Effective action and phase structure of multi-layer sine-Gordon type models

Abstract

We analyze the effective action and the phase structure of Ν-layer sine-Gordon type models, generalizing the results obtained for the two-layer sine-Gordon model found in [I. Nándori, S. Nagy, K. Sailer, U.D. Jentschura, Nucl. Phys. B, 725 (2005) 467–492]. Besides the obvious field theoretical interest, the layered sine-Gordon model has been used to describe the vortex properties of high transition temperature superconductors, and the extension of the previous analysis to a general N-layer model is necessary for a description of the critical behaviour of vortices in realistic multi-layer systems. The distinction of the Lagrangians in terms of mass eigenvalues is found to be the decisive parameter with respect to the phase structure of the N-layer models, with neighboring layers being coupled by quadratic terms in the field variables. By a suitable rotation of the field variables, we identify the periodic modes (without explicit mass terms) in the N-layer structure, calculate the effective action and determine their Kosterlitz–Thouless type phase transitions to occur at a coupling parameter β²_c,N=8Nπ, where N is the number of layers (or flavors in terms of the multi-flavor Schwinger model)

Comparison of renormalization group schemes for sine-Gordon-type models

“…Equation (28) provides again an UV scaling law that is very much like those of Eqs. (16) and (24). In order to find the validity range of the mass-corrected UV scaling law and to map the phase structure, one has to solve Eq.…”

“…It is related to the critical ratio of QED 2 , which separates the confining and the half-asymptotic phases of the fermionic model, which has been calculated by semiclassical and lattice methods [19][20][21]. The LSG model is used to describe the vortex dynamics of magnetically coupled layered superconductors [15,[22][23][24][25] and considered to be the bosonized form of the multiflavor Schwinger model (i.e. multiflavor QED 2 ) [16,25,26].…”

Anisotropic long-range spin systems

“…On the other hand naturally occurring layered supercondutors range from compounds of transition-metal dichalcogenides layers intercalated with organic, insulating molecules [11] to cuprates [8]. Vortex dynamics in magnetically coupled layered superconductors was studied [12] by a multi-layer sine-Gordon type model [13]. Layered ultracold superfluids can be induced by using a deep optical lattice in one spatial direction for fermions [14] or bosons [15].…”

Symmetries and phase structure of the layered sine-Gordon model

“…Here, we generalized the RG analysis for N layers which allowed us to consider the dependence of the phase structure on the number of the layers. In order to be able to compare the results of our RG analysis to that of the perturbative treatment performed for the LSG model [15], we performed first a rotation of the fields before applying the WH-RG method.…”

“…First, we would like to compare the result of our RG analysis to that of the perturbative treatment discussed in Ref. [15] where the rotated Nlayer SG model is studied. In the infrared (IR) region, with k ≪ M (with M being the mass eigenvalue and k is the momentum cutoff), it is allowed to use perturbation theory but only for the non-periodic modes [16].…”