Non-Perturbative Renormalization Group for Ising-Nematic Criticality: A Closed-Form Nonlocal Ansatz
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913172066140160 |
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| author | Kim, Hyeon Jung Kim, Kyoung-Min Kim, Ki-Seok |
| author_facet | Kim, Hyeon Jung Kim, Kyoung-Min Kim, Ki-Seok |
| contents | The two-dimensional metallic quantum critical problem is a long-standing puzzle that is widely believed to hold the key to resolving ubiquitous non-Fermi liquid behavior in strongly correlated electronic systems. In this study, we present a non-perturbative renormalization group (RG) analysis of the metallic Ising-nematic quantum critical point in two dimensions, formulated directly around an intrinsically nonlocal infrared (IR) boson propagator. Rather than treating the anomalous dynamical critical exponent $a$ as a fixed phenomenological parameter, we regard it as an intrinsic component of the fixed-point data to be determined from the internal consistency of the low-energy patch field theory under highly anisotropic scaling dimensions ($[k_0]=a+1$, $[k_x]=2$, $[k_y]=1$). While the leading two-loop diagrammatics vanish identically due to kinematic pole configurations, our three-loop evaluation reveals a profound structural asymmetry between the sectors: the fermion self-energy and Yukawa vertex receive non-vanishing logarithmic corrections, whereas the corresponding bosonic counter-term remains strictly zero. Consequently, we find that no self-consistent, intersecting fixed-point solution for the exponent $a$ exists within the three-loop truncation, failing to reproduce the physical value of $a \approx 1.85$ observed in quantum Monte Carlo simulations. We conjecture that the cross-linked topology of the four-loop boson self-energy diagrams is exactly marginal and yields the minimal, mandatory bosonic counter-term required to restore multi-sector self-consistency. Our framework establishes a rigid multi-loop matching scheme necessary to uniquely pin down the critical exponent, and uncovers a stable phase space for field anomalous dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Perturbative Renormalization Group for Ising-Nematic Criticality: A Closed-Form Nonlocal Ansatz Kim, Hyeon Jung Kim, Kyoung-Min Kim, Ki-Seok Strongly Correlated Electrons The two-dimensional metallic quantum critical problem is a long-standing puzzle that is widely believed to hold the key to resolving ubiquitous non-Fermi liquid behavior in strongly correlated electronic systems. In this study, we present a non-perturbative renormalization group (RG) analysis of the metallic Ising-nematic quantum critical point in two dimensions, formulated directly around an intrinsically nonlocal infrared (IR) boson propagator. Rather than treating the anomalous dynamical critical exponent $a$ as a fixed phenomenological parameter, we regard it as an intrinsic component of the fixed-point data to be determined from the internal consistency of the low-energy patch field theory under highly anisotropic scaling dimensions ($[k_0]=a+1$, $[k_x]=2$, $[k_y]=1$). While the leading two-loop diagrammatics vanish identically due to kinematic pole configurations, our three-loop evaluation reveals a profound structural asymmetry between the sectors: the fermion self-energy and Yukawa vertex receive non-vanishing logarithmic corrections, whereas the corresponding bosonic counter-term remains strictly zero. Consequently, we find that no self-consistent, intersecting fixed-point solution for the exponent $a$ exists within the three-loop truncation, failing to reproduce the physical value of $a \approx 1.85$ observed in quantum Monte Carlo simulations. We conjecture that the cross-linked topology of the four-loop boson self-energy diagrams is exactly marginal and yields the minimal, mandatory bosonic counter-term required to restore multi-sector self-consistency. Our framework establishes a rigid multi-loop matching scheme necessary to uniquely pin down the critical exponent, and uncovers a stable phase space for field anomalous dimensions. |
| title | Non-Perturbative Renormalization Group for Ising-Nematic Criticality: A Closed-Form Nonlocal Ansatz |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.30715 |