Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
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DOI：
10.1088/0953-4075/46/13/134014
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
G. Mazzucchi;L. Lepori;A. Trombettoni
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文献类型：
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作者：
G. Mazzucchi;L. Lepori;A. Trombettoni
我们研究了具有π通量的合成规范场在2D和3D晶格中跳跃的吸引相互作用费米子的超流性质。这样选择的原因是π-通量立方格子显示狄拉克点，并且在空间方向(例如，TZ)上减小跳跃系数，这些狄拉克点是不变的：然后可以研究朝向π-通量正方形格子的3D-2D内插。我们还考虑了在二维π通量正方形晶格和蜂窝几何之间提供连续内插的晶格构型。我们通过平均场分析研究了相互作用和维度对超流能隙、化学势和临界温度的影响，结果表明这些量沿着内插模式连续变化。在零温半填充的二维情况下，在临界(负)相互作用UC处发生量子相变，呈现作为|U−UC|函数的带隙的线性临界指数。我们证明了在三维空间中，这种量子相变再次被恢复，指出对于每一个有限的Tz值，能隙的临界指数从1变为1/2。
We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, tz), these Dirac points are unaltered: it is then possible to study the 3D–2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean-field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and half-filling, there is a quantum phase transition occurring at a critical (negative) interaction Uc presenting a linear critical exponent for the gap as a function of |U − Uc|. We show that in three dimensions, this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of tz.