.

• The Interplay of Disorder and Thermal Fluctuations in Strongly Coupled Electron-Phonon Systems, Sanjeev Kumar and Pinaki Majumdar, preprint, cond-mat 0406084.

• Metal-Insulator Transitions in the Disordered Holstein-Double Exchange Model in Three Dimension, Sanjeev Kumar and Pinaki Majumdar, cond-mat 0406085.

Other Activities:

• Two lectures at I.I.Sc Bangalore in Aug 2003: (i) Strong Correlation Models of Fermions Coupled to Classical Degrees of Freedom and (ii) Nanoscale Phase Coexistence.

• Lecture ay I.M.Sc Chennai: Nanoscale Phase Coexistence, Percolative Transport, and Memory Effects, Aug. 2003.

• Lecture in the `Novel Materials' Conference, Jan 2004 at SNBNCBS Calcutta, Phase Coexistence and Percolative Quantum Transport.

• Lecture at I.I.T Roorkee, March 2004: Phase Competetion and Quantum Transport in Correlated Electron Systems.

Other Activities:

I taught the graduate course in Statistical Mechanics (Jan-May 2004), and organised the Physics Talent Search test.