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Anjan Kundu

Publications and source records attributed to Anjan Kundu.

At least 55 records · Page 3Linked to original sources
arXiv2003

Unifying Approaches in Integrable Systems: Quantum and Statistical, Ultralocal and Nonultralocal

The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures. We restrict to quantum and statistical models belonging to trigonometric and rational classes with (2 x 2)- Lax operators. The ultralocal models can be classified successfully through their associated quantum algebra and are governed by the Yang-Baxter equation, while the nonultralocal models, the theory of which is still in the developmental stage, allow systematization through the braided Yang-Baxter equation. Along with the known integrable models some possible directions for investigation in this field and generation of such new models are suggested.

hep-th↗
arXiv2002

Ultralocal solutions for quantum integrable nonultralocal models

A challenge in the theory of integrable systems is to show for every nonultralocal quantum integrable model, a possible connection to an ultralocal model. Some of such gauge connections were discovered earlier. We complete the task by identifying the same for the remaining ones along with two new models. We also unveil the underlying algebraic structure for these nonultralocal models.

hep-th↗
arXiv2002

New nonultralocal quantum integrable models through gauge transformation

One of the few schemes for obtaining an integrable nonultralocal quantum model is its possible generation from an ultralocal model by a suitable gauge transformation. Applying this scheme we discover two new nonultralocal models, which fit well into the braided Yang-Baxter relations ensuring their quantum integrability. Our first model is generated from a lattice Liouville-like system, while the second one which is an exact lattice version of the light-cone sine-Gordon is gauge transformed from a model, which gives also the quantum mKdV for a different gauge choice.

hep-th↗
arXiv2002

New series of integrable vertex models through a unifying approach

Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q -> 1. Exact solutions are formulated through algebraic Bethe ansatz and a novel possibility of hybrid vertex models is introduced.

cond-mat↗
arXiv2002

Generation of new classes of integrable quantum and statistical models

A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models and obtain new series of vertex models related to q-spin, q-boson and their hybrid combinations. Generic q, q roots of unity and q -> 1 yield different classes of integrable models. Exact solutions through algebraic Bethe ansatz is formulated for all models in a unified way.

cond-mat↗
arXiv2001

Integrability and exact solution of correlated hopping multi-chain electron systems

Exact quantum integrability is established for a class of multi-chain electron models with correlated hopping and spin models with interchain interactions, by constructing the related Lax operators and R-matrices through twisting and gauge transformations. Exact solution of the eigenvalue problem for commuting conserved quantities of such systems is achieved through Algebraic Bethe ansatz, on the examples of Hubbard and t-J models with correlated hopping. Our systematic construction identifies the integrable subclass of such known solvable models and also generates new systems including the generalized t-J models. At the same time it makes proper correction to a well known model and resolves recent controversies regarding the equivalence and solvability of some known models.

cond-mat↗
arXiv2000

Refinement of Bethe ansatz string and its alternative

The well known string solution to Bethe ansatz equations is shown to be inconsistent in its widely accepted form. A valid refinement demanding higher order corrections in subsequent roots is identified. A new alternative string solution is proposed for finite long chains, consistent with the non-Bethe strings observed earlier.

cond-mat↗
arXiv2000

Exact solution of Calogero model with competing long-range interactions

An integrable extension of the Calogero model is proposed to study the competing effect of momentum dependent long-range interaction over the original ${1 \ov r^2}$ interaction. The eigenvalue problem is exactly solved and the consequences on the generalized exclusion statistics, which appears to differ from the exchange statistics, are analyzed. Family of dual models with different coupling constants is shown to exist with same exclusion statistics.

cond-mat↗
arXiv2000

Exact solution of a many body problem with nearest and next-nearest neighbour interactions

Recently a partially solvable many-body problem with nearest and next-nearest neighbour interactions is proposed [cond-mat/9904121]. We show that by adding a suitably chosen momentum dependent nearest neighbour interaction, such a model can be converted into an integrable system with Lax operator formulation and related conserved quantities. We also solve the eigenvalue problem for the model exactly and as a byproduct obtain some identities involving associated Laguerre polynomials.

cond-mat↗
arXiv2000

Phase diagram of an exactly solvable t-J ladder model

We study a system of one-dimensional t-J models coupled to a ladder system. A special choice of the interaction between neighbouring rungs leads to an integrable model with supersymmetry, which is broken by the presence of rung interactions. We analyze the spectrum of low-lying excitations and ground state phase diagram at zero temperature.

cond-mat↗
arXiv1999

Construction of variable mass sine-Gordon and other novel inhomogeneous quantum integrable models

The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit inhomogeneity. Such models include variable mass sine-Gordon model, cylindrical NLS, spin chains with impurity, inhomogeneous Toda chain, the Ablowitz-Ladik model etc.

solv-int↗
arXiv1999

Algebraic construction of quantum integrable models including inhomogeneous models

Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at its various realizations and limits can generate a wide range of integrable models. They cover quantum lattice as well as field models associated with the quantum $R$-matrix of trigonometric type or at the undeformed $q \to 1$ limit similar models belonging to the rational class. The classical limit likewise yields the corresponding classical discrete and field models. Thus along with the generation of known integrable models in a unifying way a new class of inhomogeneous models including variable mass sine-Gordon model, inhomogeneous Toda chain, impure spin chains etc. are constructed.

hep-th↗
arXiv1999

Soliton solutions, Liouville integrability and gauge equivalence of Sasa Satsuma equation

Exact integrability of the Sasa Satsuma eqation (SSE) in the Liouville sense is established by showing the existence of an infinite set of conservation laws. The explicit form of the conserved quantities in term of the fields are obtained by solving the Riccati equation for the associated 3x3 Lax operator. The soliton solutions in particular, one and two soliton solutions, are constructed by the Hirota's bilinear method. The one soliton solutions is also compared with that found through the inverse scattering method. The gauge equivalence of the SSE with a generalized Landau Lifshitz equation is established with the explicit construction o

solv-int↗
arXiv1999

Algebraic approach in unifying quantum integrable models

A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known discrete and field models a new class of inhomogeneous and impurity models are obtained.

hep-th↗
arXiv1998

Exactly integrable family of generalized Hubbard models with twisted Yangian symmetry

A strongly correlated electron system with controlled hopping, in the line of the recently proposed generalized Hubbard models as candidates for high T_c-superconductors, is considered. The model along with a whole class of such systems are shown to be completely integrable with explicit quantum R-matrices and the Lax operators. Inspite of novelties in the Bethe ansatz solution, the final results do not deviate much from those of the standard Hubbard model. However, the symmetry of the model is changed to a recently discovered twisted Yangian symmetry.

cond-mat↗
arXiv1997

Exact solution of quasi two and three dimensional quantum spin models

A class of quasi two and three dimensional quantum lattice spin models with nearest and next nearest neighbour interactions is proposed. The basic idea of construction is to introduce interactions in an array of XXZ spin chains through twisting transformation. The models belong to quantum integrable systems allowing explicit R-matrix solution. The eigenvalue problem can be solved exactly using some symmetry of the models.

cond-mat↗