We consider here the massive Thirring model regularized with the $\mathrm{XYZ}$ spin chain. We numerically calculate the mass ratios of particles which lie in the discrete part of the spectrum and obtain results in accordance with the DHN formula and in disagreement with recent calculations in the literature based on the numerical Bethe ansatz and infinite momentum frame methods. We also analyze the short distance behavior of these states and evaluate the conformal dimensions. This paper, taken together with the previous one for the sine-Gordon model, confirms the duality relation between two models formulated by Klassen and Melzer [Int. J. Mod. Phys. A 8, 4131 (1993)].We consider here the massive Thirring model regularized with the $\mathrm{XYZ}$ spin chain. We numerically calculate the mass ratios of particles which lie in the discrete part of the spectrum and obtain results in accordance with the DHN formula and in disagreement with recent calculations in the literature based on the numerical Bethe ansatz and infinite momentum frame methods. We also analyze the short distance behavior of these states and evaluate the conformal dimensions. This paper, taken together with the previous one for the sine-Gordon model, confirms the duality relation between two models formulated by Klassen and Melzer [Int. J. Mod. Phys. A 8, 4131 (1993)].

arXiv:hep-th/0004099Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJun 27, 20002 citations

Bosonisation in one-dimensional fermion systems and applications to spin chains

Camilo Andrés Moreno Alfaro

Bosonisation is a technique for studying one-dimensional fermion systems by the means of transforming them to a boson system. S. Coleman showed that the correlation functions for the Sine Gordon field, a massless boson with a cosine interaction term, coincide with those of the massive Thirring model, which is a Dirac fermion with self-interactions. An explicit map can be found between these two systems, and it can in fact be generalised to an entire class of fermions in which the boson-fermion correspondence is a well-defined operator equality in Fock space. More generally, it is a widely used technique to transform a model into another whose nature simplifies the solution or allows for obtaining more information that appears more clearly in the new representation. Another example is the Jordan Wigner transformation, which associates quantum spin chains to one-dimensional fermions. Some aspects about the statistical properties of the chain can be inferred from the fermionic representation, and more properties can be studied by applying bosonisation and examine the system in this new representation.Bosonisation is a technique for studying one-dimensional fermion systems by the means of transforming them to a boson system. S. Coleman showed that the correlation functions for the Sine Gordon field, a massless boson with a cosine interaction term, coincide with those of the massive Thirring model, which is a Dirac fermion with self-interactions. An explicit map can be found between these two systems, and it can in fact be generalised to an entire class of fermions in which the boson-fermion correspondence is a well-defined operator equality in Fock space. More generally, it is a widely used technique to transform a model into another whose nature simplifies the solution or allows for obtaining more information that appears more clearly in the new representation. Another example is the Jordan Wigner transformation, which associates quantum spin chains to one-dimensional fermions. Some aspects about the statistical properties of the chain can be inferred from the fermionic representation, and more properties can be studied by applying bosonisation and examine the system in this new representation.

Jul 7, 20260 citations

Statistical mechanics of quantum spin systems

Derek W. Robinson

Communications in Mathematical PhysicsJun 1, 196765 citations

The phase diagram of the one-dimensional quantum sine-Gordon system ( $β^{2}=4π)$ with a linear spatial modulationThe phase diagram of the one-dimensional quantum sine-Gordon system ($β^{2}=4π)$ with a linear spatial modulation

Zhiguo Wang, Yumei Zhang

The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, $β^{2}$ =4 $π$ . The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable.The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, $β^{2}$ =4$π$. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable.

arXiv:cond-mat/0104161Apr 10, 20010 citations

Thermodynamics of the quantum spin-S XXZ chain

Onofre Rojas, S. M. de Souza, E. V. Corrêa Silva +1 more

The European Physical Journal BSep 1, 20059 citations

We consider here the massive Thirring model regularized with the

\mathrm{XYZ}

spin chain. We numerically calculate the mass ratios of particles which lie in the discrete part of the spectrum and obtain results in accordance with the DHN formula and in disagreement with recent calculations in the literature based on the numerical Bethe ansatz and infinite momentum frame methods. We also analyze the short distance behavior of these states and evaluate the conformal dimensions. This paper, taken together with the previous one for the sine-Gordon model, confirms the duality relation between two models formulated by Klassen and Melzer [Int. J. Mod. Phys. A 8, 4131 (1993)].

The phase diagram of the one-dimensional quantum sine-Gordon system (

β^{2}=4π)

with a linear spatial modulation

The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case,

β^{2}

π

. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable.