Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture
81
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value $langle e^{frac{i}{2}nbetavarphi}rangle$ of the exponential fields in the massive phase ($n$ is integer and $2pi/beta$ denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01.
rate research
Read More
In this paper we study the $c$-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the $c$-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency $beta^2$, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points ($beta^2 <8pi$) to the infrared limit is in good quantitative agreement with the expected $Delta c=1$ result. The behavior of the $c$-function in the other parts of the flow diagram is also discussed. Finally, we point out that also including higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i. e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used.
We reexamine the two-dimensional linear O(2) model ($varphi^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension $eta(Tkt)simeq 0.24$ and the stiffness jump $rho_s(Tkt^-)simeq 0.64$ at the transition temperature $Tkt$, in very good agreement with the exact results $eta(Tkt)=1/4$ and $rho_s(Tkt^-)=2/pi$, as well as an essential singularity of the correlation length in the high-temperature phase as $Tto Tkt$.
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilsons RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.
Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar $phi^4$ theory in all dimensions between two and four and as a function of the temperature. The accurate description of the momentum dependence of the two-point function, required to get the spectrum of the theory, is provided by means of the Blaizot--Mendez-Galain--Wschebor approximation scheme. We confirm the existence of a bound state in dimension three, with a mass within 1% of previous Monte-Carlo and numerical diagonalization values.
We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results are used to confirm the validity of a previously proposed analytical Ansatz for the initial state in the sinh-Gordon quench.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
