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arXiv:2112.02881

Timescale of local moment screening across and above the Mott transition

Léo Gaspard, Jan M. Tomczak

Published Dec 6, 2021• 6 citations
arXivHTMLPDF

Abstract

A material's phase diagram typically indicates the types of realized long-range orders, corresponding to instabilities in static response functions. In correlated systems, however, key phenomena crucially depend on dynamical processes, too: In a Mott insulator, the electrons' spin moment fluctuates in time, while it is dynamically screened in Kondo systems. Here, we introduce a timescale $t_m$ characteristic for the screening of the local spin moment and demonstrate that it fully characterizes the dynamical mean-field phase diagram of the Hubbard model: The retarded magnetic response delineates the Mott transition and provides a new perspective on its signatures in the supercritical region above. We show that $t_m$ has knowledge of the Widom line and that it can be used to demarcate the Fermi liquid from the bad metal regime. Additionally, it reveals new structures inside the Fermi liquid phase: First, we identify a region with preformed local moments that we suggest to have a thermodynamic signature. Second, approaching the Mott transition from weak coupling, we discover a regime in which the spin dynamics becomes adiabatic, in the sense that it is much slower than valence fluctuations. Our findings provide resolution limits for magnetic measurements and may build a bridge to the relaxation dynamics of non-equilibrium states.

DOI
10.48550/arxiv.2112.02881

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A material's phase diagram typically indicates the types of realized long-range orders, corresponding to instabilities in static response functions. In correlated systems, however, key phenomena crucially depend on dynamical processes, too: In a Mott insulator, the electrons' spin moment fluctuates in time, while it is dynamically screened in Kondo systems. Here, we introduce a timescale tmt_mtm​ characteristic for the screening of the local spin moment and demonstrate that it fully characterizes the dynamical mean-field phase diagram of the Hubbard model: The retarded magnetic response delineates the Mott transition and provides a new perspective on its signatures in the supercritical region above. We show that tmt_mtm​ has knowledge of the Widom line and that it can be used to demarcate the Fermi liquid from the bad metal regime. Additionally, it reveals new structures inside the Fermi liquid phase: First, we identify a region with preformed local moments that we suggest to have a thermodynamic signature. Second, approaching the Mott transition from weak coupling, we discover a regime in which the spin dynamics becomes adiabatic, in the sense that it is much slower than valence fluctuations. Our findings provide resolution limits for magnetic measurements and may build a bridge to the relaxation dynamics of non-equilibrium states.
At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy, and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint, and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region.
We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.
We investigate the onset of a not-decaying asymptotic behavior of temporal magnetic correlations in the Hubbard model in infinite dimensions. This long-term memory feature of dynamical spin correlations can be precisely quantified by computing the difference between the zero-frequency limit of the Kubo susceptibility and the corresponding static isothermal one. Here, we present a procedure for reliably evaluating this difference starting from imaginary time-axis data, and apply it to the testbed case of the Mott-Hubbard metal-insulator transition (MIT). At low temperatures, we find long-term memory effects in the entire Mott regime, abruptly ending at the first order MIT. This directly reflects the underlying local moment physics and the associated degeneracy in the many-electron spectrum. At higher temperatures, a more gradual onset of an infinitely-long time-decay of magnetic correlations occurs in the crossover regime, not too far from the Widom line emerging from the critical point of the MIT. Our work has relevant algorithmic implications for the analytical continuation of dynamical susceptibilities in strongly correlated regimes and offers a new perspective for unveiling fundamental properties of the many-particle spectrum of the problem under scrutiny.
Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.
Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain ttt and interchain ${t}_{\ensuremath{\perp}}$ hopping amplitudes at half filling. A fixed value of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}=\ensuremath{-}{t}_{\ensuremath{\perp}}/2$ removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime ${t}_{\ensuremath{\perp}}/t\ensuremath{\lesssim}0.3$ displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.
Strongly correlated electron systems show a rich variety of interesting physical phenomena. However, their theoretical description poses a highly non-trivial task, and even the simplest models cannot be solved exactly. In this thesis the intricate behavior of the single impurity Anderson model (SIAM) and the Hubbard model is investigated. The main emphasis is laid on two-particle Green functions of these systems. To this end, existing approximation schemes are extended to be capable of treating susceptibilities as well. The quality and range of applicability of these approximations is discussed in detail. The physical pictures behind the phenomena encountered in these systems are introduced. A prominent many-body effect is the emergence of temperature dependent low energy quasiparticles in both models. The occurrence of such excitations is a result of the dynamical screening of local magnetic moments, a characteristic feature of the Kondo effect. It is argued, that within the presented approximations, the low temperature phase of these models can usually be described as a Fermi liquid. As a counterexample, the Hubbard model is shown to exhibit pronounced non-Fermi liquid behavior in situations, where a van Hove singularity in the non-interacting density of states is found in the vicinity of the Fermi level. The magnetic properties of the Hubbard model are discussed in view of the two archetypical pictures of magnetism: local moment magnetism and itinerant Stoner-magnetism. Critical temperatures for antiferromagnetic, ferromagnetic and incommensurate phase transitions are calculated, and the influence of the lattice structure and frustration is examined. In strongly correlated metallic situations, the complicated competition between Kondo-screening and local moment magnetism can lead to a reentrant behavior of the N\'eel temperature. A direct signature of the Kondo effect in the Hubbard model is found in the dynamic magnetic susceptibility, where a localized collective mode emerges at very low temperatures. It is connected to the breakup of a singlet formed by the local moments with their Kondo-screening cloud, and consequently the excitation energy is of the order of the low energy scale T*.