Phonon Dispersion Relations in Two-dimensional Peierls Phase

Chiba, Shutaro

doi:10.1143/jpsj.73.2473

Cited by 13 publications

(4 citation statements)

References 15 publications

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“…Most importantly, we determine the nature of the BOW pattern, thus resolving a long-standing question [29][30][31]. Furthermore, we present numerical evidence that, in the ground state, the electron-phonon coupling must exceed a finite critical value for BOW to be established, unlike in the Holstein model where the Peierls CDW phase is present for any finite coupling on a square lattice.…”

Section: Introductionmentioning

confidence: 82%

“…Tang and Hirsch [29] argued that a q = (π, π) phonon, polarized along the x-axis (or y-axis), provides the largest energy gain when a displacement δ is introduced to the frozen lattice. Subsequent work [30,31] challenged this result, making the claim that the optimal energy was achieved by a superposition of a broad spectrum of lattice momenta, rather than individual values at the borders of the Brillouin zone.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model

Xing,

Chiu,

Poletti

et al. 2020

Preprint

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Over the last several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon modes and the on-site charge density. A quite different, and interesting, case is one in which the phonons live on the bonds, and hence modulate the electron hopping. This situation, described by the Su-Schrieffer-Heeger (SSH) Hamiltonian, has so far only been studied with quantum Monte Carlo in one dimension. Here we present results for the 2D SSH model, and show that a bond ordered wave (BOW) insulator is present in the ground state at half-filling, and argue that a critical value of the electron-phonon coupling is required for its onset, in contradistinction with the 1D case where BOW exists for any nonzero coupling. We determine the precise nature of the bond ordering pattern, which has hitherto been controversial, and the critical transition temperature, which is associated with a spontaneous breaking of Z4 symmetry.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model

Xing,

Chiu,

Poletti

et al. 2020

Preprint

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“…We apply the linear-mode analysis [4] to a two-dimensional version of the SSH model. The model Hamiltonian is written as follows:…”

Section: Methods Of Numerical Calculationsmentioning

confidence: 99%

“…Throughout this paper, we assume the periodic boundary conditions for both directions. Omitting the details of derivation [4], we show the ÿnal form of the linear mode equation…”

Section: Methods Of Numerical Calculationsmentioning

confidence: 99%

Phonon dispersion relations in a two-dimensional electron–lattice system at non-zero temperatures

Chiba

2004

Physica E: Low-dimensional Systems and Nanostructures

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Multimode Peierls distortion in triangular lattice

Miyoshi¹,

Terai²

2012

Physica Status Solidi (b)

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We have studied the multimode Peierls states in the electron–lattice system on a triangular lattice with a three‐quarter‐filled electronic band. Below the transition temperature, we have found many stable states of nearly same free‐energy. Focusing our attention on the lowest free‐energy state, we have found that the Peierls order parameter continuously increases from zero just below the transition temperature. When the temperature is raised from the region lower than the critical temperature, multiple phonon modes are simultaneously softened at the same temperature as when the temperature is lowered from the region higher that the critical temperature. These results tell us that the transition is of the second order. The non‐softened modes are also found to condense due to nonlinear coupling between the non‐softened modes and the softened modes. The degeneracy of the phonon modes observed at the higher temperature region is partially lifted at the lower temperature region.

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Phonon Dispersion Relations in Two-dimensional Peierls Phase

Cited by 13 publications

References 15 publications

Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model

Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model

Phonon dispersion relations in a two-dimensional electron–lattice system at non-zero temperatures

Multimode Peierls distortion in triangular lattice

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