论文标题
在小磁场处的5/2量化霍尔状态下可能恢复粒子孔对称性
Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
论文作者
论文摘要
通过对填充$ν= 5/2 $的实验观察的实验观察，这与Pfaffian和Antipfaffian国家不相容，我们已经将$ 5/2 $ $ 5/2 $量化的Hamiltonian的Hamiltonian扩展到$ 5/2 $ 1/\ sqrt {b} $控制Landau级别的混合，其中$ e_c $是库仑能量，而$ω_c$ cyclotron频率。这种有效的哈密顿量的确切对角线表明，与Pfaffian和在二阶诱导的反夫夫的重叠的差异通过三阶校正减少，并且消失在$κ= 0.4 $左右，这表明这些状态在能量在能量上在磁场上的能量更接近。此外，我们表明，在$κ$的这一范围内，有限大小的频谱是量子相变的典型特征，其能量间隙的降低很大，并且激发态之间的水平交叉点。这些结果表明，在较小的磁场上将量子相变到具有新兴粒子孔对称性的相位可能性，这将解释$ 5/2 $ $ 5/2 $量化的霍尔状态的$ 5/2 $的热电导。
Motivated by the experimental observation of a quantized 5/2 thermal conductance at filling $ν=5/2$, a result incompatible with both the Pfaffian and the Antipfaffian states, we have pushed the expansion of the effective Hamiltonian of the $5/2$ quantized Hall state to third-order in the parameter $κ=E_c/\hbar ω_c \propto 1/\sqrt{B}$ controlling the Landau level mixing , where $E_c$ is the Coulomb energy and $ω_c$ the cyclotron frequency. Exact diagonalizations of this effective Hamiltonian show that the difference in overlap with the Pfaffian and the AntiPfaffian induced at second-order is reduced by third-order corrections and disappears around $κ=0.4$, suggesting that these states are much closer in energy at smaller magnetic field than previously anticipated. Furthermore, we show that in this range of $κ$ the finite-size spectrum is typical of a quantum phase transition, with a strong reduction of the energy gap and with level crossings between excited states. These results point to the possibility of a quantum phase transition at smaller magnetic field into a phase with an emergent particle-hole symmetry that would explain the measured $5/2$ thermal conductance of the $5/2$ quantized Hall state.
