<b><i>XXZ</i></b>spin chain in a transverse field as a regularization of the sine-Gordon model

Pallua, S.; Prester, Predrag Dominis

doi:10.1103/physrevd.59.125006

Cited by 5 publications

(6 citation statements)

References 28 publications

(62 reference statements)

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“…They differ from those conjectured in [17] only for the second breather, which has scaling dimension equal to that of the first breather. These results are in agreement with those in [22] for the SGM. This result for the scaling dimension of the second breather was analyticaly confirmed in [26] using an extension of nonlinear integral equation method (NLIE).…”

Section: Uv (Conformal) Limit Of Particle Statessupporting

confidence: 93%

“…But even we couldn't make an extrapolation (because of the poor scaling in the μ → ∞ limit) for the lowest "continuum" state in 0 + for values of g where the DHN formula predicts that it should be of B1 B1 type, its scaling law in the μ → 0 limit clearly shows that its scaling dimension is the one we expect for the B1 B1 lowest continuum state, i.e., d 4,0 . We should mention also that spectra in 0 − and π − are exactly degenerated which means that the F and F mass gaps are equal even on the lattice, which was not the case in similar analyses of the SGM in [22].…”

Section: Mass Spectrummentioning

confidence: 90%

“…We should mention also that spectra in 0 − and π − are exactly degenerated which means that the F andF mass gaps are equal even on the lattice, which was not the case in similar analyses of the SGM in [22].…”

Section: Mass Spectrummentioning

confidence: 90%

“…Recently [22] we have performed a similar calculation for the SGM. The regularization in this case was the XXZ spin chain in a transverse field.…”

Section: Introductionmentioning

confidence: 99%

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Properties of the massive Thirring model from theXYZspin chain

2000

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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)].

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Section: Uv (Conformal) Limit Of Particle Statessupporting

confidence: 93%

Section: Mass Spectrummentioning

confidence: 90%

Section: Mass Spectrummentioning

confidence: 90%

“…Recently [22] we have performed a similar calculation for the SGM. The regularization in this case was the XXZ spin chain in a transverse field.…”

Section: Introductionmentioning

confidence: 99%

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Properties of the massive Thirring model from theXYZspin chain

2000

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“…The QFT is the SU (2)-Thirring model (the sine-Gordon model at a special value of its coupling constant -different values of the coupling are recovered by approaching the critical line in other ways, see e.g. [21,22]). This model has a spectrum of two asymptotic particles of equal mass.…”

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confidence: 99%

Universal corrections to the entanglement entropy in gapped quantum spin chains: A numerical study

Levi

Castro-Alvaredo

Doyon³

2013

Phys. Rev. B

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We carry out a numerical study of the bi-partite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the anti-ferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU (2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behaviour of the entropy. We numerically confirm that, in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to K0(2mr) where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted in [1,2] for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behaviour following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length. Introduction and discussion. Entanglement is a fundamental property of the state of a quantum system. In the context of quantum computation, it is a crucial resource [3]. Conceptually, it characterizes the structure of quantum fluctuations in a more universal way than other widely studied objects such as correlation functions. Developing theoretical measures of entanglement is therefore important to further understand the structure of quantum states, a problem of particular interest and difficulty for quantum many-body systems. A popular measure of entanglement is the bi-partite entanglement entropy. It measures the entanglement between two complementary sets of observables in a quantum system [4]. Interestingly, the entanglement entropy exhibits universal behaviour near quantum critical points: it has features which do not depend on the details of the model but rather on its universality class. In the last decade, this property has made the study of the entanglement entropy a very active field of research.

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