Excitation spectrum of doped two-leg ladders: A field theory analysis

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 antikinks 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.

Figure 1

The two-dimensional projection of the phase diagram for $K_c>1∕2$. The thick lines represent first-order phase transitions. At $K_c<1∕2$ the SC phases are replaced by the Wigner crystal.

Figure 2

A qualitative picture of the spectrum of the $\mathrm{O}\left(N\right)\times \mathrm{O}\left(M\right)$ GN model.

Figure 3

A qualitative picture of the spectrum of the model interpolating between the $\mathrm{O}\left(N\right)\times {\mathbb{Z}}_2$ and $\mathrm{O}(N+1)$ GN models.

Figure 4

RG flows (88) for $C_{1∕2}=0$. The thick line represents the flow with $C_{-1∕2}=0$.

Figure 5

RG flows (88) for $C_{1∕2}>0$. The thick line represents the flow with $C_{-1∕2}=0$.

Figure 6

The qualitative picture of the mass spectrum of the $\mathrm{O}\left(3\right)\times \mathrm{O}\left(3\right)$ GN model as a function $1∕C_{1∕2}$. The dashed lines show masses of mesons.