arXiv subjects
Publications and source records attributed to D. Controzzi.
We propose an exact solution of a model describing a low energy behavior of cold isospin S=3/2 fermionic atoms on a one-dimensional optical lattice. Depending on the band filling the effective field theory has a form of a deformed Gross-Neveu model with either $O(7)\times \mathbb{Z}_2$ (half filling) or $U(1)\times O(5)\times \mathbb{Z}_2$ symmetry.
We study the finite-size behavior of the low-lying excitations of spin-1/2 Heisenberg chains with dimerization and next-to-nearest neighbors interaction, J_2. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results, and shows that, for different values of the dimerization parameter δ, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of \ell=L/ξ(where L is the length of the chain and ξis the correlation length). At J_2=J_2c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luscher's theory. For small δwe find a very good agreement for \ell > 4 or 7 depending on the excitation considered.
We consider the two-dimensional $\rm O(3)$ non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl.Phys. B336 (1990), 457], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient $θ$ of the topological term is quantized as $θ=2πs$, with $s$ integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-$s$ Heisenberg model. We generalize the analysis to sigma models with other symmetries.
We apply quantum field theory to study the excitation spectrum of doped two-leg ladders. It follows from our analysis that throughout most of the phase diagram the spectrum consists of degenerate quartets of kinks and anti-kinks and a multiplet of vector particles split according to the symmetry of the problem as 3 + 2 +1. This basic picture experiences corrections when one moves through the phase diagram. In some regions the splitting may become very small and in others it is so large that some multiplets are pushed in the continuum and become unstable. At second order transition lines masses of certain particles vanish. Very close to the first order transition line additional generations of particles emerge. Strong interactions in some sectors may generate additional bound states (like breathers) in the asymmetric charge sector. We briefly describe the properties of various correlation functions in different phases.
We extend form-factor perturbation theory to non--integrable deformations of massless integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory.
We show that the description of $c=1$ Conformal Field Theory in terms of quasiparticles satisfying fractional statistics can be obtained from the sine-Gordon model with a chemical potential $A$, in the limit where $A \gg M$. These quasiparticles are related to the excitations of the Calogero-Sutherland (CS) model. We provide a direct calculation of their 2-particle S-matrix using Korepin's method. We also reconsider the computation of the CS S-matrix in terms of particles with fractional charge.
Form Factor Perturbation Theory is applied to study the spectrum of the O(3) non--linear sigma model with the topological term in the vicinity of $θ= π$. Its effective action near this value is given by the non--integrable double Sine--Gordon model. Using previous results by Affleck and the explicit expressions of the Form Factors of the exponential operators $e^{\pm i\sqrt{8π} ϕ(x)}$, we show that the spectrum consists of a stable triplet of massive particles for all values of $θ$ and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of $θ$ close to $π$ whereas it becomes a resonance below a critical value $θ_c$.
We consider the problem of an heavy particle in a double well potential (DWP) interacting with an electron bath. Under general assumptions, we map the problem to a three-color logarithmic gas model, where the size of the core of the charged particles is proportional to the tunneling time, $τ_{tun}$, of the heavy particle between the two wells. For times larger then $τ_{tun}$ this model is equivalent to the anisotropic two-channel Kondo (2CK) model in a transverse field. This allows us to establish a relationship between the microscopic parameters of DWP and the 2CK problem. We show that the strong coupling fixed point of the 2CK model can never be reached for the DWP problem, in agreement with the results of Kagan and Prokof'ev, [Sov.Phys. JEPT, 69, 836 (1989)] and Aleiner et al., [Phys. Rev. Lett. 86, 2629 (2001)].
We consider two families of exactly solvable models describing thermal fluctuations in two-dimensional superconductors coupled to phonons living in an insulating layer, and study the stability of the superconducting state with respect to vortices. The two families are characterized by one or two superconducting planes. The results suggest that the effective critical temperature increases with the thickness of the insulating layer. Also the presence of the additional superconducting layer has the same effect.
We study the Thermodynamic Bethe Ansatz equations for a one-parameter quantum field theory recently introduced by V.A.Fateev. The presence of chemical potentials produces a kink condensate that modifies the excitation spectrum. For some combinations of the chemical potentials an additional gapless mode appears. Various energy scales emerge in the problem. An effective field theory, describing the low energy excitations, is also introduced.
The breakdown of the Kondo effect may be the origin of the anomalous properties of the heavy-fermion compounds at low temperatures. We study the dynamics of one impurity embedded in an antiferromagnetic host at the quantum critical point and show that the impurity is not screened and develops a power law correlation function. This suggests that the breakdown of the Kondo effect can simply be a consequence of the system's proximity to the quantum critical point.