283 research outputs found
Chaos in the thermodynamic Bethe ansatz
We investigate the discretized version of the thermodynamic Bethe ansatz
equation for a variety of 1+1 dimensional quantum field theories. By computing
Lyapunov exponents we establish that many systems of this type exhibit chaotic
behaviour, in the sense that their orbits through fixed points are extremely
sensitive with regard to the initial conditions.Comment: 10 pages, Late
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Integrable models with unstable particles
We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to integrable models, we subsequently propose a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We describe the general Lie algebraic structure which underlies theories with unstable particles and formulate a decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. We extend these ideas to theories with an infinite spectrum of unstable particles. We provide new expressions for the scattering amplitudes in the soliton-antisoliton sector of the elliptic sine-Gordon model in terms of infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. For that situation we compute the complete S-matrix of all sectors. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal SO(n)-affine Toda field theory
Finite temperature correlation functions from form factors
We investigate proposals of how the form factor approach to compute correlation functions at zero temperature can be extended to finite temperature. For the two-point correlation function we conclude that the suggestion to use the usual form factor expansion with the modification of introducing dressing functions of various kinds is only suitable for free theories. Dynamically interacting theories require a more severe change of the form factor program
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Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising Model
In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model in the ordered regime, both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions
Decoupling the SU(N)2-homogeneous sine-Gordon model
We provide a systematic construction for all n-particle form factors of the SU(N)2/U(1)N-1-homogeneous sine-Gordon model in terms of general determinant formulas for a large class of local operators. The ultraviolet limit is carried out and the corresponding Virasoro central charge, together with the conformal dimensions of various operators, are identified. The renormalization-group flow is studied and we find a precise rule, depending on the relative order of magnitude of the resonance parameters, according to which the theory decouples into new cosets along the flow
Unstable particles versus resonances in impurity systems, conductance in quantum wires
We compute the DC conductance for a homogeneous sine-Gordon model and an
impurity system of Luttinger liquid type by means of the thermodynamic Bethe
ansatz and standard potential scattering theory. We demonstrate that unstable
particles and resonances in impurity systems lead to a sharp increase of the
conductance as a function of the temperature, which is characterized by the
Breit-Wigner formula.Comment: 5 pages Latex, 1 figure replaced, version to appear in J. Phys.
Higher particle form factors of branch point twist fields in integrable quantum field theories
In this paper we compute higher particle form factors of branch point twist
fields. These fields were first described in the context of massive
1+1-dimensional integrable quantum field theories and their correlation
functions are related to the bi-partite entanglement entropy. We find analytic
expressions for some form factors and check those expressions for consistency,
mainly by evaluating the conformal dimension of the corresponding twist field
in the underlying conformal field theory. We find that solutions to the form
factor equations are not unique so that various techniques need to be used to
identify those corresponding to the branch point twist field we are interested
in. The models for which we carry out our study are characterized by staircase
patterns of various physical quantities as functions of the energy scale. As
the latter is varied, the beta-function associated to these theories comes
close to vanishing at several points between the deep infrared and deep
ultraviolet regimes. In other words, renormalisation group flows approach the
vicinity of various critical points before ultimately reaching the ultraviolet
fixed point. This feature provides an optimal way of checking the consistency
of higher particle form factor solutions, as the changes on the conformal
dimension of the twist field at various energy scales can only be accounted for
by considering higher particle form factor contributions to the expansion of
certain correlation functions.Comment: 25 pages, 4 figures; v2 contains small correction
Boundary Quantum Field Theories with Infinite Resonance States
We extend a recent work by Mussardo and Penati on integrable quantum field
theories with a single stable particle and an infinite number of unstable
resonance states, including the presence of a boundary. The corresponding
scattering and reflection amplitudes are expressed in terms of Jacobian
elliptic functions, and generalize the ones of the massive thermal Ising model
and of the Sinh-Gordon model. In the case of the generalized Ising model we
explicitly study the ground state energy and the one-point function of the
thermal operator in the short-distance limit, finding an oscillating behaviour
related to the fact that the infinite series of boundary resonances does not
decouple from the theory even at very short-distance scales. The analysis of
the generalized Sinh-Gordon model with boundary reveals an interesting
constraint on the analytic structure of the reflection amplitude. The roaming
limit procedure which leads to the Ising model, in fact, can be consistently
performed only if we admit that the nature of the bulk spectrum uniquely fixes
the one of resonance states on the boundary.Comment: 18 pages, 11 figures, LATEX fil
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