Fermi Surface Symmetric Mass Generation (2210.16304v1)

Abstract: Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction.

• The paper demonstrates symmetric mass generation by introducing a mass gap in Fermi liquids without conventional fermion bilinear condensation.
• It employs (1+1)D and (2+1)D lattice models using six-fermion and charge fusion interactions to cancel Fermi surface anomalies.
• The study offers theoretical insights for designing novel materials with engineered electronic properties, such as unconventional superconductors.

Fermi Surface Symmetric Mass Generation: An Overview

The paper "Fermi Surface Symmetric Mass Generation" by Da-Chuan Lu, Meng Zeng, Juven Wang, and Yi-Zhuang You introduces a novel exploration into the symmetric mass generation (SMG) in Fermi liquid systems. Symmetric mass generation is a process that involves introducing a mass gap to gapless fermions through non-perturbative interactions without yielding any fermion bilinear condensation, diverging from conventional Higgs-type mechanisms.

The authors extend the concept of SMG from previously studied zero Fermi volume Dirac/Weyl/Majorana fermions to Fermi liquids characterized by finite Fermi volumes. This extension involves the examination of gap generation at the Fermi surface through interaction effects without breaking the U(1) loop group symmetry or instigating topological order development. By focusing on systems in (1+1)D and (2+1)D where several Fermi surfaces can collectively negate the Fermi surface anomaly, the paper reveals how non-perturbative interactions can uniquely facilitate the gapping of Fermi surfaces.

Core Contributions and Methodology

The paper presents examples of Fermi surface SMG using lattice models to demonstrate how symmetric gapping of Fermi surfaces can be achieved while preserving U(1) symmetry. Two primary examples are analyzed:

1. (1+1)D Lattice Model: The authors construct a lattice model involving two distinct types of fermions with different U(1) charges occupying a single spatial dimension. This model provides a realization of anomaly-free Fermi liquids by ensuring that the fillings satisfy a charge compensation condition that cancels the Fermi surface anomaly. The SMG mechanism is realized through six-fermion interactions, which convert a Fermi liquid into a gapped insulator in a manner that defies symmetry breaking. The RG flow analysis shows the transition from Fermi liquid to SMG insulator is akin to a Berezinskii-Kosterlitz-Thouless (BKT) transition.
2. (2+1)D Lattice Model: Here, the interplay between Kagome and triangular lattice systems demonstrates the feasibility of Fermi surface SMG in higher dimensions. In this model, a charge fusion interaction allows for transitions from Fermi liquid to SMG states, observable at strong interaction strengths. The work provides insights into the conditions necessary for the successful termination of Fermi surface anomalies and subsequent generation of a mass gap through rigorous theoretical and numerical exploration.

Implications and Future Directions

The theoretical implications of this paper extend toward a broader understanding of quantum anomaly applications in condensed matter physics, particularly in designing symmetric gapping strategies for Fermi surfaces. Experimentally, these insights could influence the development of novel materials with engineered electronic properties where control over Fermi surface states is desirable, such as topologically ordered phases or unconventional superconductors.

The findings open avenues for future research focusing on:

• Exploration of SMG in higher dimensions and complex lattice geometries.
• Experimental realizations of the predicted gap generation mechanisms in materials.
• Further delineation of SMG transitions and critical phenomena associated with interactions at various Fermi surface configurations.

While the paper provides a foundational framework, a detailed examination of the critical behaviors during the SMG transition, potentially involving functional renormalization group methods, could provide deeper insights into the precise nature of emergent states at symmetry-protecting critical points.

In summary, this paper advances the theoretical landscape of symmetric mass generation in Fermi systems, challenging conventional paradigms by emphasizing the profound impact of interaction-driven phenomena in preserving symmetries and inducing novel quantum phases.