arXiv subjects

Guo-Zhu Liu

Publications and source records attributed to Guo-Zhu Liu.

At least 19 recordsLinked to original sources

arXiv2026

Rapid cooling of the Cassiopeia A neutron star due to superfluid quantum criticality

The rapid cooling of the neutron star in Cassiopeia A is speculated to arise from an enhanced neutrino emission caused by the onset of $^3P_2$-wave neutron superfluidity in the core. However, the neutrino emissivity due to Cooper-pair breaking and formation is in tension with the requirements for explaining the observed cooling rate. Here, we show that such a rapid cooling can be explained once the non-Fermi liquid behavior of the non-superfluid neutron liquid induced by superfluid quantum criticality is included into the theoretical description of neutron star cooling, without assuming the existence of additional energy loss processes. Our results indicate that the neutron star in Cassiopeia A remains in the thermal relaxation stage, which is greatly prolonged by the non-Fermi liquid behavior. The good agreement between our theoretical results and recent observational cooling data points to the pivotal role played by superfluid quantum criticality in neutron stars.

astro-ph.HE↗

arXiv2026

New solution to the hyperon puzzle of neutron stars: Quantum many-body effects

The hyperon puzzle refers to the challenge of reconciling the existence of hyperons in neutron star cores and the observed high masses of neutron stars. The recent discovery of PSR J0952-0607 ($2.35\pm0.17 M_{\odot}$) has intensified this challenge. Existing solutions fail to achieve such a high mass, and often predict unrealistically fast cooling that is at odds with observations. Here, we propose a novel solution to the hyperon puzzle. Using the Dyson-Schwinger equation approach, we incorporate the quantum many-body effects caused by strong baryon-meson interactions into the equation of state for cold baryonic matter and find it stiff enough to support a maximum hyperon-star mass of $M_{\mathrm{max}} \approx 2.59 M_{\odot}$, which can explain all the observed high neutron-star masses. The resulting proton and hyperon fractions are remarkably low, thus the nucleonic and hyperonic direct Urca processes are significantly suppressed. As a result, fast cooling typically does not occur in ordinary neutron stars.

nucl-th↗

arXiv2025

Superconductivity near an Ising nematic quantum critical point in two dimensions

Near a two-dimensional Ising-type nematic quantum critical point, the quantum fluctuations of the nematic order parameter are coupled to the electrons, leading to non-Fermi liquid behavior and unconventional superconductivity. The interplay between these two effects has been extensively studied through the Eliashberg equations for the superconducting gap. However, previous studies often rely on various approximations that may introduce uncertainties in the results. Here, we re-visit the issue of how the superconducting transition temperature $T_{c}$ is affected by removing certain common approximations. We numerically solve the self-consistent Dyson-Schwinger equations of the electron propagator $G(p)$, the nematic propagator $D(q)$, and the vertex function $Γ_{\mathrm{v}}^{\mathrm{1L}}(p+q,p)$ expanded up to the triangle order, without introducing further approximations. Our calculations reveal that the extended $s$-wave superconducting gap is the only convergent solution to the nonlinear gap equations. We investigate the evolution of $T_{c}$ as the system approaches the nematic quantum critical point from the disordered (tetragonal) phase. Under the bare vertex approximation, $T_{c}$ is monotonically enhanced. However, when vertex corrections are incorporated, $T_{c}$ initially increases but then decreases, with the maximum value of $T_{c}$ occurring at a point away from the quantum critical point. The obtained gap symmetry and the non-monotonic behavior of $T_{c}$ are compared with recent experiments on doped FeSe materials.

cond-mat.supr-con↗

arXiv2025

Superfluid quantum criticality and the thermal evolution of neutron stars

The neutron star starts to cool down shortly after its birth by emitting neutrinos. As it becomes cold enough, the Cooper pairs of neutrons are formed, triggering a superfluid transition. Previous studies on neutron superfluidity focused on finite-temperature transitions, with little attention paid to the potentially important quantum critical phenomena associated with superfluidity. Here, we provide the first theoretical analysis of superfluid quantum criticality, concentrating on its impact on neutron star cooling. Extensive calculations found that superfluidity occurs within a finite range of neutron star density $ρ$. The density serves as a nonthermal parameter for a superfluid quantum phase transition. In a broad quantum critical region, gapless neutrons are strongly coupled to the quantum critical fluctuations of the superfluid order parameter. We handle this coupling using both perturbation theory and renormalization group methods and find that it leads to non-Fermi liquid behavior, which yields a logarithmic $T\ln(1/T)$ correction to the neutron specific heat $c_{\mathrm{n}}\propto T$ and also dramatically alters the neutrino emissivity. Quantum critical phenomena emerge much earlier than the onset of superfluidity and persist throughout almost the entire lifetime of a neutron star. At low temperatures, these phenomena coexist with superfluidity in the neutron star interior but occupy different layers. We incorporate superfluid quantum criticality into the theoretical description of neutron star cooling and show that it substantially prolongs the thermal relaxation time. By varying the strength of superfluid fluctuations and other quantities, we obtain an excellent fit to the observed cooling data of a number of neutron stars. Our results indicate an intriguing correlation between superfluid quantum criticality and the thermal evolution of neutron stars.

nucl-th↗

arXiv2024

Nonperturbative study of quantum many-body correlation effects in neutron stars: Equation of state

Although neutron stars have been studied for decades, their internal structure remains enigmatic, mainly due to large uncertainties in the equation of state. In neutron stars, the nucleons are strongly interacting by exchanging mesons, which can lead to significant quantum many-body correlation effects. Mean-field calculations failed to capture these effects. Here, we develop a nonperturbative quantum field-theoretic approach to handle strongly correlated dense nuclear matter within the framework of quantum hadrodynamics. We show that the many-body effects can be incorporated in the Dyson-Schwinger equation of the nucleon propagator. Based on a linear $σ$-$ω$-$ρ$ model, we successfully reproduce six empirical observable quantities of saturation nuclear matter by tuning six parameters. After including the many-body effects into the equation of state of realistic neutron star matter, we obtain a mass-radius relation that is comparable with recent astrophysical observations of neutron stars.

nucl-th↗

arXiv2024

Reply to "Comment on `Towards exact solutions of superconducting $T_c$ induced by electron-phonon interaction' "

In a series of papers, we have proposed a non-perturbative field-theoretic approach to deal with strong electron-phonon and strong Coulomb interactions. The key ingredient of such an approach is to determine the full fermion-boson vertex corrections by solving a number of self-consistent Ward-Takahashi identities. Palle (see Phys. Rev. B 110, 026501 (2024), arXiv:2404.02918) argued that our Ward-Takahashi identities failed to include some important additional terms and thus are incorrect. We agree that our Ward-Takahashi identities have ignored some potentially important contributions and here give some remarks on the role played by the additional terms.

cond-mat.supr-con↗

arXiv2023

Theoretical study of phonon-mediated superconductivity beyond Migdal-Eliashberg approximation and Coulomb pseudopotential

In previous theoretical studies of phonon-mediated superconductors, the electron-phonon coupling is treated by solving the Migdal-Eliashberg equations under the bare vertex approximation, whereas the effect of Coulomb repulsion is incorporated by introducing one single pseudopotential parameter. These two approximations become unreliable in low carrier-density superconductors in which the vertex corrections are not small and the Coulomb interaction is poorly screened. Here, we shall go beyond these two approximations and employ the Dyson-Schwinger equation approach to handle the interplay of electron-phonon interaction and Coulomb interaction in a self-consistent way. We first derive the exact Dyson-Schwinger integral equation of the full electron propagator. Such an equation contains several unknown single-particle propagators and fermion-boson vertex functions, and thus seems to be intractable. To solve this difficulty, we further derive a number of identities satisfied by all the relevant propagators and vertex functions and then use these identities to show that the exact Dyson-Schwinger equation of electron propagator is actually self-closed. This self-closed equation takes into account not only all the vertex corrections, but also the mutual influence between electron-phonon interaction and Coulomb interaction. Solving it by using proper numerical methods leads to the superconducting temperature $T_{c}$ and other quantities. As an application of the approach, we compute the $T_{c}$ of the interfacial superconductivity realized in the one-unit-cell FeSe/SrTiO$_{3}$ system. We find that $T_{c}$ can be strongly influenced by the vertex corrections and the competition between phonon-mediated attraction and Coulomb repulsion.

cond-mat.supr-con↗

arXiv2023

Pion-mediated Cooper pairing of neutrons: beyond the bare vertex approximation

In some quantum many particle systems, the fermions could form Cooper pairs by exchanging intermediate bosons. This then drives a superconducting phase transition or a superfluid transition. Such transitions should be theoretically investigated by using proper non-perturbative methods. Here we take the neutron superfluid transition as an example and study the Cooper pairing of neutrons mediated by neutral $π$-mesons in the low density region of a neutron matter. We perform a non-perturbative analysis of the neutron-meson coupling and compute the pairing gap $Δ$, the critical density $ρ_{c}$, and the critical temperature $T_c$ by solving the Dyson-Schwinger equation of the neutron propagator. We first carry out calculations under the widely used bare vertex approximation and then incorporate the contribution of the lowest-order vertex correction. This vertex correction is not negligible even at low densities and its importance is further enhanced as the density increases. The transition critical line on density-temperature plane obtained under the bare vertex approximation is substantially changed after including the vertex correction. These results indicate that the vertex corrections play a significant role and need to be seriously taken into account.

nucl-th↗

arXiv2022

A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene

In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the Dyson-Schwinger equation of the full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized velocity of Dirac fermions and show that its energy (momentum) dependence is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.

cond-mat.str-el↗

arXiv2022

Fermion dispersion renormalization in a two-dimensional semi-Dirac semimetal

We present a non-perturbative study of the quantum many-body effects caused by the long-range Coulomb interaction in a two-dimensional semi-Dirac semimetal. This kind of semimetal may be realized in deformed graphene and a class of other realistic materials. In the non-interacting limit, the dispersion of semi-Dirac fermion is linear in one direction and quadratic in the other direction. When the impact of Coulomb interaction is taken into account, such a dispersion can be significantly modified. To reveal the correlation effects, we first obtain the exact self-consistent Dyson-Schwinger equation of the full fermion propagator and then extract the momentum dependence of the renormalized fermion dispersion from the numerical solutions. Our results show that the fermion dispersion becomes linear in two directions. These results are compared to previous theoretical works on semi-Dirac semimetals.

cond-mat.str-el↗

arXiv2021

Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems

Studying the strong correlation effects in interacting Dirac fermion systems is one of the most challenging problems in modern condensed matter physics. The long-range Coulomb interaction and the fermion-phonon interaction can lead to a variety of intriguing properties. In the strong-coupling regime, weak-coupling perturbation theory breaks down. The validity of $1/N$ expansion with $N$ being the fermion flavor is also in doubt since $N$ equals to $2$ or $4$ in realistic systems. Here, we investigate the interaction between (1+2)- and (1+3)-dimensional massless Dirac fermions and a generic scalar boson, and develop an efficient non-perturbative approach to access the strong-coupling regime. We first derive a number of self-consistently coupled Ward-Takahashi identities based on a careful symmetry analysis and then use these identities to show that the full fermion-boson vertex function is solely determined by the full fermion propagator. Making use of this result, we rigorously prove that the full fermion propagator satisfies an exact and self-closed Dyson-Schwinger integral equation, which can be solved by employing numerical methods. A major advantage of our non-perturbative approach is that there is no need to employ any small expansion parameter. Our approach provides a unified theoretical framework for studying strong Coulomb and fermion-phonon interactions. It may also be used to approximately handle the Yukawa coupling between fermions and order-parameter fluctuations around continuous quantum critical points. Our approach is applied to treat the Coulomb interaction in undoped graphene. We find that the renormalized fermion velocity exhibits a logarithmic momentum-dependence but is nearly energy independent, and that no excitonic gap is generated by the Coulomb interaction. These theoretical results are consistent with experiments in graphene.

cond-mat.str-el↗

arXiv2021

Towards exact solutions for the superconducting $T_c$ induced by electron-phonon interaction

Electron-phonon interaction plays an important role in metals and can lead to superconductivity and other instabilities. Previous theoretical studies on superconductivity are largely based on the Migdal-Eliashberg theory, which neglects all the vertex corrections to electron-phonon coupling and breaks down in many unconventional superconductors. Here, we go beyond the Migdal-Eliashberg approximation and develop a nonperturbative Dyson-Schwinger equation approach to deal with the superconducting transition. Remarkably, we take into account all the vertex corrections by solving two coupled Ward-Takahashi identities derived from two global U(1) symmetries and rigorously prove that the fully renormalized electron propagator satisfies a self-closed integral equation that is directly amenable to numerical computations. Our approach works equally well in the weak and strong coupling regimes and provides an efficient method to determine superconducting $T_c$ and other quantities. As an application, our approach is used to investigate the high-$T_c$ superconductivity in one-unit-cell FeSe/SrTiO$_3$.

cond-mat.supr-con↗

arXiv2019

Quantum Criticality of Excitonic Insulating Transition in Nodal Line Semimetal ZrSiS

Pezzini et al. reported an unconventional mass enhancement in topological nodal line semimetal ZrSiS (Nat. Phys. 14, 178 (2018), whose origin remains puzzling. In this material, strong short-range interactions might induce excitonic particle-hole pairs. Here we study the renormalization of fermion velocities and find that the mass enhancement in ZrSiS can be well understood if we suppose that ZrSiS is close to the quantum critical point between semimetal and excitonic insulator. Near this quantum critical point, the fermion velocities are considerably reduced by excitonic quantum fluctuation, leading to fermion mass enhancement. The quasiparticle residue is suppressed as the energy decreases but is finite at zero energy. This indicates that ZrSiS is a strongly correlated Fermi liquid, and explains why the mass enhancement is weaker than non-Fermi liquids. Our results suggest that ZrSiS is a rare example of 3D topological semimetal exhibiting unusual quantum criticality.

cond-mat.str-el↗

arXiv2019

Absence of emergent supersymmetry at superconducting quantum critical points in Dirac and Weyl semimetals

Supersymmetry plays a crucial role in superstring theory and high-energy physics, but has never been observed in experiments. Recently, an effective space-time supersymmetry was argued to emerge in the low-energy region by tuning Dirac or Weyl semimetal to approach a superconducting quantum critical point, at which the Dirac or Weyl fermion and the bosonic order parameter are both massless. Here, we study under what circumstances can space-time supersymmetry be realized at a quantum critical point. We demonstrate that the Yukawa-type coupling between the massless fermion and massless boson can dynamically generate an infinite number of non-supersymmetric terms in the effective field theory of the boson. Owing to these terms, no space-time supersymmetry emerges at the superconducting quantum critical points. The results provide important constraint on the exploration of emergent space-time supersymmetry in condensed matter systems.

cond-mat.str-el↗

arXiv2019

Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point

Two-dimensional Dirac fermions are subjected to two types of interactions, namely the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $α$ is larger than some critical value $α_c$, whereas the latter drives an antiferromagnetic Mott transition when its strength $U$ exceeds a threshold $U_c$. Here, we study the impacts of the interplay of these two interactions on excitonic pairing with the Dyson-Schwinger equation approach. We find that the critical value $α_c$ is increased by weak short-range interaction. As $U$ increases to approach $U_c$, the quantum fluctuation of antiferromagnetic order parameter becomes important and interacts with the Dirac fermions via the Yukawa coupling. After treating the Coulomb interaction and Yukawa coupling interaction on an equal footing, we show that $α_c$ is substantially increased as $U \rightarrow U_c$. Thus, the excitonic pairing is strongly suppressed near the antiferromagnetic quantum critical point. We obtain a global phase diagram on the $U$-$α$ plane, and illustrate that the excitonic insulating and antiferromagnetic phases are separated by an intermediate semimetal phase. These results provide a possible explanation of the discrepancy between recent theoretical progress on excitonic gap generation and existing experiments in suspended graphene.

cond-mat.str-el↗

arXiv2019

Fate of superconductivity in disordered Dirac and semi-Dirac semimetals

The influence of weak disorder on the superconductivity in ordinary metals can be formally described by the Abrikosov-Gorkov diagrammatic approach. The vertex correction is ignored in this approach because an inequality $k_F l \gg 1$, where $k_F$ is the Fermi momentum and $l$ mean free path, is satisfied in ordinary metals with a large Fermi surface. In a Dirac semimetal that has discrete Fermi points, this inequality may break down even for arbitrarily weak disorder since $k_F \rightarrow 0$, and thus the vertex correction could be important. We incorporate the vertex correction into the self-consistent equations of the superconducting gap and the disorder scattering rate, and then apply the generalized approach to study how $s$-wave superconductivity is affected by random chemical potential in two- and three-dimensional Dirac semimetals, as well as two-dimensional semi-Dirac semimetal. In the clean limit, superconductivity is formed only when the pairing interaction strength is greater than some critical value in these materials. Adding random chemical potential to the system promotes superconductivity by generating a finite fermionic density of states at the Fermi level. In three-dimensional Dirac semimetal, the critical attraction strength is reduced by weak disorder, but remains finite. In the other two cases, superconductivity is induced by arbitrarily weak attraction. Including the vertex correction does not change these qualitative results, and actually could further promote superconductivity in the weak-attraction regime. Bilayer graphene is quite special in that its zero-energy density of states is nonzero despite the existence of Fermi points. Due to this peculiar property, superconductivity is always slightly suppressed by random chemical potential, and the impact of vertex correction is nearly negligible.

cond-mat.supr-con↗

arXiv2019

Topological quantum critical point in a triple-Weyl semimetal: non-Fermi-liquid behaviors and instabilities

We study the quantum critical phenomena emerging at the transition from triple-Weyl semimetal to band insulator, which is a topological phase transition described by the change of topological invariant. The critical point realizes a new type of semimetal state in which the fermion dispersion is cubic along two directions and quadratic along the third. Our renormalization group analysis reveals that, the Coulomb interaction is marginal at low energies and even arbitrarily weak Coulomb interaction suffices to induce an infrared fixed point. We compute a number of observable quantities, and show that they all exhibit non-Fermi liquid behaviors at the fixed point. When the interplay between the Coulomb and short-range four-fermion interactions is considered, the system becomes unstable below a finite energy scale. The system undergoes a first-order topological transition when the fermion flavor $N$ is small, and enters into a nematic phase if $N$ is large enough. Non-Fermi liquid behaviors are hidden by the instability at low temperatures, but can still be observed at higher temperatures. Experimental detection of the predicted phenomena is discussed.

cond-mat.str-el↗

arXiv2018

Effects of the Dirac cone tilt in two-dimensional Dirac semimetal

Two-dimensional Dirac semimetal with tilted Dirac cone has recently attracted increasing interest. Tilt of Dirac cone can be realized in a number of materials, including deformed graphene, surface state of topological crystalline insulator, and certain organic compound. We study how Dirac cone tilting affects the low-energy properties by presenting a renormalization group analysis of the Coulomb interaction and quenched disorder. Random scalar potential or random vector potential along the tilting direction cannot exist on its own as it always dynamically generates a new type of disorder, which dominates at low energies and turns the system into a compressible diffusive metal. Consequently, the fermions acquire a finite disorder scattering rate. Moreover, the isolated band-touching point is replaced by a bulk Fermi arc in the Brillouin zone. These results are not qualitatively changed when the Coulomb interaction is incorporated. In comparison, random mass and random vector potential along the non-tilting direction can exist individually, without generating other types of disorder. They both suppress tilt at low energies, and do not produce bulk Fermi arc. Upon taking the Coulomb interaction into account, the system enters into a stable quantum critical state, in which the fermion field acquires a finite anomalous dimension but the dynamical exponent $z=1$. These results indicate that Dirac cone tilt does lead to some qualitatively different low-energy properties comparing to the untilted system.

cond-mat.str-el↗