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arXiv:2409.04308

Magnetic quantum criticality: The role of the Fermi surface geometry

D. R. Fus, S. Adler, M. O. Malcolms, Alexander Vock, Karsten Held, A. A. Katanin, Thomas Schäfer, A. Toschi

Published Sep 6, 2024• 0 citations
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Abstract

We investigate magnetic quantum phase-transitions in bulk correlated metals. To this end, we focus on the Hubbard model on different cubic lattices as a function of temperature and electronic density, determining the relevant regimes around its quantum magnetic transition, i.e. classical, quantum critical, and quantum disordered, as well as the corresponding (thermal/non-thermal) quantum critical exponents. Our numerical results, based on dynamical mean-field theory, together with supporting analytical derivations, rigorously demonstrate how and why the presence of different kinds of Kohn anomalies on the underlying Fermi surface (i) drives the quantum critical behavior above the quantum critical point and (ii) shapes the whole phase diagram around it. Our findings highlight the importance of an explicit inclusion of such Fermi surface geometrical properties into the universality class definition for magnetic quantum phase-transitions in correlated metals.

DOI
10.48550/arxiv.2409.04308

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We investigate magnetic quantum phase-transitions in bulk correlated metals. To this end, we focus on the Hubbard model on different cubic lattices as a function of temperature and electronic density, determining the relevant regimes around its quantum magnetic transition, i.e. classical, quantum critical, and quantum disordered, as well as the corresponding (thermal/non-thermal) quantum critical exponents. Our numerical results, based on dynamical mean-field theory, together with supporting analytical derivations, rigorously demonstrate how and why the presence of different kinds of Kohn anomalies on the underlying Fermi surface (i) drives the quantum critical behavior above the quantum critical point and (ii) shapes the whole phase diagram around it. Our findings highlight the importance of an explicit inclusion of such Fermi surface geometrical properties into the universality class definition for magnetic quantum phase-transitions in correlated metals.
Quantum phase transitions in strongly correlated electron materials are one of the most intriguing phenomena in condensed matter physics. In fact, the rich phase-diagrams of these systems usually allow for the presence of several quantum phase transitions. At the same time, a comprehensive theoretical description of the quantum critical properties of correlated electrons has been not fully developed yet. For one of the most fundamental model in solid state physics, the 3D Hubbard model, quantum critical behaviour appears to violate the conventional Hertz-Millis- Moriya theory. This unexpected finding has been ascribed to the presence of specific features on the Fermi surface (FS), such as Kohn points and/or lines. If this is the case, the correct description of 3D correlated metal should be already accessible by means of Dynamical Mean Field Theory (DMFT) calculations. DMFT, in fact, preserves the information about the FS geometry and correctly captures temporal fluctuations, crucial for the description of quantum criticality. The main aim of this work is to test the hypothesis that DMFT treatment is sufficient to describe the quantum critical behaviour of 3D correlated metals, without resorting to more advanced (and much heavier!) quantum many-body schemes. Our DMFT results for the hole-doped 3D-Hubbard model have allowed to determine the location of the quantum-critical point of the magnetic transition and to highlight promising trends for the associated quantum critical exponents.
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that-in contradiction to the conventional Hertz-Millis-Moriya theory-its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong.
Quantum criticality of metal-insulator transitions in correlated electron systems is shown to belong to an unconventional universality class with violation of the Ginzburg-Landau-Wilson (GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square lattices are capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transitions and with a number of numerical results beyond the mean-field level, implying that preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. It further clarifies the whole structure of singularities by a unified treatment of the bandwidth-control and filling-control transitions. Detailed analyses of the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical ``opalescence.'' The mechanism of emerging marginal quantum critical point is ascribed to a positive feedback and interplay between the preexisting gap formation present even in metals and kinetic energy gain (loss) of the metallic carrier. Analyses of crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in (V,Cr)2O3{(\mathrm{V},\mathrm{Cr})}_{2}{\mathrm{O}}_{3}(V,Cr)2​O3​ and $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{ET}$-type organic conductors provide us with evidence for the existence of the present marginal quantum criticality.
Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The third category involves a change in the volume enclosed by the Fermi surface without any symmetry breaking: one phase is a Fermi liquid (FL) with the conventional Luttinger volume, while the other phase is a `fractionalized Fermi liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a spin liquid with fractionalized excitations. It is a relatively simple matter to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL transition can also be present in single-band Hubbard-like models: this is efficiently described by the `ancilla' method, which shows that the transition is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is argued to apply to the metallic states of the hole-doped cuprates. In the clean limit, the critical properties of the quantum transitions in the three categories are distinct, but all lead to perfect metal transport in the quantum-critical regime. Impurity-induced `Harris disorder', with spatial fluctuations in the local position of the quantum critical point, is a relevant perturbation to the clean critical points. In the presence of Harris disorder, all three categories exhibit strange metal behavior, which can be described by a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.
Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder-driven semimetal to metal quantum phase transition of three-dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical and approximate field-theoretic calculations. As a result, we establish the robust existence of a non-Gaussian universality class, and also construct the relevant low-energy effective field theory that could guide the understanding of quantum critical scaling for many strange metals. Using the kernel polynomial method (KPM), we provide numerical results for the calculated dynamical exponent (zzz) and correlation length exponent ($\ensuremath{\nu}$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field-theoretical analysis.
Plenty experimental evidence indicates that quantum critical phenomena give rise to much of the rich physics observed in strongly correlated itinerant electron systems such as the high temperature superconductors. A quantum critical point of particular interest is found at the zero-temperature onset of spin-density wave order in two- dimensional metals. The appropriate low-energy theory poses an exceptionally hard problem to analytic theory, therefore the unbiased and controlled numerical approach pursued in this thesis provides important contributions on the road to comprehensive understanding. After discussing the phenomenology of quantum criticality, a sign- problem-free determinantal quantum Monte Carlo approach is introduced and an extensive toolbox of numerical methods is described in a self-contained way. By the means of large-scale computer simulations we have solved a lattice realization of the universal effective theory of interest. The finite-temperature phase diagram, showing both a quasi-long-range spin-density wave ordered phase and a d-wave superconducting dome, is discussed in its entirety. Close to the quantum phase transition we find evidence for unusual scaling of the order parameter correlations and for non-Fermi liquid behavior at isolated hot spots on the Fermi surface.