Dielectric Catastrophe at the Mott Transition

Aebischer, C.; Baeriswyl, D.; Noack, R. M.

doi:10.1103/physrevlett.86.468

Cited by 107 publications

(55 citation statements)

References 20 publications

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“…This divergence is weaker than the one found for non-interacting electrons (with δ = 0) and in the metallic phase of the t-t ′ -Hubbard model. 30 A finite-size scaling analysis of both the bondorder susceptibility and the electric susceptibility yield the same critical exponents at U c1 . However, the value, η 1 ≈ 0.45, is not consistent with the critical exponents of the classical two-dimensional Ising model.…”

Section: Discussionmentioning

confidence: 99%

“…For U ≪ U c1 and increasing L, χ el converges to a finite value, similar to the behavior in a non-interacting band insulator and in the correlated insulator phase of the t-t ′ -Hubbard model. 30 The data clearly develop a maximum at U c1 whose height increases markedly with system size, indicating a divergence at the first critical point. The finite-size scaling of this height is consistent with a power-law increase, L 2−η1 , with η 1 ≈ 0.46.…”

Section: B the Electric Susceptibility And The Density-density Corrementioning

confidence: 99%

“…The electric susceptibility has been used to investigate the metal-insulator transition in the t-t ′ -Hubbard model. 30 In this model, both a phase in which χ el diverges as L 2 (a perfect metal) and a phase in which for increasing system size χ el scales to a finite value (an insulator) were found when varying U for fixed nearest-neighbor hopping t and next-nearest-neighbor hopping t ′ .…”

Section: B the Electric Susceptibility And The Density-density Corrementioning

confidence: 99%

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Quantum critical behavior of the one-dimensional ionic Hubbard model

et al. 2004

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We study the zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give strong evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong coupling phase can only partly be understood in terms of the strong coupling behavior of the ordinary Hubbard model.

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Section: Discussionmentioning

confidence: 99%

Section: B the Electric Susceptibility And The Density-density Corrementioning

confidence: 99%

Section: B the Electric Susceptibility And The Density-density Corrementioning

confidence: 99%

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Quantum critical behavior of the one-dimensional ionic Hubbard model

et al. 2004

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“…4, clearly excludes ac conductivity as an explanation of the observed CMC. However, from a theoretical point of view, e.g., based on the Clausius-Mosotti equation or other theoretical considerations [19,20], a simultaneous decrease of the dc resistivity and increase of the dielectric constant can arise when approaching a metal-insulator transition from the insulating side. Indeed such a behavior was observed in some doped semiconductors [ 19,21].…”

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confidence: 99%

Colossal Magnetocapacitance and Colossal Magnetoresistance inHgCr2S4

et al. 2006

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We present a detailed study of the dielectric and charge transport properties of the antiferromagnetic cubic spinel HgCr 2 S 4 . Similar to the findings in ferromagnetic CdCr 2 S 4 , the dielectric constant of HgCr 2 S 4 becomes strongly enhanced in the region below 60 -80 K, which can be ascribed to polar relaxational dynamics triggered by the onset of ferromagnetic correlations. In addition, the observation of polarization hysteresis curves indicates the development of ferroelectric order below about 70 K. Moreover, our investigations in external magnetic fields up to 5 T reveal the simultaneous occurrence of magnetocapacitance and magnetoresistance of truly colossal magnitudes in this material.PACS numbers: 75.80.+q, 77.22.Gm The detection of c olossal magnetoresistance in a number of perovskite-related manganites [1] maybe was the most notable discovery in solid state physics since the emergence of high-T c superconductors. Very recently another "colossal" effect with tremendous prospects for applications in modern microelectronics attracted considerable attention: In several, partly quite different materials an extremely strong coupling of magnetic and dielectric properties, termed "magnetocapacitive" or "magnetoelectric" effect, was found [2,3]. Among these, the cubic spinel CdCr 2 S 4 stands out by showing simultaneous ferromagnetic (FM) and relaxor ferroelectric behavior [3] and by setting a record value of the magnetocapacitive effect with an increase of the dielectric constant ε' of up to 3000% in a magnetic field of 10 T [4]. At the FM transition at T c ≈ 84 K, the dielectric constant shows a strong increase, which was ascribed to a speeding up of relaxational dynamics under the formation of magnetic order [ 4]. However, c learly the microscopic origin of the extraordinary behavior of CdCr 2 S 4 is far from being understood. A similar, but weaker effect was recently reported in isostructural CdCr 2 Se 4 [5] exhibiting FM order below T c ≈ 125 K. In the present letter, we provide dielectric data on HgCr 2 S 4 , which in contrast to CdCr 2 S 4 does not show any long-range FM order but exhibits a complex antiferromagnetic (AFM) type of order below 22 K [ 6]. Nevertheless, it shows a colossal magnetocapacitance (CMC) of even larger amplitude than in CdCr 2 S 4 and, m ost remarkably, the simultaneous occurrence of colossal magnetoresistance (CMR). In addition, our experiments indicate that in HgCr 2 S 4 , similar to our findings in CdCr 2 S 4 , short range ferroelectric order develops at low temperatures.All measurements were performed on single crystals of HgCr 2 S 4 , grown by chemical transport. Measurements with silver paint and sputtered gold contacts applied to opposite sides of the samples were performed. Details on crystal preparation and experimental methods are given in Refs. [3,6]. A thorough characterization of the magnetic properties of HgCr 2 S 4 [6] revealed an AFM state with non-collinear spin configuration below 22 K [ 7]. In moderate external magnetic fields up to 0.5 T, the AFM transi...

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“…λ N represents how electrons can broaden in an insulating state; we can judge that the system is insulating (metallic), if λ N remains finite (diverges) as the system size is increased to infinity. Thus, a Mott transition point can be determined by the diverging point of λ N , without carrying out differentiating operations in contrast to D. In early studies for one-dimensional systems, λ N or a corresponding susceptibility was calculated using exact diagonalization [11], quantum Monte Carlo method [12], and density matrix renormalization group [13]. Regarding VMC, λ N was calculated for a hydrogen chain [14]; it seems that λ N can be a good measure.…”

Section: Introductionmentioning

confidence: 99%

Variational Approach to Localization Length for Two-Dimensional Hubbard Model

Tamura

Yokoyama²

2014

Proceedings of the International Conference on Strongly Correlated Electron Systems (SCES2013)

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As a measure to ascertain whether a system is metallic or insulating, localization length λ N , which represents the spread of electron distribution, can be a useful quantity, especially for approaching a metal-insulator transition from the insulator side. We try to calculate λ N using a variational Monte Carlo method for normal (paramagnetic), superconducting and antiferromagnetic states in the squarelattice Hubbard model. It is found that the behavior of λ N is consistent with what is expected from other quantities, and gives information complementary to another measure, the Drude weight.

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Dielectric Catastrophe at the Mott Transition

Cited by 107 publications

References 20 publications

Quantum critical behavior of the one-dimensional ionic Hubbard model

Quantum critical behavior of the one-dimensional ionic Hubbard model

Colossal Magnetocapacitance and Colossal Magnetoresistance inHgCr2S4

Variational Approach to Localization Length for Two-Dimensional Hubbard Model

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