Figure 1

Cartoon depictions of possible ordered phases at $1∕2$ filling. The dots represent excess fermion occupation on the sites. The ellipses represent excess dimerization on the bonds. The arrows represent local currents. Note that the OAF and the BDW coexist—see Sec. 3 for an explanation.Reuse & Permissions

Figure 2

Phase diagram at $B=0$ (after Ref. 16). Phase boundaries correspond to the lines $V=0$, $U∕2V=-2+{\tau }^2$ and $U∕2V=-{\tau }^2$.Reuse & Permissions

Figure 3

(Color online) The weak-coupling phase diagram in the magnetic field. We plot the flux along the vertical axis and the angle $\theta$ (defined as $\theta ={\tan }^{-1}U∕2V$) along the horizontal axis. As the phases depend on the signs of the interaction parameters, they are indicated at the top of the diagram. Ordered phases are illustrated pictorially in Fig. 1. The corresponding order parameters are listed in Table . The disordered phases are characterized by dominant correlations (indicated in parentheses). For large values of the flux $({\sin }^2\pi f>1-{\tau }^2)$, there is a band gap in the noninteracting picture. The thick solid lines (blue and green online) represent U(1) Gaussian transitions between mutually dual ground states with long-range order, and the thick dotted lines (black and red online) are Berezinski-Kosterlitz-Thouless phase transitions corresponding to opening of a gap in one of the sectors.Reuse & Permissions

Figure 4

Possible types of the single-particle spectrum as a function of in-chain momentum. For any given $\tau$, increasing the flux will eventually open a band-gap in the noninteracting spectrum. Close to this transition one of the two bands is almost empty while the other is almost full. At this point, curvature effects of the spectrum become important; these are beyond the scope of this paper.Reuse & Permissions

Figure 5

The phase diagram of the noninteracting system. The vertical axis is the external flux and the horizontal axis is the ratio between interchain and in-chain hopping amplitudes. Figure 4 demonnstrates the four typical shapes of the spectrum corresponding to the four corners in which the phase diagram is separated by the two lines, Eq. (6).Reuse & Permissions

Figure 6

(Color online) Diamagnetic current as a function of flux in the absence of interaction. Only one period in $f$ is shown. The cusps correspond to the band gap opening.Reuse & Permissions