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arXiv:2307.12223 · Physical review. B./Physical review. B

Green's function zeros in Fermi surface symmetric mass generation

Da-Chuan Lu, Meng Zeng, Yi‐Zhuang You

Published Nov 13, 2023• 6 citations
arXivHTMLPDF

Abstract

The Fermi surface symmetric mass generation (SMG) is an intrinsically interaction-driven mechanism that opens an excitation gap on the Fermi surface without invoking symmetry-breaking or topological order. We explore this phenomenon within a bilayer square lattice model of spin-1/2 fermions, where the system can be tuned from a metallic Fermi liquid phase to a strongly interacting SMG insulator phase by an interlayer spin-spin interaction. The SMG insulator preserves all symmetries and has no mean-field interpretation at the single-particle level. It is characterized by zeros in the fermion Green's function, which encapsulate the same Fermi volume in momentum space as the original Fermi surface, a feature mandated by the Luttinger theorem. Utilizing both numerical and field-theoretical methods, we provide compelling evidence for these Green's function zeros across both strong and weak coupling regimes of the SMG phase. Our findings highlight the robustness of the zero Fermi surface, which offers promising avenues for experimental identification of SMG insulators through spectroscopy experiments despite potential spectral broadening from noise or dissipation.

DOI
10.1103/physrevb.108.205117

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The Fermi surface symmetric mass generation (SMG) is an intrinsically interaction-driven mechanism that opens an excitation gap on the Fermi surface without invoking symmetry-breaking or topological order. We explore this phenomenon within a bilayer square lattice model of spin-1/2 fermions, where the system can be tuned from a metallic Fermi liquid phase to a strongly interacting SMG insulator phase by an interlayer spin-spin interaction. The SMG insulator preserves all symmetries and has no mean-field interpretation at the single-particle level. It is characterized by zeros in the fermion Green's function, which encapsulate the same Fermi volume in momentum space as the original Fermi surface, a feature mandated by the Luttinger theorem. Utilizing both numerical and field-theoretical methods, we provide compelling evidence for these Green's function zeros across both strong and weak coupling regimes of the SMG phase. Our findings highlight the robustness of the zero Fermi surface, which offers promising avenues for experimental identification of SMG insulators through spectroscopy experiments despite potential spectral broadening from noise or dissipation.
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-TcT_cTc​ superconductor La3Ni2O7\rm{La}_3 \rm{Ni}_2 \rm{O}_7La3​Ni2​O7​. 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 La3Ni2O7\rm{La}_3 \rm{Ni}_2 \rm{O}_7La3​Ni2​O7​.
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)(1+1)(1+1)-dimensional [(1+1)D][(1+1)\mathrm{D}][(1+1)D] and (2+1)(2+1)(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)D(1+1)\mathrm{D}(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.
Symmetric mass generation (SMG) insulators are interaction-driven, featureless Mott insulating states in quantum many-body fermionic systems. Recent advancements suggest that zeros in the fermion Green's function could lead to non-vanishing negative optical conductivity in SMG insulators, even below the charge excitation gap. This study explores the origin of this unusual behavior through the lens of pole-zero duality, highlighting a critical issue where the current operator becomes unbounded, rendering the response function unphysical. By employing a lattice model, we derive a well-behaved lattice regularization of the current operator, enabling a detailed study of optical conductivity in SMG insulators. Utilizing both analytical and numerical methods, including strong-coupling expansions, we confirm that SMG insulators exhibit no optical conductivity at low energies below the charge gap, effectively resolving the paradox. This work not only deepens our understanding of quantum many-body phenomena but also lays a robust theoretical groundwork for future experimental explorations of SMG materials.
It is known that, under short-range interactions many topological superconductors (TSC) and topological insulators (TI) are trivialized, which means the boundary state of the system can be trivially gapped out by interaction without leading to symmetry breaking or topological ground state degeneracy. This phenomenon is also referred to as "symmetric mass generation" (SMG), and has attracted broad attentions from both the condensed matter and high energy physics communities. However, after the trivialization caused by interaction, some trace of the nontrivial topology of the system still persists. Previous studies have indicated that interacting topological TSC and TI could be related to the "zero" of Green's function, namely the fermion Green's function G(iω→0)=0G(\mathrm{i} ω\rightarrow 0) = 0G(iω→0)=0. In this work, through the general "decorated defect" construction of symmetry protected topological (SPT) states, we demonstrate the existence of Green's function zero after SMG, by mapping the evaluation of the Green's function to the problem of a single particle path integral. This method can be extended to the cases without spatial translation symmetry, where the momentum space which hosts many quantized topological numbers is no longer meaningful. Using the same method one can demonstrate the existence of the Green's function zero at the "avoided topological transition" in the bulk of the system.
Abstract Symmetric mass generation (SMG) transitions defy the conventional Landau–Ginzburg–Wilson paradigm by opening a many-body gap without spontaneous symmetry breaking or topological order, attracting intense interest across particle physics and condensed matter physics. Here, we utilize unbiased quantum Monte Carlo simulations to investigate the equilibrium and nonequilibrium critical dynamics of the SMG transition in a bilayer honeycomb lattice model. We unambiguously confirm the existence of an SMG transition at J c = 2.584(4) that separates the Dirac semimetal phase from a symmetry-preserving SMG phase. High-precision extraction of the critical exponents reveals a novel universality class that profoundly departs from mean-field theory. We then extend our study to the nonequilibrium regime, exploring the driven dynamics of the SMG transition. Notably, despite the breakdown of the prerequisites for the celebrated Kibble–Zurek mechanism, the nonequilibrium SMG transition still follows the generalized finite-time scaling. By bridging equilibrium criticality and nonequilibrium dynamics, our work uncovers the universal critical properties of SMG transitions, providing a solid theoretical basis for future experimental studies of SMG physics.
Understanding unconventional superconductivity (SC) driven by strong electronic correlations is a central challenge in condensed matter physics. In this work, we employ sign-problem-free quantum Monte Carlo (QMC) simulations to systematically investigate a bilayer fermionic model featuring strong interlayer antiferromagnetic (AFM) exchange and on-site repulsive Hubbard interactions. This system serves as a prototypical model for realizing a symmetric mass generation (SMG) insulator. Our numerically exact results unambiguously demonstrate that robust superconducting pairing emerges upon doping the SMG phase. Remarkably, we find that the SC order is significantly enhanced by the repulsive Hubbard interaction. Given its potential relevance to the essential features of the high-TcT_cTc​ superconductor La3Ni2O7\mathrm{La}_{3}\mathrm{Ni}_{2}\mathrm{O}_{7}La3​Ni2​O7​ under pressure, our study establishes a new paradigm for superconductivity arising from a doped SMG parent state and provides key theoretical guidance for future experimental investigations.