arXiv subjects

Samir K. Paul

Publications and source records attributed to Samir K. Paul.

16 recordsLinked to original sources

arXiv2017

Chern-Simons Gauge Invariance and Boundary Conformal Fields

The topological non-Abelian Chern-Simons theory with a boundary is shown to require a scalar field companion in order to preserve overall gauge-invariance both in the 3 dimensional manifold, as well as on its boundary. This scalar field, originally being a pure-gauge Chern-Simons excitation that indicates the most general topological gauge structure in the bulk, is found to be crucial for dynamic scalar excitation on the 2 dimensional generic boundary manifold, the latter naturally representing a conformal mode. This gauge/CFT correspondence is general, for a compact gauge group.

hep-th↗

arXiv2016

Semi-phenomenological analysis of neutron scattering results for quasi-two dimensional quantum anti-ferromagnet

The available results from the inelastic neutron scattering experiment performed on the quasi-two dimensional spin $\frac{1}{2}$ anti-ferromagnetic material $La_2 Cu O_4$ have been analysed theoretically. The formalism of ours is based on a semi-classical like treatment involving a model of an ideal gas of mobile vortices and anti-vortices built on the background of the N$\acute{e}$el state, using the bipartite classical spin configuration corresponding to an XY- anisotropic Heisenberg anti-ferromagnet on a square lattice. The results for the integrated intensities for our spin $\frac{1}{2}$ model corresponding to different temperatures, show occurrence of vigorous unphysical oscillations, when convoluted with a realistic spectral window function. These results indicate failure of the conventional semi-classical theoretical model of ideal vortex/anti-vortex gas arising in the Berezinskii-Kosterlitz-Thouless theory for the low spin magnetic systems. A full fledged quantum mechanical formalism and calculations seem crucial for the understanding of topological excitations in such low spin systems. Furthermore, a severe disagreement is found to occur at finite values of energy transfer between the integrated intensities obtained theoretically from the conventional formalism and those obtained experimentally. This further suggests strongly that the full quantum treatment should also incorporate the interaction between the fragile-magnons and the topological excitations. This is quite plausible in view of the recent work establishing such a process in XXZ quantum ferromagnet on 2D lattice. The high spin XXZ quasi-two dimensional antiferromagnet like $MnPS_3$ however follows the conventional theory quite well

cond-mat.str-el↗

arXiv2015

The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two dimensional lattice and their stability

We present a scheme for the construction of quantum states of vortex like topological excitations corresponding to spin- 1/2 strongly XY anisotropic nearest neighbor Heisenberg Ferromagnet on two dimensional lattice. The procedure involving Pauli spin basis states is carried out corresponding to both infinite dilute limit and finite density limit of vortex/anti-vortex. It is found that the corresponding quantum mechanical states representing charge 1 quantum vortices/ anti-vortices can be expressed as linear combinations of single magnon states, composite multi-magnon states and the ground state. Detailed calculations show that these states are quantum mechanically stable states of the Hamiltonian only when the system size exceeds certain threshold value. Our analysis indicates that the interactions between different magnon modes can very well generate these topological excitations. Possible applications of our calculations to real magnetic systems are also discussed. Magnetic measurements probing spin dynamics may be undertaken to verify the existence of the threshold size for the stability of vortices.

cond-mat.str-el↗

arXiv2012

Theoretical analysis of neutron scattering results for quasi-two dimensional ferromagnets

A theoretical study has been carried out to analyse the available results from the inelastic neutron scattering experiment performed on a quasi-two dimensional spin-1/2 ferromagnetic material $K_2CuF_4$. Our formalism is based on a conventional semi-classical like treatment involving a model of an ideal gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results for dynamical structure functions for our model corresponding to spin-1/2, show occurrence of negative values in a large range of energy transfer even encompassing the experimental range, when convoluted with a realistic spectral window function. This result indicates failure of the conventional theoretical framework to be applicable to the experimental situation corresponding to low spin systems. A full quantum formalism seems essential for treating such systems.

cond-mat.str-el↗

arXiv2010

Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface

In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from the $L^2$ metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic form. The prequantum line bundle turns out to be Quillen's determinant line bundle with a modified Quillen metric. Next, as in the case of abelian vortices, we construct Quillen line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrised by $Ψ_0$, a section of a certain bundle.

hep-th↗

arXiv2010

Physical realization and possible identification of topological excitations in quantum Heisenberg anti-ferromagnet on a two dimensional lattice

Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice . Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations . The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure . The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice . It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices) .

cond-mat.stat-mech↗

arXiv2008

Physical realization and identification of topological excitations in quantum Heisenberg ferromagnet on lattice

Physical spin configurations corresponding to topological excitations expected to be present in the XY limit of a purely quantum spin 1/2 Heisenberg ferromagnet, are probed on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed in terms of coherent spin field components as limiting case of meronic (anti-meronic) configurations. The crucial role of the associated Wess-Zumino term is highlighted in our procedure. It is shown that this term can identify a large class of vortices (anti-vortices). In particular the excitations having odd topological charges form this class and also exihibit a self-similar pattern regarding the internal charge distribution. This manifestation of different behaviour of the odd and the even topological sectors is very prominent in the strongly quantum regime but fades away as we go to higher spins. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices).

cond-mat.stat-mech↗

arXiv2007

Physical realization and possible identification of topological excitations in quantum Heisenberg ferromagnet on lattice

Physical configurations corresponding to topological excitations present in the XY limit of a quantum spin 1/2 Heisenberg ferromagnet, are investigated on a two dimensional square lattice. Quantum vortices(anti-vortices) are constructed in terms of terms of coherent spin field components and the crucial role of the associated Wess-Zumino term is highlighted. It is shown that this term can identify a large class of vortices(anti-vortices). In particular the excitations with odd topological charge belonging to this class, are found to exhibit a self-similar pattern regarding the internal charge distribution. Our formalism is distinctly different from the coventional approach for the construction of quantum vortices(anti-vortices).

cond-mat.stat-mech↗

arXiv2003

Ising Model on periodic and quasi-periodic chains in presence of magnetic field: some exact results

We present a general procedure for calculating the exact partition function of an Ising model on a periodic chain in presence of magnetic field considering both open and closed boundary conditions. Using same procedure on a quasiperiodic (Fibonacci) chain we have established a recurrence relation among partition functions of different Fibonacci generations from n-th to (n+6)-th. In the large N limit we find $(2τ+ 1){F_{n+1}}={F_{n+2}}$; where $τ$ is the golden mean and $F_n$ stands for free energy/spin for the n-th generation. We have also studied chemical potential in both cases.

cond-mat.stat-mech↗

arXiv2003

Coherent States with SU(N) Charges

We define coherent states carrying SU(N) charges by exploiting generalized Schwinger boson representation of SU(N) Lie algebra. These coherent states are defined on $2 (2^{N - 1} - 1)$ complex planes. They satisfy continuity property and provide resolution of identity. We also exploit this technique to construct the corresponding non-linear SU(N) coherent states.

quant-ph↗

arXiv2002

The appearence of the resolved singular hypersurface {x_0}{x_1}-{{x_2}^n} =0 in the classical phase space of the Lie group SU(n)

A classical phase space with a suitable symplectic structure is constructed together with functions which have Poisson brackets algebraically identical to the Lie algebra structure of the Lie group SU(n). In this phase space we show that the orbit of the generators corresponding to the simple roots of the Lie algebra give rise to fibres that are complex lines containing spheres. There are n-1 spheres on a fibre and they intersect in exactly the same way as the Cartan matrix of the Lie algebra. This classical phase space bundle,being compact,has a description as a variety.Our construction shows that the variety containing the intersecting spheres is exactly the one obtained by resolving the singularities of the variety {x_0}{x_1}-{{x_2}^n}=0 in {C^3}. A direct connection between this singular variety and the classical phase space corresponding to the Lie group SU(n) is thus established.

hep-th↗

arXiv2001

Ising Model On A Fibonacci Lattice with Magnetic Field

We represent a general procedure for calculating the partition function of an Ising model on a one dimensional Fibonacci lattice in presence of magnetic field.This partition function can be written as a sum of partition functions of usual open Ising chains in presence of magnetic field with coefficients having Fibonacci symmetries.An exact expression for the partition function of the usual open Ising model is found.We observe that "Mirror Symmetry" is a characteristic property of all Fibonacci generations.Further nth and (n+6)th generations have the same topology.We have also established a recurrence relation among partition functions of different Fibonacci generations from nth to (n+6)th.

cond-mat.stat-mech↗

arXiv2001

Effective Theory For Quantum Spin System In Low Dimension - Beyond Long-Wavelength Limit

An effective theory for quantum spin system in low dimension is constructed in the finite-q regime. It is shown that there are field configurations for which Wess-Zumino term contributes to the partition functions as topological term for ferromagnet as well as antiferromagnet in both one and two dimensional lattice,in contrast to the long wave length regime.

cond-mat↗

arXiv1999

Possible Existence Of Topological Excitations In Quantum Spin Models In Low Dimensions

The possibility of existence of topological excitations in the anisotropic quantum Heisenberg model in one and two spatial dimensions is studied using coherent state method. It is found that a part of the Wess-Zumino term contributes to the partition function, as a topological term for ferromagnets in the long wavelength limit in both one and two dimensions. In particular, the XY limit of the two-dimensional anisotropic ferromagnet is shown to retain the topological excitations, as expected from the quantum Kosterlitz-Thouless scenario.

cond-mat.str-el↗

arXiv1994

N = 2 Super $W_{\infty}$ Algebra and its Nonlinear Realization Through Super KP Formulation

A nonlinear realization of super $W_{\infty}$ algebra is shown to exist through a consistent superLax formulation of super KP hierarchy. The reduction of the superLax operator gives rise to the Lax operators for $N=2$ generalized super KdV hierarchies, proposed by Inami and Kanno. The Lax equations are shown to be Hamiltonian and the associated Poisson bracket algebra among the superfields, consequently, gives rise to a realization of nonlinear super $W_{\infty}$ algebra.

hep-th↗

arXiv1993

$SL(n,R)$ KDV Hierarchy and its Nonpolynomial Realization Through Kac-Moody Currents

It is shown that $SL(n,R)$ KdV hierarchy can be expressed as definite nonpolynomials in Kac Moody currents and their derivatives by the action of Borel subgroup of $SL(n,R)$ on the phase space of centrally extended $sl(n,R)$ Kac Moody currents. Construction of Lax pair is shown, confirming Drinfeld Sokolov type Hamiltonian reduction. This suggests an example of a moduli space with symplectic structure corresponding to extended conformal symmetries.

hep-th↗