AI 中文总结
本文通过Jordan-Wigner变换，精确研究含四自旋相互作用的扩展各向同性$XY$链的临界相，揭示其Lifshitz型拓扑相变、量子相变特性及交变磁场下的基态相图与相关奇异物理行为。
AI 中文摘要
利用Jordan-Wigner变换，我们精确计算了自旋$S=1/2$的含四自旋相互作用的各向同性$XX$链的基态及低温热力学性质。在等效无自旋费米子（SF）表象下，该系统可视为具有最近邻（$J$）和次近邻（$J^*/4$）跳跃的格点费米气体。研究表明，随四自旋耦合增强，在$J^*_c=4J/3$处系统发生Lifshitz型拓扑相变，特征为费米点数目加倍。该量子相变（QPT）点标志着从标准$XX$链的无隙自旋液体相，转变为具有不同自旋关联幂律衰减特征的另一无隙自旋液体相。在相变点，自由费米子色散关系在费米点处变平，这决定了态密度的奇异性质$\rho(\boldsymbol{\nu})\boldsymbol{\nu}/J)^{-2/3}$，进而导致系统热容呈现非常规温度依赖关系$C\boldsymbol{\nu}/J^*)^{1/3}$，以及磁化率的奇异行为$\boldsymbol{\nu}(H)\boldsymbol{\nu}/J^*)^{-2/3}$。在交变磁场下，该系统具有丰富的基态相图，包含完全极化（铁磁）、有隙反铁磁（AFM）和自旋液体相。从有隙AFM相到无隙极化自旋液相的相变点处，系统表现出磁化强度的快速增长$m\boldsymbol{\nu}(H-H_c)^{1/6}$，以及磁化率的奇异行为$\boldsymbol{\nu}(H)\boldsymbol{\nu}(H-H_c)^{-5/6}$。
英文摘要
Using the Jordan-Wigner transformation we calculate exactly the ground state and low-temperature thermodynamic properties of the spin $S=1/2$ isotropic $XX$ chain with four spin interaction. In terms of the equivalent spinless fermion (SF) representation the system is viewed as a lattice fermion gas with nearest-neighbor ($J$) and next-next-next-neighbor ($J^{\ast}/4$) hopping. It is shown that with the increase of four spin coupling, at $J^{\ast}_{c} = 4J/3$ the system experiences the Lifshitz type topological phase transition characterized by the tripling of Fermi points. The quantum phase transition (QPT) point marks transition from a gapless spin-liquid phase of standard $XX$ chain into again a gapless spin-liquid phase with different character of power-low decay of spin correlations. At the transition point the free fermion dispersion relation shows flattering at Fermi points, what determines singular character of density of states $ρ(ω)\sim (ω/J)^{-2/3}$ and as a consequence unconventional temperature dependence of heat capacity of the system $C\sim (T/J^{\ast})^{1/3}$, and singular magnetic susceptibility of the system $χ(H)\sim (H/J^{\ast})^{-2/3}$. In the case of alternating magnetic field the system is characterized by the rich ground state phase diagram which contains fully polarized (ferromagnetic), gapped antiferromagnetic (AFM) and spin liquid phases. At the transition point from the gapped AFM phase into the gapless polarized spin liquid phase the system shows rapid increase of magnetization $m\sim(H-H_c)^{1/6}$ and magnetic susceptibility a singular behavior as $χ(H)\sim (H-H_c)^{-5/6}$.
