Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
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DOI：
10.1103/physrevb.65.155113
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发表时间：
2001-02
影响因子：
3.7
通讯作者：
P. Sengupta;A. Sandvik;D. Campbell
中科院分区：
文献类型：
--
作者：
P. Sengupta;A. Sandvik;D. Campbell
我们用随机级数展开的量子蒙特卡罗方法研究了一维扩展Hubbard模型在半填充态下的相图。我们证实了Nakamura[J.Phys]最近预测的一种新的长程有序键序波(BOW)相的存在。SoC。日本。68,3123(1999)]在参数空间的一个小范围内，我们讨论了这些态之间的跃迁性质，并计算了一些临界指数。此外，我们精确地确定了多临界点{(U}m}，V}_{m})=(4.7\ifmmode\pm\else\textpm\fi{}0.1，2.51\ifmmode\pm\else\textpm\fi{}0.04)$)的位置(以能量单位表示，其中跳跃积分被归一为一)，在此位置上，两个连续的SDW-弓-CDW跃迁被一个不连续的(一阶)直接SDW-CDW跃迁所代替。我们还讨论了空穴掺杂对CDW态和弓形态的影响。我们发现，在这两种情况下，基态都是路德-金刚砂液体，即自旋能隙保持不变，但掺杂后半填充态的电荷能隙立即关闭。对于我们所考虑的参数，电荷和键序关联随距离r衰减为${r}^{\susureath{-}{K}_{\susureath{\rho}}，其中${K}_{\susureath{\rho}}$约为$0.5$。我们还讨论了在量子相变研究中使用并行回火(或交换蒙特卡罗)char22{}的优点，这是我们与量子蒙特卡罗\char22{}相结合的一种扩展系综方法。
We use a stochastic series-expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half-filling for small to intermediate values of the on-site U and nearest-neighbor V repulsions. We confirm the existence of a novel, long-range-ordered bond-order-wave (BOW) phase recently predicted by Nakamura [J. Phys. Soc. Jpn. 68, 3123 (1999)] in a small region of the parameter space between the familiar charge-density-wave (CDW) state for $V\ensuremath{\gtrsim}U/2$ and the state with dominant spin-density-wave (SDW) fluctuations for $V\ensuremath{\lesssim}U/2.$ We discuss the nature of the transitions among these states and evaluate some of the critical exponents. Further, we determine accurately the position of the multicritical point, ${(U}_{m}{,V}_{m})=(4.7\ifmmode\pm\else\textpm\fi{}0.1,2.51\ifmmode\pm\else\textpm\fi{}0.04)$ (in energy units where the hopping integral is normalized to unity), above which the two continuous SDW-BOW-CDW transitions are replaced by one discontinuous (first-order) direct SDW-CDW transition. We also discuss the evolution of the CDW and BOW states upon hole doping. We find that in both cases the ground state is a Luther-Emery liquid, i.e., the spin gap remains but the charge gap existing at half-filling is immediately closed upon doping. The charge and bond-order correlations decay with distance r as ${r}^{\ensuremath{-}{K}_{\ensuremath{\rho}}},$ where ${K}_{\ensuremath{\rho}}$ is approximately $0.5$ for the parameters we have considered. We also discuss advantages of using parallel tempering (or exchange Monte Carlo)\char22{}an extended ensemble method that we here combine with quantum Monte Carlo\char22{}in studies of quantum phase transitions.