arXiv subjects

Anupam Garg

Publications and source records attributed to Anupam Garg.

At least 37 records · Page 2Linked to original sources

arXiv2001

SU(2) instantons with boundary jumps and spin tunneling in magnetic molecules

Coherent state path integrals are shown in general to contain instantons with jumps at the boundaries, i.e., with boundary points lying outside classical parameter or phase space. As an example, the magnetic molecule Fe_8 is studied using a realistic Hamiltonian, and instanons with jumps are shown to dominate beyond a certain external magnetic field. An approximate formula is found for the fields where ground state tunneling is quenched in this molecule.

cond-mat.mes-hall↗

arXiv2000

Spin tunnelling in Molecular Magnets

We study spin tunneling in magnetic molecules, with special reference to Fe8. The article aims to give a pedagogical discussion of what is meant by the tunneling of a spin, and how tunneling amplitudes or energy level splittings may be calculated using path integral and discrete phase integral methods. In the case of Fe8, an issue of great interest is the oscillatory tunnel splittings as a function of applied magnetic field that have recently been observed. These oscillations are due to the occurrence of diabolical points in the magnetic field space. It is shown how this effect comes about in both the path-integral and the discrete phase integral methods. In the former it arises due to the presence of a Berry-like phase in the action, which gives rise to an interference between tunneling trajectories. In the latter, it arises due to the presence of further neighbor terms in the recursion relation for the energy eigenfunction. These terms give rise to turning points which have no analog in the one-dimensional continuum quasiclassical method. Explicit results are obtained for the location of the diabolical points in Fe8.

cond-mat.mes-hall↗

arXiv2000

Spin tunnelling in mesoscopic systems

We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied magnetic field, vanishing completely at special points in the space of magnetic fields, known as diabolical points. This phenomena is explained in terms of two approaches, one based on spin-coherent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for the diabolical points are obtained for a model Hamiltonian.

cond-mat.mes-hall↗

arXiv2000

Diabolical Points in Molecular Magnets with a Four-Fold Easy Axis

We study the points of degeneracy (diabolical points) in magnetic molecules such as Mn_{12}-acetate that have an easy axis of four-fold symmetry. This is done for general magnetic field that need not be oriented along a high-symmetry direction. We develop a perturbative technique that gives the diabolical points as the roots of a small number of polynomials in the transverse component of the magnetic field and the fourth order basal plane anisotropy. In terms of these roots we obtain approximate analytic formulas that apply to any system with total spin S \le 10. The analytic results are found to compare reasonably well with exact numerical diagonalization for the case of Mn12. In addition, the perturbation theory shows that the diabolical points may be indexed by the magnetic quantum numbers of the levels involved, even at large transverse fields. Certain points of degeneracy are found to be mergers (or near mergers) of two or three diabolical points beacuse of the symmetry of the problem.

cond-mat↗

arXiv2000

Topological Quenching of Spin Tunneling in Mn_12-acetate Molecules

We investigate the topological quenching of spin tunneling in Mn_12-acetate molecules with an applied magnetic field along the hard axis. The model Hamiltonian describing this system has a fourth-order term due to the tetragonal anisotropy. We treat this model using the discrete phase integral formalism in which the Schrodinger equation corresponding to the Hamiltonian becomes a nine-term recursion relation. We solve this recursion relation and find that the tunnel splitting is quenched at certain values of the applied field. We also present a qualitative treatment based on the instanton approach.

cond-mat.mes-hall↗

arXiv2000

The Semiclassical Propagator for Spin Coherent States

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the ``extra phase'' discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behaviour to $O(T^2)$, and demonstrate its consistency under dissection of the path

cond-mat↗

arXiv2000

Diabolical Points in Magnetic Molecules: An Exactly Solvable Model

The magnetic molecule Fe_8 has been observed to have a rich pattern of degeneracies in its magnetic spectrum as the static magnetic field applied to the molecule is varied. The points of degeneracy, or diabolical points in the magnetic field space, are found exactly in the simplest model Hamiltonian for this molecule. The points are shown to form a perfect centered rectangular lattice, and are shown to be multiply diabolical in general. The multiplicity is found. An earlier semiclassical solution to this problem is thereby shown to be exact in leading order in 1/J where J is the spin.

cond-mat.str-el↗

arXiv2000

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: II. Asymmetric Configurations

The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is further studied using the discrete phase integral (or Wentzel-Kramers-Brillouin) method. The analysis of the previous paper is extended to the case where the magnetic field has both hard and easy components, so that the Hamiltonian has no obvious symmetry. Herring's formula is now inapplicable, so the problem is solved by finding the wavefunction and using connection formulas at every turning point. A general formula for the energy surface in the vicinity of the diabolo is obtained in this way. This formula gives the tunneling apmplitude between two wells unrelated by symmetry in terms of a small number of action integrals, and appears to be generally valid, even for problems where the recursion contains more than five terms. Explicit results are obtained for the diabolical points in the model for Fe_8. These results exactly parallel the experimental observations. It is found that the leading semiclassical results for the diabolical points appear to be exact, and the points themselves lie on a perfect centered rectangular lattice in the magnetic field space. A variety of evidence in favor of this perfect lattice hypothesis is presented.

cond-mat↗

arXiv2000

Discrete phase integral method for five-term recursion relations

A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrodinger equation for certain spin Hamiltonians. The conditions for the validity of the phase integral approximation are derived. It is shown that in contrast to the three-term problem, it is now possible to get a turning points "under the barrier", i.e., in the classically forbidden region, as well as inside the classically allowed region. Further, no qualitatively new types of turning points arise in recursion relations with still higher numbers of terms. The phase integral approximation breaks down at the new turning points, requiring new connection formulas, which are derived.

math-ph↗

arXiv2000

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: I. Symmetric Configurations

The perfect quenching of spin tunneling that has previously been discussed in terms of interfering instantons, and has recently been observed in the magnetic molecule \Fe8, is treated using a discrete phase integral (or Wentzel-Kramers-Brillouin) method. The simplest model Hamiltonian for the phenomenon leads to a Schrödinger equation that is a five-term recursion relation. This recursion relation is reflection-symmetric when the magnetic field applied to the molecule is along the hard magnetic axis. A completely general Herring formula for the tunnel splittings for all reflection-symmetric five-term recursion relations is obtained. Using connection formulas for a new type of turning point that may be described as lying "under the barrier", and which underlies the oscillations in the splitting as a function of magnetic field, this Herring formula is transformed into two other formulas that express the splittings in terms of a small number of action and action-like integrals. These latter formulas appear to be generally valid, even for problems where the recursion contains more than five terms. The results for the model Hamiltonian are compared with experiment, numerics, previous instanton based approaches, and the limiting case of no magnetic field.

cond-mat↗

arXiv2000

Tunnel splittings for one dimensional potential wells revisited

The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary problems. This formula is applied to simple model problems. The prefactor for the splitting in the text book by Landau and Lifshitz is amended so as to apply to the ground and low lying excited states.

cond-mat↗

arXiv2000

Diabolical points in the magnetic spectrum of Fe_8 molecules

The magnetic molecule Fe_8 has been predicted and observed to have a rich pattern of degeneracies in its spectrum as an external magnetic field is varied. These degeneracies have now been recognized to be diabolical points. This paper analyzes the diabolicity and all essential properties of this system using elementary perturbation theory. A variety of arguments is gievn to suggest that an earlier semiclassical result for a subset of these points may be exactly true for arbitrary spin

cond-mat↗

arXiv1999

Coherent Magnetic Moment Reversal in Small Particles with Nuclear Spins

A discrete WKB method is developed for calculating tunnel splittings in spin problems. The method is then applied to the issue of how nuclear spins affect the macroscopic quantum coherence of the total magnetic moment in small magnetic particles. The results are compared with numerical work, and with previous instanton based analytic approaches.

cond-mat↗

arXiv1999

Application of the discrete Wentzel-Kramers-Brillouin method to spin tunneling

A discrete version of the WKB method is developed and applied to calculate the tunnel splittings between classically degenerate states of spin Hamiltonians. The results for particular model problems are in complete accord with those previously found using instanton methods. The discrete WKB method is more elementary and also yields wavefunctions.

cond-mat↗

arXiv1999

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.

cond-mat↗

arXiv1999

Large transverse field tunnel splittings in the Fe_8 spin Hamiltonian

The spin Hamiltonian that describes the molecular magnet Fe$_8$ has biaxial symmetry with mutually perpendicular easy, medium, and hard magnetic axes. Previous calculations of the ground state tunnel splittings in the presence of a magnetic field along the hard axis are extended, and the meaning of the previously discovered oscillation of this splitting is further clarified.

cond-mat↗

arXiv1998

Lattice Distortion Mediated Paramagnetic Relaxation in High-Spin High-Symmetry Molecular Magnets

Field-dependent maxima in the relaxation rate of the magnetic molecules Mn_12-Ac and Fe_8-tacn have commonly been ascribed to some resonant tunneling phenomenon. We argue instead that the relaxation can be understood as purely due to phonons. The rate maxima arise because of a Jahn-Teller-like distortion caused by the coupling of lattice phonons to degenerate Zeeman levels of the molecule at the top of the barrier. The binding energy of the distorted intermediate states lowers the barrier height and increases the relaxation rate. A nonperturbative calculation of this effect is carried out for a model system. An approximate result for the field variation near a maximum is found to agree reasonably with experiment.

cond-mat↗

arXiv1998

Vibrational Decoherence in Ion-Trap Quantum Computers

Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions. Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous emission from excited states of the ions. The calculation is made tractable by exploiting the vast difference in time scales between the vibrational excitations and the intra-ionic electronic excitations. Since the latter are several orders of magnitude faster, an adiabatic approximation is used to integrate them out and find the inclusive probability P(t) for the elec- tronic state of the ions to evolve as it would in the absence of vibrational coupling, and the ions to evolve into any state whatsoever. The decoherence time is found at zero temperature and for any number of ions N in the computer. Comparison is made with the spontaneous emission decoherence, and the implications for how trap voltages and other parameters should be scaled with N are discussed.

quant-ph↗