Properties of the massive Thirring model from theXYZspin chain

Abstract

We consider here the massive Thirring model regularized with the XY Z 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)].

Reply to “Comment on ‘Properties of the massive Thirring model from theXYZspin chain’ ”

“…In addition they claim that the mass gap in our calculation is approximately equal to the "resolution" 2π/L. From all this, Fujita et al conclude that our results [1] cannot be very reliable for the bound state spectrum of the massive Thirring model. Let us now review standard lattice philosophy.…”

“…In the comment on our paper [1] Fujita, Kobayashi and Takahashi claim that our results for the mass spectrum of the massive Thirring model (MTM) are not reliable [2]. In particular, they claim that if one uses spin chain regularisation it is necessary to diagonalize the spin chain Hamiltonian with a number of sites N larger than 1000.…”

“…Of course, one cannot exclude the possibility that for values of scaling parameter larger than accesed there is a complete change of scaling behavior so that the obtained extrapolated results are wrong [15]. Let us now apply the above textbook analysis to our lattice calculation (XY Z spin chain regularisation of MTM) [1]. For the sake of clarity we restrict ourself to a interval of coupling constant where elementary fermion is the particle with the lowest mass.…”

Comment on “Properties of the massive Thirring model fromXYZspin chain”

“…In this comment, we show that the calculation of Kolanovic et al [1] is far from reliable due to the rough resolution of their calculations. That is, the energy resolution in their calculation is not smaller than the mass parameter they used, and therefore there is no chance to obtain the binding energy of the system which should be in the continuum limit.…”

“…Therefore, the results of ref. [1] can not be very reliable for the bound state spectrum of the massive Thirring model. But, of course, it does not necessarily mean that the spectrum of Dashen et al [2] is incorrect.…”