1,556 research outputs found
Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory
A non-linear integral equation (NLIE) governing the finite size effects of
excited states of even topological charge in the sine-Gordon (sG) / massive
Thirring (mTh) field theory, deducible from a light-cone lattice formulation of
the model, has been known for some time. In this letter we conjecture an
extension of this NLIE to states with odd topological charge, thus completing
the spectrum of the theory. The scaling functions obtained as solutions to our
conjectured NLIE are compared successfully with Truncated Conformal Space data
and the construction is shown to be compatible with all other facts known about
the local Hilbert spaces of sG and mTh models. With the present results we have
achieved a full control over the finite size behaviour of energy levels of
sG/mTh theory.Comment: LaTeX2e, 12 pp., 3 eps figs. Remarks on locality adde
Non linear integral equation and excited--states scaling functions in the sine-Gordon model
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz
equations for finite size) is generalized to excited states, that is states
with holes and complex roots over the antiferromagnetic ground state. We
consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of
length using the light-cone approach, in which the sG/mT model is obtained
as the continuum limit of an inhomogeneous six vertex model. This NLIE is an
useful starting point to compute the spectrum of excited states both
analytically in the large (perturbative) and small (conformal) regimes
as well as numerically.Comment: LaTeX file, 40 pages, 4 figures in a tar.Z file (3 figures added and
few misprints corrected w.r.t. previous version
Yang--Baxter symmetry in integrable models: new light from the Bethe Ansatz solution
We show how any integrable 2D QFT enjoys the existence of infinitely many
non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry
algebra. These charges are generated by quantum monodromy operators and provide
a representation of deformed affine Lie algebras. We review and generalize
the work of de Vega, Eichenherr and Maillet on the bootstrap construction of
the quantum monodromy operators to the sine--Gordon (or massive Thirring)
model, where such operators do not possess a classical analogue. Within the
light--cone approach to the mT model, we explicitly compute the eigenvalues of
the six--vertex alternating transfer matrix \tau(\l) on a generic physical
state, through algebraic Bethe ansatz. In the thermodynamic limit \tau(\l)
turns out to be a two--valued periodic function. One determination generates
the local abelian charges, including energy and momentum, while the other
yields the abelian subalgebra of the (non--local) YB algebra. In particular,
the bootstrap results coincide with the ratio between the two determinations of
the lattice transfer matrix.Comment: 30 page
Improved Hartree--Fock resummations and spontaneous symmetry breaking
The standard Hartree--Fock approximation of the invariant
model suffers from serious renormalization problems. In addition, when the
symmetry is spontaneously broken, another shortcoming appears in relation to
the Goldstone bosons: they fail to be massless in the intermediate states. In
this work, within the framework of out--of--equilibrium Quantum Field Theory,
we propose a class of systematic improvements of the Hartree--Fock resummation
which overcomes all the above mentioned difficulties while ensuring also exact
Renormalization--Group invariance to one loop.Comment: 42 pages, 9 figure
The renormalized and Renormalization-Group invariant Hartree-Fock approximation
We study the renormalization problem for the Hartree--Fock approximation of
the invariant model in the symmetric phase and show how to
systematically improve the corresponding diagrammatic resummation to achieve
the correct renormalization properties of the effective field equations,
including Renormalization--Group invariance with the one--loop beta function.
These new Hartree--Fock dynamics is still of mean field type but includes
memory effects which are generically nonlocal also in space.Comment: 32 pages, 13 figure
Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for
magnetic chains and field theories that includes the finite size (and zero
temperature) calculations for lattice BA models. In all cases, the free energy
follows by quadratures from the solution of a {\bf single} non-linear integral
equation (NLIE). [A system of NLIE appears for nested BA]. We derive the NLIE
for: a) the six-vertex model with twisted boundary conditions; b) the XXZ chain
in an external magnetic field and c) the sine-Gordon-massive Thirring
model (sG-mT) in a periodic box of size \b \equiv 1/T using the light-cone
approach. This NLIE is solved by iteration in one regime (high in the XXZ
chain and low in the sG-mT model). In the opposite (conformal) regime, the
leading behaviors are obtained in closed form. Higher corrections can be
derived from the Riemann-Hilbert form of the NLIE that we present.Comment: Expanded Introduction. Version to appear in Nucl. Phys. B. 60 pages,
TeX, Uses phyzz
A local and integrable lattice regularization of the massive Thirring model
The light--cone lattice approach to the massive Thirring model is
reformulated using a local and integrable lattice Hamiltonian written in terms
of discrete fermi fields. Several subtle points concerning boundary conditions,
normal--ordering, continuum limit, finite renormalizations and decoupling of
fermion doublers are elucidated. The relations connecting the six--vertex
anisotropy and the various coupling constants of the continuum are analyzed in
detail.Comment: Latex, 24 pages, some corrected misprints and minor changes, 2
Postscript figures unchange
Finite volume spectrum of N=1 superminimal models perturbed by
We describe an extension of the nonlinear integral equation (NLIE) tehnique
to N=1 superminimal models perturbed by . Along the way, we also
complete our previous studies of the finite volume spectrum of the N=1
supersymmetric sine-Gordon model by considering the attractive regime and more
specifically, breather states
Ultraviolet cascade in the thermalization of the classical phi^4 theory in 3+1 dimensions
We investigate the dynamics of thermalization and the approach to equilibrium
in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium
dynamics is studied by numerically solving the equations of motion in a light-
cone-like discretization of the model for a broad range of initial conditions
and energy densities.A smooth cascade of energy towards the ultraviolet is
found to be the basic mechanism of thermalization.After an initial transient
stage,at a time scale of several hundreds inverse masses,the squared of the
field gradient becomes larger than the nonlinear term and a stage of universal
cascade emerges. As the cascade progresses, the modes with higher wavenumbers
exhibit weaker and weaker nonlinearities well described by the Hartree
approximation while the infrared modes retain strong selfinteractions. Two
timescales for equilibration appears.For k^2>(t) we observe an effective
thermalization with a time scale in the thousands of inverse masses and the
Hartree approximation holds. By effective thermalization we mean that the
observable acquires the equilibrium functional form with an effective time
dependent temperature Teff, which slowly decreases with time. Infrared modes
with k^2 (t) equilibrate only by time scales in the millions of
inverse masses. Infrared modes with k^2 (t) equilibrate only by time
scales in the millions.Virialization and the equation of state start to set
much earlier than effective thermalization.The applicability of these results
in quantum field theory for large occupation numbers and small coupling is
analyzed.Comment: 47 pages, 31 figures. Presentation improved, 4 new figure
- …