Sanjeev Kumar

Research Summary:

Motivated by the experiments on the manganites, we are working on problems involving the lattice fermions strongly coupled to the classical spins and the adiabatic phonons. The manganite physics is extremely rich and a wide variety of phases and phenomena have been observed in the experiments. The theoretical understanding, however, is far from complete. The main difficulty seems to be the lack of reliable many body methods for handling such strong coupling problems.

Given all the complexities, the monte-carlo simulations seem to be the only unbiased method to study such problems. Unfortunately, the standard Exact-Diagonalisation based monte-carlo is extremely costly in terms of cpu time and restricts us to very small lattice sizes ( N &sim 100 ). Although ED+MC on small sizes can give us insight into the thermodynamic properties, it is simply not good enough to make statements about the nature of transport properties of the system.

Over the last few years we have developed many-body methods for handling the strong coupling Classical-Quantum problems. These methods retain all the features of the ED+MC but try to access larger sizes. These have been successfully used by us for studying some outstanding problems relevant to the manganites and other strongly correlated systems. Here I briefly describe the two methods that we have recently developed and used.

(1) The Effective Hamiltonian Approach:
In the ED+MC approach a single update of the classical variable requires the full solution of the Schroedinger Equation. In a typical Monte-Carlo study one needs a large number of updates on classical variables before the system is in statistical equilibrium. This means that the time required by this approach &tau_N &sim N_MC N⁴ leading to N_max =100. In some models it is possible to write out the effective Hamiltonians (H_eff)for the Classical Variables, with the parameters specified by the expectation values of the electronic operators in a state which in turn is determined by the H_eff itself. This leads to a coupled problem which needs to be solved self-consistently. The advantage is that the monte-carlo update now requires comparing classical energies which is O(1) process in contrast to the O(N³) diagonalisation and one can easily study systems which are an order of magnitude larger than the N_max for ED+MC . The detailed form of the Effective Hamiltonian is model dependent. We have used this scheme to study :
(a) The Disordered Double Exchange Model.
(b) Double Exchange competing with Superexchange and the effect of weak disorder on the 1st order phase boundary.

(2) Travelling Cluster Approximation (TCA): In this scheme we propose that in order to update a classical variable x_i, it is enough to look at a cluster Hamiltonian H_c on a lattice L_c^d around the site x_i. Now the Monte-Carlo update requires diagonalising an Hamiltonian which has much smaller Hilbert space.Remember that a different Hamiltonian (H_c)has to be constructed in order to update a different site. This scheme is ofcourse exact in the limit L_c → L and &tau_N &sim N_MC N N_c³ so one can again access N &sim 1000 with ease. We have studied models involving the interplay of lattice, spin and charge degrees of freedom in the presence of disorder, using the TCA approach.

Publications:

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

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

• Anti-Localisation to Strong Localisation: The Interplay of Magnetic Scattering and Structural Disorder: Sanjeev Kumar and Pinaki Majumdar
  Europhys. Lett. vol 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, Pinaki Majumdar
  cond-mat/0406083

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

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

Conference/Workshops Attended:

• Summer College on Physics and Chemistry of Rare Earth Manganites, June-2003, ICTP, Trieste.

• A Meeting on Parallel Computing.
  Nov. 26-28, 2003, BARC, Mumbai.

• A Conference on Spintronics.
  Dec. 1-2, 2003, BARC, Mumbai.

Invited Lectures/Seminars:

• Nanoscale Phase Coexistence and Percolative Quantum Transport. Poster at Manganites Conference in ICTP,Trieste.

• Strong Correlation Models of Lattice Fermions Coupled to Classical Fields.
  Thesis Seminar: HRI, Allahabad.