Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation

Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the $\mathbb{Z}_2^{\mathcal{C}}\times\mathbb{Z}_2^{\mathcal{R}}\times\mathbb{Z}_2^{\mathcal{T}}$ for scalar bosons. In fact, the CRT symmetry for fermions can be extended by internal symmetries such as fermion parity, thereby forming a group extension of the $\mathbb{Z}_2$ direct product. Conventionally, a Majorana fermion is defined by one Dirac fermion with trivial cha...

Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as $\mathbb{Z}_2$-involutions in the passive transformation on the spacetime coordinates; but together with a charge conjugation C, the total C-P-R-T symmetries have enriched active transformations on fields in representations of the spacetime-internal symmetry groups of quantum field theories (QFTs). In this work, we derive that these symmetries can be further fractionalized, especial...

Charge conjugation (C), mirror reflection (R), time reversal (T), and fermion parity $(-1)^{\rm F}$ are basic discrete spacetime and internal symmetries of the Dirac fermions. In this article, we determine the group, called the C-R-T fractionalization, which is a group extension of $\mathbb{Z}_2^{\rm C}\times\mathbb{Z}_2^{\rm R}\times\mathbb{Z}_2^{\rm T}$ by the fermion parity $\mathbb{Z}_2^{\rm F}$, and its extension class in all spacetime dimensions $d$, for a single-partic...

The K\"ahler-Dirac fermion, recognized as an elegant geometric approach, offers an alternative to traditional representations of relativistic fermions. Recent studies have demonstrated that symmetric mass generation (SMG) can precisely occur with two copies of K\"ahler-Dirac fermions across any spacetime dimensions. This conclusion stems from the study of anomaly cancellation within the fermion system. Our research provides an alternative understanding of this phenomenon from...

The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechan...

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the ...

We study a single exactly massless staggered fermion in the fundamental representation of an $SU(2)$ gauge group. We utilize an nHYP-smeared fermion action supplemented with additional heavy Pauli-Villars fields which serve to decrease lattice artifacts. The phase diagram exhibits a clear two-phase structure with a conformal phase at weak coupling and a novel new phase, the Symmetric Mass Generation (SMG) phase, appearing at strong coupling. The SMG phase is confining with al...

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation...

We show that massless Kaehler-Dirac (KD) fermions exhibit a mixed gravitational anomaly involving an exact $U(1)$ symmetry which is unique to KD fields. Under this $U(1)$ symmetry the partition function transforms by a phase depending only on the Euler character of the background space. Compactifying flat space to a sphere we learn that the anomaly vanishes in odd dimensions but breaks the symmetry down to $Z_4$ in even dimensions. This $Z_4$ is sufficient to prohibit bilinea...

We investigate the implications of the quantized vectorial and axial charges in the lattice Hamiltonian of multi-flavor staggered fermions in $(1+1)$ dimensions. These lattice charges coincide with those of the $U(1)_V$ and $U(1)_A$ global symmetries of Dirac fermions in the continuum limit, whose perturbative chiral anomaly matches the non-Abelian Onsager algebra on the lattice. In this note, we focus on the lattice models that flow to continuum quantum field theories of Dir...