Symmetric mass generation (SMG) is a mechanism to give gapless fermions a mass gap by nonperturbative interactions without generating any fermion bilinear condensation. The previous studies of SMG have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this paper, we generalize the concept of SMG to Fermi liquid (FL) with a finite Fermi volume and discuss how to gap out the Fermi surfaces (FSs) by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of FS SMG in both $(1+1)$ -dimensional $[(1+1)\mathrm{D}]$ and $(2+1)$ -dimensional FL systems when several FSs together cancel the FS 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 nonperturbative interaction mechanism is the only way to gap out the FSs. This symmetric FS reconstruction is in contrast to the conventional symmetry-breaking gapping mechanism in the FL. As a side product, our model provides a pristine one-dimensional lattice regularization for the $(1+1)\mathrm{D}$ 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.Symmetric mass generation (SMG) is a mechanism to give gapless fermions a mass gap by nonperturbative interactions without generating any fermion bilinear condensation. The previous studies of SMG have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this paper, we generalize the concept of SMG to Fermi liquid (FL) with a finite Fermi volume and discuss how to gap out the Fermi surfaces (FSs) by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of FS SMG in both $(1+1)$-dimensional $[(1+1)\mathrm{D}]$ and $(2+1)$-dimensional FL systems when several FSs together cancel the FS 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 nonperturbative interaction mechanism is the only way to gap out the FSs. This symmetric FS reconstruction is in contrast to the conventional symmetry-breaking gapping mechanism in the FL. As a side product, our model provides a pristine one-dimensional lattice regularization for the $(1+1)\mathrm{D}$ 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.

arXiv:2210.16304Physical review. B./Physical review. BMay 17, 202320 citations

Mass Generation in a Fermionic Model with Finite Range Time Dependent Interactions

Vieri Mastropietro

arXiv:cond-mat/0507717Communications in Mathematical PhysicsNov 7, 20063 citations

The one-dimensional Fermi gas model

Jenő Sólyom

Annals of the Israel Physical SocietyJan 1, 19780 citations

Hartree-Fock approach to dynamical mass generation in the generalized ( 2+1 )-dimensional Thirring model

T. G. Khunjua, К. Г. Клименко, Roman N. Zhokhov

The ( $2+1$ )-dimensional generalized massless Thirring model with four-component Fermi fields is investigated by the Hartree-Fock method. The Lagrangian of this model is constructed from two different four-fermion structures. One of them takes into account the vector $\ifmmode\times\else\texttimes\fi{}$ vector channel of fermion interaction with coupling constant ${G}_{v}$ , the other, the scalar $\ifmmode\times\else\texttimes\fi{}$ scalar channel with coupling ${G}_{s}$ . At some relation between bare couplings ${G}_{s}$ and ${G}_{v}$ , the Hartree-Fock equation for self-energy of fermions can be renormalized, and dynamical generation of the Dirac and Haldane fermion masses is possible. As a result, a phase portrait of the model consists of two nontrivial phases. In the first one the chiral symmetry is spontaneously broken due to dynamical appearance of the Dirac mass term, while in the second phase a spontaneous breaking of the spatial parity $\mathcal{P}$ is induced by a Haldane mass term. It is shown that in the particular case of a pure Thirring model, i.e., at ${G}_{s}=0$ , the ground state of the system is indeed a mixture of these phases. Moreover, it was found that dynamical generation of fermion masses is possible for any finite number of Fermi fields.The ($2+1$)-dimensional generalized massless Thirring model with four-component Fermi fields is investigated by the Hartree-Fock method. The Lagrangian of this model is constructed from two different four-fermion structures. One of them takes into account the vector $\ifmmode\times\else\texttimes\fi{}$ vector channel of fermion interaction with coupling constant ${G}_{v}$, the other, the scalar $\ifmmode\times\else\texttimes\fi{}$ scalar channel with coupling ${G}_{s}$. At some relation between bare couplings ${G}_{s}$ and ${G}_{v}$, the Hartree-Fock equation for self-energy of fermions can be renormalized, and dynamical generation of the Dirac and Haldane fermion masses is possible. As a result, a phase portrait of the model consists of two nontrivial phases. In the first one the chiral symmetry is spontaneously broken due to dynamical appearance of the Dirac mass term, while in the second phase a spontaneous breaking of the spatial parity $\mathcal{P}$ is induced by a Haldane mass term. It is shown that in the particular case of a pure Thirring model, i.e., at ${G}_{s}=0$, the ground state of the system is indeed a mixture of these phases. Moreover, it was found that dynamical generation of fermion masses is possible for any finite number of Fermi fields.

arXiv:2208.11735Physical review. D/Physical review. D.Oct 10, 20223 citations

Fermi surface symmetric mass generation: a quantum Monte-Carlo study

Wei-Xuan Chang, Sibo Guo, Yi‐Zhuang You +1 more

The symmetric mass generation (SMG) phase is an insulator in which a single-particle gap is intrinsically opened by the interaction, without involving symmetry spontaneously breaking or topological order. Here, we perform unbiased quantum Monte-Carlo simulation and systematically investigate a bilayer fermionic model hosting Fermi surface SMG in the strongly interacting regime. With increasing interaction strength, the model undergoes a quantum phase transition from an exciton insulator to an SMG phase, belonging to the (2+1)-dimensional O(4) universality class. We access the spectral properties of the SMG phase, resembling a Mott insulating phase with relatively flat dispersion and pronounced spectral broadening. The dispersion of Green's function zeros is extracted from spectral function, featuring a surface at zero frequency precisely located at the original non-interacting Fermi surface, which constitutes a hallmark of the Fermi surface SMG phase. The bilayer model we study is potentially relevant to the newly discovered high- $T_c$ superconductor $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$ . Our results in SMG phase qualitatively capture the salient features of spectral function unveiled in recent ARPES experiments, shedding new insight on the underlying physics of $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$ .The symmetric mass generation (SMG) phase is an insulator in which a single-particle gap is intrinsically opened by the interaction, without involving symmetry spontaneously breaking or topological order. Here, we perform unbiased quantum Monte-Carlo simulation and systematically investigate a bilayer fermionic model hosting Fermi surface SMG in the strongly interacting regime. With increasing interaction strength, the model undergoes a quantum phase transition from an exciton insulator to an SMG phase, belonging to the (2+1)-dimensional O(4) universality class. We access the spectral properties of the SMG phase, resembling a Mott insulating phase with relatively flat dispersion and pronounced spectral broadening. The dispersion of Green's function zeros is extracted from spectral function, featuring a surface at zero frequency precisely located at the original non-interacting Fermi surface, which constitutes a hallmark of the Fermi surface SMG phase. The bilayer model we study is potentially relevant to the newly discovered high-$T_c$ superconductor $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$. Our results in SMG phase qualitatively capture the salient features of spectral function unveiled in recent ARPES experiments, shedding new insight on the underlying physics of $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$.

arXiv:2311.09970Nov 16, 20231 citation

The one-dimensional Fermi gas

Hanoch Gutfreund

Annals of the Israel Physical SocietyJan 1, 19780 citations

(1+1)

-dimensional

[(1+1)\mathrm{D}]

and

(2+1)

-dimensional FL systems when several FSs together cancel the FS 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 nonperturbative interaction mechanism is the only way to gap out the FSs. This symmetric FS reconstruction is in contrast to the conventional symmetry-breaking gapping mechanism in the FL. As a side product, our model provides a pristine one-dimensional lattice regularization for the

(1+1)\mathrm{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 (

2+1

)-dimensional generalized massless Thirring model with four-component Fermi fields is investigated by the Hartree-Fock method. The Lagrangian of this model is constructed from two different four-fermion structures. One of them takes into account the vector $\ifmmode\times\else\texttimes\fi{}$ vector channel of fermion interaction with coupling constant

{G}_{v}

, the other, the scalar $\ifmmode\times\else\texttimes\fi{}$ scalar channel with coupling

{G}_{s}

. At some relation between bare couplings

{G}_{s}

and

{G}_{v}

, the Hartree-Fock equation for self-energy of fermions can be renormalized, and dynamical generation of the Dirac and Haldane fermion masses is possible. As a result, a phase portrait of the model consists of two nontrivial phases. In the first one the chiral symmetry is spontaneously broken due to dynamical appearance of the Dirac mass term, while in the second phase a spontaneous breaking of the spatial parity

\mathcal{P}

is induced by a Haldane mass term. It is shown that in the particular case of a pure Thirring model, i.e., at

{G}_{s}=0

, the ground state of the system is indeed a mixture of these phases. Moreover, it was found that dynamical generation of fermion masses is possible for any finite number of Fermi fields.

T_c

superconductor

\rm{La}_3 \rm{Ni}_2 \rm{O}_7

. Our results in SMG phase qualitatively capture the salient features of spectral function unveiled in recent ARPES experiments, shedding new insight on the underlying physics of

\rm{La}_3 \rm{Ni}_2 \rm{O}_7