Superconductivity and charge density wave order in the two-dimensional Holstein model

Bradley, Owen; Batrouni, G. G.; Scalettar, Richard

doi:10.1103/physrevb.103.235104

Cited by 36 publications

(16 citation statements)

References 49 publications

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“…For βt ≤ 20, although χ s increases when the temperature is reduced, it presents just a weak dependence with the lattice size (not shown). As already pointed out in the literature, the critical temperature for the Kosterlitz-Thouless transition at fixed ω 0 /t = 1 should be very low 13,27,29 , and unfeasible to reach from a technical point of view. However, due to the suppression of the charge-charge correlations, the attractive effective interaction between electrons must lead to a SC phase at the ground state 21,26,51 , for |t /t| ≥ 0.35.…”

Section: Resultsmentioning

confidence: 97%

“…In particular, its properties have been explored in many different aspects, e.g. by examining the effects of anharmonicity, strain, disorder, or electronic doping [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] . Here, instead, we investigate how the overlap between farther orbitals affects the leading CDW order.…”

Section: Introductionmentioning

confidence: 99%

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The two-dimensional $t$-$t^{\prime}$ Holstein model

Araújo,

de Lima,

Sorella

et al. 2021

Preprint

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The competition and interplay between charge-density wave and superconductivity have become a central subject for quasi-2D compounds. Some of these materials, such as the transition-metal dichalcogenides, exhibit strong electron-phonon coupling, an interaction that may favor both phases, depending on the external parameters, such as hydrostatic pressure. In view of this, here we analyze the single-band t-t Holstein model in the square lattice, adding a next-nearest neighbor hopping t in order to play the role of the external pressure. To this end, we perform unbiased quantum Monte Carlo simulations with an efficient inversion sampling technique appropriately devised for this model. Such a methodology drastically reduces the autocorrelation time, and increases the efficiency of the Monte Carlo approach. By investigating the charge-charge correlation functions, we obtain the behavior of the critical temperature as a function of t , and from compressibility analysis, we show that a first-order metal-to-insulator phase transition occurs. We also provide a low-temperature phase diagram for the model.

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Section: Resultsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

The two-dimensional $t$-$t^{\prime}$ Holstein model

Araújo,

de Lima,

Sorella

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…When doped sufficiently away from half filling, and at sufficiently low temperature, the system is expected to transition to a superconducting phase. 35,36 We measure the CDW order using the staggered charge susceptibility…”

Section: Full 2d Systemmentioning

confidence: 99%

Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations

Miles,

Cohen-Stead,

Bradley

et al. 2022

Preprint

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We present a method to facilitate Monte Carlo simulations in the grand canonical ensemble given a target mean particle number. The method imposes a fictitious dynamics on the chemical potential, to be run concurrently with the Monte Carlo sampling of the physical system. Corrections to the chemical potential are made according to time-averaged estimates of the mean and variance of the particle number, with the latter being proportional to thermodynamic compressibility. We perform a variety of tests, and in all cases find rapid convergence of the chemical potential-inexactness of the tuning algorithm contributes only a minor part of the total measurement error for realistic simulations.

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“…15 Apart from the polarons, the Holstein model can also host a Peierls-type lattice instability, 120 the so-called charge-density wave (CDW) phase at half filling. [121][122][123][124][125][126][127][128] By tuning parameters of the 1D Holstein model, one can predict a transition between the CDW and Luttinger-liquid metallic phases. 125,126 The CDW-to-metallic transition has recently been observed in experiments.…”

Section: Introductionmentioning

confidence: 99%

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

Brink,

Gräber,

Hopjan

et al. 2022

Preprint

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We benchmark a set of quantum-chemistry methods including the multitrajectory Ehrenfest, the fewest-switches surface-hopping, and the multiconfigurational Ehrenfest method against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method in general only captures the ultra-short time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior, but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

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Superconductivity and charge density wave order in the two-dimensional Holstein model

Cited by 36 publications

References 49 publications

The two-dimensional $t$-$t^{\prime}$ Holstein model

The two-dimensional $t$-$t^{\prime}$ Holstein model

Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

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