Finite-temperature numerical renormalization group study of the Mott transition

Bulla, Ralf; Costi, T. A.; Vollhardt, D.

doi:10.1103/physrevb.64.045103

Cited by 285 publications

(331 citation statements)

References 50 publications

(104 reference statements)

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“…This behavior has been detected experimentally by photoemission experiments [77]. Altogether, the thermodynamic transition line U c (T ) corresponding to the Mott-Hubbard MIT is found to be of first order at finite temperatures, and is associated with a hysteresis region in the interaction range U c1 < U < U c2 , where U c1 and U c2 are the interaction values at which the insulating and metallic solution, respectively, vanish [33,37,78,79,76,80]. As shown in Fig.…”

Section: Dmft and The Three-peak Structure Of The Spectral Functionmentioning

confidence: 72%

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Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

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Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter. Motivation Electronic CorrelationsAlready in 1937, at the outset of modern solid state physics, de Boer and Verwey [1] drew attention to the surprising properties of materials with incompletely filled 3d-bands. This observation prompted Mott and Peierls [2] to discuss the interaction between the electrons. Ever since transition metal oxides (TMOs) were investigated intensively [3]. It is now well-known that in many materials with partially filled electron shells, such as the 3d transition metals V and Ni and their oxides, or 4f rare-earth metals such as Ce, electrons occupy narrow orbitals. The spatial confinement enhances the effect of the Coulomb interaction between the electrons, making them "strongly correlated". Correlation effects can lead to profound quantitative and qualitative changes of the physical properties of electronic systems as compared to non-interacting particles. In particular, they often respond very strongly to changes in external parameters. This is expressed by large renormalizations of the response functions of the system, e.g., of the spin susceptibility and the charge compressibility. In particular, the interplay between the spin, charge and orbital degrees of freedom of the correlated d and f electrons and with the lattice degrees of freedom leads to an amazing multitude of ordering phenomena and other fascinating properties, including high temperature superconductivity, colossal magnetoresistance and Mott metal-insulator transitions [3].arXiv:1109.4833v1 [cond-mat.str-el]

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Section: Dmft and The Three-peak Structure Of The Spectral Functionmentioning

confidence: 72%

“…The inset shows the U dependence of A(ω = 0), in particular the rapid decrease for U ≈ 1.1 W ; from Ref. [76].…”

Section: Dmft and The Three-peak Structure Of The Spectral Functionmentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

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“…One such method is the numerical renormalization-group (NRG) [42,43,[46][47][48]. It consists of a logarithmic discretization of the continuum of states of the conduction-band electrons, followed by a mapping to a one-dimensional chain Hamiltonian with exponentially decreasing hopping constants.…”

Section: Model and Methodsmentioning

confidence: 99%

Entanglement switching via the Kondo effect in triple quantum dots

et al. 2014

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Abstract. We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. Using Wilson's numerical renormalization group method, we investigate quantum entanglement and its relation to the thermodynamic and transport properties in the regime where each of the dots is singly occupied on average, but with non-negligible charge fluctuations. It is shown that even in the regime of significant charge fluctuations the formation of the Kondo singlets induces switching between separable and perfectly entangled states. The quantum phase transition between unentangled and entangled states is analyzed quantitatively and the corresponding phase diagram is explained by exactly solvable spin model. In the framework of an effective model we also explain smearing of the entanglement transition for cases when the symmetry of the triple quantum dot system is relaxed.

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“…This peak smoothly disappears upon further increasing the temperature and at T = 1/5 only two broad Hubbard bands remain in the spectrum reminiscent of the Mott insulator above the critical temperature of the metal-insulator transition. 27 In Ref. 4 it was shown that this insulator-to-bad-metal crossover is reflected also in the dc and ac conductivity and is accompanied by a substantial increase of the spin susceptibility which follows the Curie-Weiss law at high T .…”

Section: A Phase Diagrammentioning

confidence: 99%

“…In the V = 0 limit we have two decoupled copies of a single-band Hubbard model with semi-circular density of states, a problem which has been extensively studied within DMFT. 23,27 It is well known that upon increasing the interaction strength U at finite, low temperature the paramagnetic phase undergoes a discontinuous transition from a metal to a MI with a hysteresis in the interval U c1 < U < U c2 . 27 At high temperatures the hysteretic behavior is replaced by a continuous crossover.…”

Section: A Phase Diagrammentioning

confidence: 99%

Correlations in a band insulator

et al. 2009

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We study a model of a covalent band insulator with on-site Coulomb repulsion at half-filling using dynamical mean-field theory. Upon increasing the interaction strength the system undergoes a discontinuous transition from a correlated band insulator to a Mott insulator with hysteretic behavior at low temperatures. Increasing the temperature in the band insulator close to the insulator-insulator transition we find a crossover to a Mott insulator at elevated temperatures. Remarkably, correlations decrease the energy gap in the correlated band insulator. The gap renormalization can be traced to the low-frequency behavior of the self-energy, analogously to the quasiparticle renormalization in a Fermi liquid. While the uncorrelated band insulator is characterized by a single gap for both charge and spin excitations, the spin gap is smaller than the charge gap in the correlated system.

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Finite-temperature numerical renormalization group study of the Mott transition

Cited by 285 publications

References 50 publications

Dynamical Mean-Field Theory

Dynamical Mean-Field Theory

Entanglement switching via the Kondo effect in triple quantum dots

Correlations in a band insulator

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