Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics

Götz, Anika; Beyl, Stefan; Hohenadler, Martin; Assaad, Fakher F.

doi:10.1103/physrevb.105.085151

Cited by 39 publications

(16 citation statements)

References 57 publications

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“…That is precisely the case of SU(2) symmetric Hubbard-Stratonovich transformations [54], but investigations in Appendix D show that the averaged spin-resolved phase similarly tracks the onset of the ordered regime when approaching the thermodynamic limit for the SU(2) honeycomb Hubbard model. Furthermore, other Hamiltonians, such as the spinless fermion Hubbard model in either the honeycomb [55] or square-lattice with a π-flux, which in the Majorana basis evade the sign problem [56,57], can be studied by examining the average sign of the Pfaffian of a single weight in that basis [58], similar to what we have done here [59]. In our results, the investigation of these three important models emphasizes that the sign of the determinants, interpreted as a minimal correlation function, is sufficient to assess critical properties, circumventing what is usually employed to determine scaling properties of physically motivated quantities.…”

Section: The Attractive Hubbard Modelmentioning

confidence: 99%

Universality and Critical Exponents of the Fermion Sign Problem

Mondaini¹,

Tarat²,

Scalettar³

2022

Preprint

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Initial characterizations of the fermion sign problem focused on its evolution with spatial lattice size L and inverse temperature β, emphasizing the implications of the exponential nature of the decay of the average sign S for the complexity of its solution and associated limitations of quantum Monte Carlo studies of strongly correlated materials. Early interest was also on the evolution of S with density ρ, either because commensurate filling is often associated with special symmetries for which the sign problem is absent, or because particular fillings are often primary targets, e.g. those densities which maximize superconducting transition temperature (the top of the 'dome' of cuprate systems). Here we describe a new analysis of the sign problem which demonstrates that the spin-resolved sign Sσ already possesses signatures of universal behavior traditionally associated with order parameters, even in the absence of symmetry protection that makes S = 1. When appropriately scaled, Sσ exhibits universal crossings and data collapse. Moreover, we show these behaviors occur in the vicinity of quantum critical points of three well understood models, exhibiting either second order or Kosterlitz-Thouless phase transitions. Our results pave the way for using the average sign as a minimal correlator that can potentially describe quantum criticality in a variety of fermionic many-body problems.

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Section: The Attractive Hubbard Modelmentioning

confidence: 99%

Universality and Critical Exponents of the Fermion Sign Problem

Mondaini¹,

Tarat²,

Scalettar³

2022

Preprint

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“…Recently, the studies of the 1D SSH model have been extended to two dimensions (2D) [40][41][42][43][44][45][46] . The optical SSH model on the square lattice without or with the Hubbard interaction U has been carefully studied by the quantum Monte Carlo (QMC) method at half filling, where the negative sign problem is absent.…”

Section: Introductionmentioning

confidence: 99%

“…For comparison, in one-dimensional (1D) SSH model, any nonzero EPI can induce the CBO, referred to as dimerization, 33,48,49 , as a result of the Peierls instability 1 . The effect of a finite Hubbard U has also been considered very recently [43][44][45][46] . Since U breaks the Z 2 symmetry, a positive U enhances the SDW in the spin channel while suppresses the CDW/sSC in the charge channel, providing a new avenue to explore the transition between SDW and VBS 44,50 .…”

Section: Introductionmentioning

confidence: 99%

A functional renormalization group study of the two dimensional Su-Schrieffer-Heeger-Hubbard model

Yang¹,

Wang²,

Wang³

2022

Preprint

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We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At halffilling and in the absence of the Hubbard interaction U , we find the d-wave Pomeranchuk instability (PI) at weak electron-phonon coupling strength λ, the degenerate spin-density-wave (SDW)/chargedensity-wave (CDW)/s-wave superconductivity (sSC) state at larger λ and higher phonon frequency ω, and the valence bond solid (VBS) state at larger λ and lower ω. After switching on a positive U , the PI and VBS states are suppressed, while the SDW state is enhanced. At finite doping, the SSH phonon is found to favor sSC at U = 0. With increasing positive U , we find d-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate U and λ, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the CDW and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction U enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC) together with the new nematic state, and provide new insights at finite doping where QMC may suffer from the minus sign problem.

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“…Either strong pairing correlations between the electrons [33] result in saturation of T c or even higher values of T c (dashed line), or competing effects resulting from the Hubbard repulsion and lattice commensurability suppress T c (dotted line). In either scenario, the system eventually becomes non-superconducting at sufficiently large densities near or at half filling (unless unnested) and, depending on the value of λ, antiferromagnetism or valence-bond-solid charge order develops [34][35][36][37].…”

mentioning

confidence: 99%

“…We envision a few possibilities: either pairing correlations continue to dominate and Tc saturates or grows (dashed line) or competing effects suppress Tc (dotted line). Ultimately, at or near half filling, barring superconductivity at weak λ in absence of nesting, Tc vanishes and, depending on the value of the electron-phonon coupling λ, a valence bond solid (VBS) or antiferromagnet (AFM) emerges [34][35][36][37] (gray region).…”

mentioning

confidence: 99%