Non-equivalence between Heisenberg XXZ spin chain and Thirring model

Fujita, Tomohiro; Kobayashi, Takuya; Hiramoto, Makoto; Takahashi, Hidenori

doi:10.1140/epjc/s2004-02093-x

Cited by 2 publications

(2 citation statements)

References 19 publications

(22 reference statements)

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“…This means that, even though the two models are mathematically shown to be equivalent to each other, they are physically very different. 25 What should be the main reason for the difference ? If one makes the field theory into the lattice, then the lattice field theory loses some important continuous symmetry like Lorentz invariance or chiral symmetry.…”

Section: Discussionmentioning

confidence: 99%

New Vacuum of Bethe Ansatz Solutions in Thirring Model

et al. 2005

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We find a new vacuum of the Bethe ansatz solutions in the massless Thirring model. This vacuum breaks the chiral symmetry and has the lower energy than the well-known symmetric vacuum energy. Further, we evaluate the energy spectrum of the one particle-one hole ($1p-1h$) states, and find that it has a finite gap. The analytical expressions for the true vacuum as well as for the lowest $1p-1h$ excited state are also found. Further, we examine the bosonization of the massless Thirring model and prove that the well-known procedure of bosonization of the massless Thirring model is incomplete because of the lack of the zero mode in the boson field.Comment: 7 page

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Section: Discussionmentioning

confidence: 99%

New Vacuum of Bethe Ansatz Solutions in Thirring Model

et al. 2005

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“…However, as we saw, the spectrum of the Thirring model gives a finite gap while the Heisenberg XXZ model predicts always gapless spectrum. This means that, even though the two models are mathematically shown to be equivalent to each other, they are physically very different [48].…”

Section: Condensatementioning

confidence: 99%

Bosons after Symmetry Breaking in Quantum Field Theory

Fujita,

Hiramoto,

Takahashi

2007

Preprint

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We present a unified description of the spontaneous symmetry breaking and its associated bosons in fermion field theory. There is no Goldstone boson in the fermion field theory models of Nambu-Jona-Lasinio, Thirring and QCD 2 after the chiral symmetry is spontaneously broken in the new vacuum. The defect of the Goldstone theorem is clarified, and the "massless boson" predicted by the theorem is virtual and corresponds to just a f ree massless fermion and antifermion pair. Further, we discuss the exact spectrum of the Thirring model by the Bethe ansatz solutions, and the analytical expressions of all the physical observables enable us to understand the essence of the spontaneous symmetry breaking in depth. Also, we examine the boson spectrum in QCD 2 , and show that bosons always have a finite mass for SU (N c ) colors. The problem of the light cone prescription in QCD 2 is discussed, and it is shown that the trivial light cone vacuum is responsible for the wrong prediction of the boson mass.

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Non-equivalence between Heisenberg XXZ spin chain and Thirring model

Cited by 2 publications

References 19 publications

New Vacuum of Bethe Ansatz Solutions in Thirring Model

New Vacuum of Bethe Ansatz Solutions in Thirring Model

Bosons after Symmetry Breaking in Quantum Field Theory

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