Role of frustration and dimensionality in the Hubbard model on the stacked square lattice: Variational cluster approach

Yoshikawa, Toshihiko; Ogata, Masao

doi:10.1103/physrevb.79.144429

Cited by 15 publications

(15 citation statements)

References 61 publications

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“…In reality, many effects beyond MFT might lead to these transitions becoming first-order, as often observed in experiment. However, numerous recent analytical and numerical studies [22,30,31,32,33,34] support the existence of continuous or only weakly discontinuous Mott transitions in frustrated geometries such as the one studied here. Because the Mott transition is suppressed to small U/t by increasing SOI, we believe the predictions of the slave-rotor MFT are reasonable both for the GMI and the TMI phases.…”

Section: Figmentioning

confidence: 99%

Mott physics and band topology in materials with strong spin–orbit interaction

Pesin

Balents²

2010

Nature Phys

1,054

1,266

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Recent theory and experiment have revealed that strong spin-orbit coupling can have dramatic qualitative effects on the band structure of weakly interacting solids. Indeed, it leads to a distinct phase of matter, the topological band insulator. In this paper, we consider the combined effects of spin-orbit coupling and strong electron correlation, and show that the former has both quantitative and qualitative effects upon the correlation-driven Mott transition. As a specific example we take Irbased pyrochlores, where the subsystem of Ir 5d electrons is known to undergo a Mott transition. At weak electron-electron interaction, we predict that Ir electrons are in a metallic phase at weak spinorbit interaction, and in a topological band insulator phase at strong spin-orbit interaction. Very generally, we show that with increasing strength of the electron-electron interaction, the effective spin-orbit coupling is enhanced, increasing the domain of the topological band insulator. Furthermore, in our model, we argue that with increasing interactions, the topological band insulator is transformed into a "topological Mott insulator" phase, which is characterized by gapless surface spin-only excitations. The full phase diagram also includes a narrow region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron-electron interaction. Introduction: The spin-orbit interaction (SOI), though apparently a "weak" relativistic correction to the Schrödinger equation (outside of high energy physics), is coming increasingly to the fore in modern condensed matter physics. The discovery of Topological Band Insulators (TBIs) in theory [1, 2,3,4] and experiment [5,6] has revealed a surprising omission in the "textbook" Bloch theory of the electronic structure of weakly correlated solids. In these remarkable materials, strong spin-orbit interactions allow a non-trivial topology of the electron bands, resulting in protected "helical" edge and surface states in two and three dimensional systems. Many other interesting phenomena, including quantum number fractionalization and magneto-electric effects have been predicted to occur in these systems, and are the subjects of a growing experimental effort. In parallel, strong SOIs have been identified in a growing variety of Mott insulators, in which the insulating behavior is driven by electron correlation rather than band structure. For instance, SOIs are likely responsible for the large Wilson ratios observed in many frustrated magnets at low temperature [7,8], and may be the driving force for the formation of a "spin-orbital liquid" in some Fe-spinels [9]. They have been experimentally shown to control the orbital state in the Ir oxide Sr 2 IrO 4 using resonant x-ray scattering [10]. A natural question is how these two classes of phenomena are connected -how does a material progress from weak to strong correlation with strong SOIs? This is the subject of the Mott transition with strong SOIs.In the search for strong SOIs, one is driven t...

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Section: Figmentioning

confidence: 99%

Mott physics and band topology in materials with strong spin–orbit interaction

Pesin

Balents²

2010

Nature Phys

1,054

1,266

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“…The advantage of VCA compared to HFA is that VCA can fully take into account static and dynamic effects of electron correlations within the range of a finite size cluster. So far, VCA and CPT applied to a variety of strongly correlated electron systems, such as the half-filled Hubbard model with competing magnetic orders in two-dimensional 20 and three-dimensional systems, 21 periodic Anderson model with the competition between magnetic ordering induced by the Ruderman-Kittel-Kasuya-Yoshida interaction and nonmagnetic Kondo screening, 22 multi-orbital system with spin-orbit coupling, XY-plane magnetic ordering, 23 etc, and it turns out that the method is useful to discuss correlation effects on the symmetry breaking or singleparticle excitation spectra, especially in the insulating state. Thus it is worth studying the EI state of the EFKM by applying VCA and CPT to investigate the effects of short range correlations on the symmetry breaking or single-particle excitations.…”

Section: Introductionmentioning

confidence: 99%

BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

2011

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We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction U in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra, as a function of U at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of BEC. Moreover, we find that HFA works well both in the weak-and strong-coupling regime, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime).

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“…A lot of activities in this area were focused on frustrated spin-half Heisenberg antiferromagnets like the J 1 -J 2 antiferromagnet on the square lattice (see, e. g. [18][19][20][21][22][23][24][25][26][27][28] and references therein) and on three-dimensional cubic lattices [29][30][31][32][33], the Heisenberg antiferromagnet (HAFM) on the star lattice [12,11,34] and last but not least the HAFM on the kagomé lattice (see the reviews [11,[35][36][37] and references therein). Due to the extreme frustration, the HAFM on the kagomé and on the star lattices shows an infinite non-trivial degeneracy of the classical ground state.…”

Section: Introductionmentioning

confidence: 99%

The Heisenberg antiferromagnet on the square-kagomé lattice

Richter¹,

Schulenburg²,

Tomczak³

et al. 2009

Condens. Matter Phys.

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We discuss the ground state, the low-lying excitations as well as high-field thermodynamics of the Heisenberg antiferromagnet on the two-dimensional square-kagomé lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is also known for the Heisenberg antiferromagnet on the kagomé and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet with a finite spin gap and with a large number of non-magnetic excitations within this gap. We also discuss the magnetization versus field curve that shows a plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states. These localized states are highly degenerate and lead to interesting features in the low-temperature thermodynamics at high magnetic fields such as an additional low-temperature peak in the specific heat and an enhanced magnetocaloric effect.

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Role of frustration and dimensionality in the Hubbard model on the stacked square lattice: Variational cluster approach

Cited by 15 publications

References 61 publications

Mott physics and band topology in materials with strong spin–orbit interaction

Mott physics and band topology in materials with strong spin–orbit interaction

BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

The Heisenberg antiferromagnet on the square-kagomé lattice

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