来自非格点矢量和轴向对称性的1+1维格点狄拉克费米子
1+1d Lattice Dirac Fermions from Non-Onsite Vector and Axial Symmetries
AI总结：
该研究构造了具有非格点矢量与轴向U(1)对称性的可严格求解1+1维格点狄拉克费米子模型，还实现了相互作用费米子Luttinger液体的可严格求解版本，并计算了自由狄拉克不动点处的领头阶无关相互作用。
AI中文摘要：
我们构造了一个可严格求解的哈密顿量格点模型，实现了1+1维狄拉克费米子，具有严格的微观矢量和轴向矢量U(1)对称性。这两者之间的混合反常由对称性的非格点作用来容纳。我们的希尔伯特空间是局域Z₂分次希尔伯特空间的Z₂分次张量积，其中包含无穷维转子自由度。在经保局域幺正映射到等价的费米子Villain希尔伯特空间后，哈密顿量变得明显可严格求解。我们的构造还允许实现相互作用费米子Luttinger液体的可严格求解版本。在自由狄拉克不动点处，我们的哈密顿量包含无关相互作用，我们对其进行了领头阶计算。
英文摘要：
We construct an exactly solvable Hamiltonian lattice model realizing a 1+1d Dirac fermion, with exact microscopic vector and axial vector $U(1)$ symmetries. The mixed anomaly between these is accommodated by the not-on-site action of the symmetries. Our Hilbert space is a $Z_2$-graded tensor product of local $Z_2$-graded Hilbert spaces which include infinite dimensional rotor degrees of freedom. The Hamiltonian becomes manifestly exactly solvable after a locality-preserving unitary mapping to an equivalent fermionic Villain Hilbert space. Our construction also allows an exactly solvable realization of interacting fermionic Luttinger liquids. At the free Dirac fixed point, our Hamiltonian contains irrelevant interactions, which we compute to leading order.
