Quantum criticality in the two-dimensional Hubbard model
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arXiv
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| Format: | Preprint |
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2026
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| author | Pelz, Mathias Kotliar, Gabriel von Delft, Jan Gleis, Andreas |
| author_facet | Pelz, Mathias Kotliar, Gabriel von Delft, Jan Gleis, Andreas |
| contents | We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, $U=7t$ and $t'=-0.3t$, we find a critical doping $p^{\ast}$ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and $d_{x^2-y^2}$-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at $p^{\ast}$. As $p^{\ast}$ is crossed from the normal Fermi liquid at $p>p^{\ast}$ into the pseudogap metal at $p<p^{\ast}$, the coherent low-energy spectral weight in the antinodal region is lost and replaced by a narrow, metallic pseudogap, while the nodal region evolves smoothly and remains comparatively coherent. This gives rise to Fermi arcs in the pseudogap metal at $p<p^{\ast}$, since the zero-frequency spectral weight remains large in the nodal region but is strongly suppressed in the antinodal region. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum criticality in the two-dimensional Hubbard model Pelz, Mathias Kotliar, Gabriel von Delft, Jan Gleis, Andreas Strongly Correlated Electrons We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, $U=7t$ and $t'=-0.3t$, we find a critical doping $p^{\ast}$ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and $d_{x^2-y^2}$-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at $p^{\ast}$. As $p^{\ast}$ is crossed from the normal Fermi liquid at $p>p^{\ast}$ into the pseudogap metal at $p<p^{\ast}$, the coherent low-energy spectral weight in the antinodal region is lost and replaced by a narrow, metallic pseudogap, while the nodal region evolves smoothly and remains comparatively coherent. This gives rise to Fermi arcs in the pseudogap metal at $p<p^{\ast}$, since the zero-frequency spectral weight remains large in the nodal region but is strongly suppressed in the antinodal region. |
| title | Quantum criticality in the two-dimensional Hubbard model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.15059 |