Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>Excitations in the Ferromagnetic Ising Field Theory in a Weak Magnetic Field: Mass Spectrum and Decay Widths

Rutkevich, S. B.

doi:10.1103/physrevlett.95.250601

Cited by 46 publications

(78 citation statements)

References 15 publications

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“…The integrand involves the connected part 7 of the time-ordered product of the Heisenberg field operators. In principle, the matrix element in (3.8) can be handled through the intermediate-state decomposition, with the use of the form-factors 10) available in an explicit form [18]. Since the form-factors (3.10) vanish at θ 1 − θ 2 = 0, this expansion directly confirms the property (3.4).…”

Section: This Leads To the Representationmentioning

confidence: 87%

“…When η changes, the spectrum of stable particles gradually changes from an infinite tower of "mesons" in the "low-T " regime at η → +∞ to a single particle in the"high-T " regime η → −∞. On a quantitative level, various expansions of some of the masses near the integrable points are available through the perturbation theory [3,[7][8][9][10][11][12][13], and rather accurate numerical data were obtained [7,8] by means of the "truncated conformal space approach" of [14], and by the numerical diagonalization of the lattice transfer-matrix [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at . Perturbative analysis

Zamolodchikov

Ziyatdinov

2011

Nuclear Physics B

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Two-particle scattering in Ising field theory in a weak magnetic field h is studied in the regime T > T c , using perturbation theory in h 2 . We calculate explicitly the cross-section of the process 2 → 3 to the order h 2 . To this order, σ 2→3 dominates σ tot (the probability of all inelastic processes) at all energies E. We show that at high energy the h 2 term in σ tot grows as 16G 3 h 2 log E, where G 3 is exactly the third moment of the Euclidean spin-spin correlation function. Going beyond the leading order, we argue that at small h 2 the probability of the 2 → 2 process decays as E −16G 3 h 2 as E → ∞.

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Section: This Leads To the Representationmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at . Perturbative analysis

Zamolodchikov

Ziyatdinov

2011

Nuclear Physics B

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“…This can proceed in a number of manners; we consider in particular the energies computed via a semiclassical approximation (the salient points of which are summarized in Appendix C). [95][96][97] One achieves consistent results by means of a Bethe-Salpeter analysis, which also allows one to obtain the wave function in Eq. (18), see also Appendix D. Computed results for the energies of meson states are also shown in Fig.…”

Section: The Nature Of the Rare Statesmentioning

confidence: 97%

Signatures of rare states and thermalization in a theory with confinement

2019

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There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new 'meson' excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously. arXiv:1808.10782v2 [cond-mat.str-el]

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“…Moreover, integrability at τ = 0 [25] also allows analytic investigation for strong magnetic field. Several studies, both analytic and numerical, have confirmed the McCoy-Wu scenario and provide us with a detailed description of the mass spectrum of Ising field theory in the full τ -h plane [3,25,10,26,24,27,28,29,30,31] (see also [32] for an introductory review of Ising field theory).…”

Section: Positive Magnetic Fieldmentioning

confidence: 99%

Confinement in the q-state Potts field theory

Delfino

Grinza

2008

Nuclear Physics B

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The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q = 4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for both mesons and baryons. Deconfined quarks (kinks) exist in a phase bounded by a first order transition on one side, and a second order transition on the other. The evolution of the mass spectrum with temperature and magnetic field is discussed.

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Large-nExcitations in the Ferromagnetic Ising Field Theory in a Weak Magnetic Field: Mass Spectrum and Decay Widths

Cited by 46 publications

References 15 publications

Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at . Perturbative analysis

Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at . Perturbative analysis

Signatures of rare states and thermalization in a theory with confinement

Confinement in the q-state Potts field theory

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