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arXiv:1707.09310 · Physical review. B./Physical review. B

Multiple crossovers and coherent states in a Mott-Peierls insulator

Óscar Nájera, Marcello Civelli, V. Dobrosavljević, Marcelo J. Rozenberg

Published Jan 9, 2018• 33 citations
arXivHTMLPDF

Abstract

We consider the dimer Hubbard model within dynamical mean-field theory to study the interplay and competition between Mott and Peierls physics. We describe the various metal-insulator transition lines of the phase diagram and the breakdown of the different solutions that occur along them. We focus on the specific issue of the debated Mott-Peierls insulator crossover and describe the systematic evolution of the electronic structure across the phase diagram. We found that at low intradimer hopping, the emerging local magnetic moments can unbind above a characteristic singlet temperature ${T}^{*}$. Upon increasing the interdimer hopping, subtle changes occur in the electronic structure. Notably, we find Hubbard bands of a mix character with coherent and incoherent excitations. We argue that this state might be relevant for materials such as ${\mathrm{VO}}_{2}$ and its signatures may be observed in spectroscopic studies, and possibly through pump-probe experiments.

DOI
10.1103/physrevb.97.045108

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We consider the dimer Hubbard model within dynamical mean-field theory to study the interplay and competition between Mott and Peierls physics. We describe the various metal-insulator transition lines of the phase diagram and the breakdown of the different solutions that occur along them. We focus on the specific issue of the debated Mott-Peierls insulator crossover and describe the systematic evolution of the electronic structure across the phase diagram. We found that at low intradimer hopping, the emerging local magnetic moments can unbind above a characteristic singlet temperature T∗{T}^{*}T∗. Upon increasing the interdimer hopping, subtle changes occur in the electronic structure. Notably, we find Hubbard bands of a mix character with coherent and incoherent excitations. We argue that this state might be relevant for materials such as VO2{\mathrm{VO}}_{2}VO2​ and its signatures may be observed in spectroscopic studies, and possibly through pump-probe experiments.
We study in detail the solution of a basic strongly correlated model,namely, the dimer Hubbard model. This model is the simplest realization ofa cluster DMFT problem.We provide a detailed description of the solutions in the ``coexistentregion'' where two (meta)stable states of the DMFT equations are found, onea metal and the other an insulator. Moreover, we describe in detail howthese states break down at their respective critical lines. We clarify thekey role played by the intra-dimer correlation, which here acts in additionto the onsite Coulomb correlations.We review the important issue of the Mott-Peierls insulator crossoverwhere we characterize a variety of physical regimes. In a subtle change inthe electronic structure the Hubbard bands evolve from purely incoherent(Mott) to purely coherent (Peierls) through a state with unexpected mixedcharacter. We find a singlet pairing temperature T* below which thelocalized electrons at each atomic site can bind into a singlet and quenchtheir entropy, this uncovers a new paradigm of a para-magnetic Mottinsulator.Finally, we discuss the relevance of our results for the interpretation ofvarious experimental studies in VO₂. We present a variety of argumentsthat allow us to advance the conclusion that the long-lived (meta-stable)metallic phase, induced in pump-probe experiments, and the thermallyactivated M₁ meta-stable metallic state in nano-domains are the same.In fact, they may all be qualitatively described by the dimerizedcorrelated metal state of our model.
We study in detail the solution of a basic strongly correlated model,namely, the dimer Hubbard model. This model is the simplest realization ofa cluster DMFT problem.We provide a detailed description of the solutions in the ``coexistentregion'' where two (meta)stable states of the DMFT equations are found, onea metal and the other an insulator. Moreover, we describe in detail howthese states break down at their respective critical lines. We clarify thekey role played by the intra-dimer correlation, which here acts in additionto the onsite Coulomb correlations.We review the important issue of the Mott-Peierls insulator crossoverwhere we characterize a variety of physical regimes. In a subtle change inthe electronic structure the Hubbard bands evolve from purely incoherent(Mott) to purely coherent (Peierls) through a state with unexpected mixedcharacter. We find a singlet pairing temperature T* below which thelocalized electrons at each atomic site can bind into a singlet and quenchtheir entropy, this uncovers a new paradigm of a para-magnetic Mottinsulator.Finally, we discuss the relevance of our results for the interpretation ofvarious experimental studies in VO₂. We present a variety of argumentsthat allow us to advance the conclusion that the long-lived (meta-stable)metallic phase, induced in pump-probe experiments, and the thermallyactivated M₁ meta-stable metallic state in nano-domains are the same.In fact, they may all be qualitatively described by the dimerizedcorrelated metal state of our model.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.
The ground-state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean-field theory. For weak to intermediate values of Coulomb repulsion UUU, the system undergoes a transition from a Mott-insulating phase to a metallic phase and then onto a band-insulating phase as the interlayer hopping is increased. In the strong-coupling case, the model exhibits a direct crossover from a Mott-insulating phase to a band-insulating phase. These results are robust with respect to the presence or absence of magnetic order.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics
Correlation-driven metal-insulator transitions and temperature-driven quantum-coherent-to-incoherent crossovers in correlated electron systems underpin the doping, temperature and frequency-resolved evolution of physical responses. Motivated by recent experimental studies that investigate the evolution of dynamical spin and charge responses, we analyze the spin and charge diffusion spectra in both half-filled and doped one-band Hubbard model using Dynamical Mean Field Theory (DMFT) combined with the Numerical Renormalization Group (NRG). We compare the relative strengths and limitations of Density Matrix NRG (DMNRG) and Full Density Matrix NRG (FDM-NRG) in capturing low-frequency spectral features and their evolution with temperature, interaction strength and band-filling. Key measures, including characteristic frequency scales, Kullback-Leibler divergence, diffusion constants, and kurtosis provide complementary but internally consistent picture for the evolution of spin and charge excitations across bandwidth as well as the band-filling driven Mott transitions and the coherent-incoherent crossover. We find that spin and charge fluctuations cross over from quantum-coherent-to-quantum-incoherent at distinct temperatures, providing a microscopic insight into the complex, two-stage, Fermi-to-non-Fermi liquid-to-bad metal crossovers seen in transport data, in particular in the dcdcdc resistivity.