Entropy- and Flow-Induced Superfluid States

Normally the role of phase fluctuations in superfluids and superconductors is to drive a phase transition to the normal state. This happens due to proliferation of topologically nontrivial phase fluctuations in the form of vortices. Here we discuss a class of systems where, by contrast, nontopological phase fluctuations can produce superfluidity. Here we understand superfluidity as a phenomenon that does not necessarily arises from a broken U(1) symmetry, but can be associated with a certain class of (approximate or exact) degeneracies of the system’s energy landscape giving raise to a U(1)-like phase.

Figure 1

Top row: potential 1 exhibits a global minimum at ${\phi }_{12}={\phi }_{13}=\pi$, and a local minimum corresponding to ${\phi }_{12}=0$. The potential is given by $V_1({\phi }_{12},{\phi }_{13})=\tanh (3–5\cos {\phi }_{12})+2.2\tanh (8\cos {\phi }_{12}+8\cos {\phi }_{13}+16)$. Potential 2 possesses minima in the form of two wells: one deep but narrow situated in ${\phi }_{12}={\phi }_{13}=\pi$, and one slightly more shallow, though wider, located in ${\phi }_{12}={\phi }_{13}=0$. The potential is given by $V_2({\phi }_{12},{\phi }_{13})=2.05\tanh (8\cos {\phi }_{12}+8\cos {\phi }_{13}+16)+2\tanh (2-\cos {\phi }_{12}-\cos {\phi }_{13})$. Potential 3 possesses a global minimum in ${\phi }_{12}={\phi }_{13}=\pi$, and a local minimum corresponding to ${\phi }_{12}=0$. The potential is given by $V_3({\phi }_{12},{\phi }_{13})=-\cos 2{\phi }_{12}-0.18\cos {\phi }_{12}+0.2(1-\cos {\phi }_{12})\cos {\phi }_{13}$. Rows (A)–(E): summary of the simulation results. The three columns correspond to potentials 1, 2, and 3. The first three rows (A)–(C) give the averages $o_1$, $o_2$, $o_3$ [Eq. (3)] for system sizes $8\le L\le 40$. These are zero if a system is in the normal state. Row (D) gives $S_{12}$ [Eq. (4)] while row (E) shows the correlator $C_{13}$ [Eq. (6)] for model 1 and $S_{13}$ [Eq. (5)] for models 2 and 3. In rows (D) and (E) data are only displayed for the system size $L=40$. In all plots there are two curves corresponding to the two different states ($\downarrow$, $\uparrow$). These two states coexist in part of the parameter range, particularly in models 1 and 2, due to hysteresis.

Figure 2

Correlator $C_{13}$ for model 1 at higher temperature. System sizes range from 4 to 28. The point on the horizontal axis $\beta \approx 0.45$, where $C_{13}$ approaches zero, corresponds to the transition where superfluidity is destroyed by vortex proliferation.