Nonuniversal Ordering of Spin and Charge in Stripe Phases

We study the interplay of topological excitations in stripe phases: charge dislocations, charge loops, and spin vortices. In two dimensions these defects interact logarithmically on large distances. Using a renormalization-group analysis in the Coulomb-gas representation of these defects, we calculate the phase diagram and the critical properties of the transitions. Depending on the interaction parameters, spin and charge order can disappear at a single transition or in a sequence of two transitions (spin-charge separation). These transitions are nonuniversal with continuously varying critical exponents. We also determine the nature of the points where three phases coexist.

Figure 1

Different types of topological defects in the charge-density (lines) and sublattice magnetization (bold arrows). (a) Combination of a stripe dislocation (dashed arrows correspond with the Burger’s vectors) and a half vortex, (b) a charge loop, and (c) a vortex.

Figure 2

Phase diagram. Thin dashed lines show where defects would become relevant for vanishing fugacities. For finite bare fugacities [9] the transitions are located at the bold lines. Phase I has no free defects and therefore CO, SO, and LO exist. In phase II, vortices proliferate and destroy SO. In phase III, free loops are present, destroying CO and SO. Eventually, all orders are absent in phase IV.

Figure 3

Top: magnification of the phase diagram near point $P_2$. In this region, phase III is extremely narrow and masked by the transition line to the right of $P_2$. Bottom: Numerically calculated effective exponent ${\nu }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ for $l_{\max }={10}^3$ along the boundary of phase I.