The fractional quantum Hall (FQH) effect was discovered in two-dimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because of the quenching of the kinetic energy, gave new meaning to the phrase "correlated matter". Most FQH phases are gapped like insulators and superconductors; however, a small subset with even denominator fractional fillings nu of the Landau level, typified by nu = 1/2, are found to be gapless, with a Fermi surface akin to metals. We discuss our results, obtained numerically using the infinite Density Matrix Renormalization Group (iDMRG) scheme, on the effect of non-isotropic distortions with discrete N-fold rotational symmetry of the Fermi surface at zero magnetic field on the Fermi surface of the correlated nu = 1/2 state. We find that while the response for N = 2 (elliptical) distortions is significant (and in agreement with experimental observations with no adjustable parameters), it decreases very rapidly as N is increased. Other anomalies, like resilience to breaking the Fermi surface into disjoint pieces, are also found. This highlights the difference between Fermi surfaces formed from the kinetic energy, and those formed of purely potential energy terms in the Hamiltonian.

中文翻译：

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复合费米子的费米面

分数量子霍尔 (FQH) 效应是在近四年前在受大垂直磁场影响的二维电子系统中发现的。它帮助启动了拓扑相领域，此外，由于动能的淬灭，给“相关物质”这个短语赋予了新的含义。大多数 FQH 相像绝缘体和超导体一样有间隙；然而，发现具有朗道能级的偶数分母分数填充 nu（以 nu = 1/2 为代表）的小子集是无间隙的，具有类似于金属的费米表面。我们讨论了使用无限密度矩阵重整化组 (iDMRG) 方案在数值上获得的结果，关于非各向同性畸变的影响，在零磁场下费米表面的离散 N 倍旋转对称性对相关 nu = 1/2 态的费米表面的影响。我们发现，虽然 N = 2（椭圆）失真的响应是显着的（并且与没有可调参数的实验观察一致），但随着 N 的增加，它的下降速度非常快。还发现了其他异常现象，例如将费米表面破碎成不相交的碎片的弹性。这突出了由动能形成的费米面与由哈密顿量中纯势能项形成的费米面之间的差异。随着 N 的增加，它下降得非常快。还发现了其他异常现象，例如将费米表面破碎成不相交的碎片的弹性。这突出了由动能形成的费米面与哈密顿量中由纯势能项形成的费米面之间的区别。随着 N 的增加，它下降得非常快。还发现了其他异常现象，例如将费米表面破碎成不相交的碎片的弹性。这突出了由动能形成的费米面与哈密顿量中由纯势能项形成的费米面之间的区别。