论文标题
Kosterlitz-tyless型量子相变的精确定位
Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions
论文作者
论文摘要
我们研究了一维无旋转费米的电荷密度波（CDW）过渡，并在半频带填充时，用最近的邻里电子传输振幅$ t $和相互作用$ v $。该模型等同于各向异性XXZ Heisenberg模型，该模型为Bethe Ansatz提供了精确的解决方案。对于$ v> v _ {\ rm c} = 2t $，CDW订单参数和单粒子间隙是有限的，但呈指数级，而Kosterlitz的特征也是如此。众所周知，很难使用近似的分析和数值方法在相图中定位这种无限级相变。二阶Hartree-fock理论在定性上适用于所有相互作用强度，并预测CDW过渡发生在$ v _ {\ rm c，2}^{（2）} \ of 1.5t $。二阶Hartree Fock理论几乎是变化的，因为准粒子激发的密度很小。我们将密度 - 矩阵重新归一化组（DMRG）应用于最高514个位点的系统尺寸的周期性边界条件，这允许将所有物理量的可靠外推到热力学极限，除关键区域外。我们研究了地下能量，间隙，顺序参数，动量分布，准粒子密度和密度密度相关函数，以定位dmrg数据的$ v _ {\ rm c} $。追踪Luttinger液体的分解和带边缘处的准粒子密度的峰，使我们能够以百分之一的精度重现$ v _ {\ rm c} $。
We investigate the charge-density wave (CDW) transition for one-dimensional spinless fermions at half band-filling with nearest-neighbor electron transfer amplitude $t$ and interaction $V$. The model is equivalent to the anisotropic XXZ Heisenberg model for which the Bethe Ansatz provides an exact solution. For $V> V_{\rm c}= 2t$, the CDW order parameter and the single-particle gap are finite but exponentially small, as is characteristic for a Kosterlitz-Thouless transition. It is notoriously difficult to locate such infinite-order phase transitions in the phase diagram using approximate analytical and numerical approaches. Second-order Hartree-Fock theory is qualitatively applicable for all interaction strengths, and predicts the CDW transition to occur at $V_{\rm c,2}^{(2)}\approx 1.5t$. Second-order Hartree Fock theory is almost variational because the density of quasi-particle excitations is small. We apply the density-matrix renormalization group (DMRG) for periodic boundary conditions for system sizes up to 514 sites which permits a reliable extrapolation of all physical quantities to the thermodynamic limit, apart from the critical region. We investigate the ground-state energy, the gap, the order parameter, the momentum distribution, the quasi-particle density, and the density-density correlation function to locate $V_{\rm c}$ from the DMRG data. Tracing the breakdown of the Luttinger liquid and the peak in the quasi-particle density at the band edge permits us to reproduce $V_{\rm c}$ with an accuracy of one percent.
