Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice

Ferrari, Francesco; Becca, Federico

doi:10.1103/physrevb.98.100405

Cited by 74 publications

(82 citation statements)

References 44 publications

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“…Similar excitations associated with small spin clusters were also observed in the spinel lattice 36 . Our neutron measurements are also in agreement with recent Monte-Carlo calculations of the dynamical structure factor for the frustrated honeycomb lattice 15 that show a deconfined twospinon continuum 37 with enhanced intensity at the zone boundary due to proximity of a quantum critical point.…”

Section: Discussionsupporting

confidence: 88%

Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

et al. 2020

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Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S = 1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest-neighbour interactions. We demonstrate that YbBr3 avoids order down to at least T = 100 mK and features a dynamic spin–spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.

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Section: Discussionsupporting

confidence: 88%

Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

et al. 2020

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“…( π 2 , π 2 ) (π, 0) (π, π) ( π 2 , π 2 ) (0, 0) (0, π) q ( π 2 , π 2 ) (π, 0) (π, π) ( π 2 , π 2 ) (0, 0) (0, π) q [46] for details). We applied a Gaussian broadening of σ = 0.02J1 to the variational results.…”

Section: Resultsmentioning

confidence: 99%

Dynamical Structure Factor of the J1−J2 Heisenberg Model on the Triangular Lattice: Magnons, Spinons, and Gauge Fields

2019

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Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering. In this work, we investigate the low-energy properties of the S = 1/2 Heisenberg model on the triangular lattice, including both nearest-neighbor J1 and next-nearest-neighbor J2 super-exchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models. For J2 = 0, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations at K points (i.e., at the corners of the Brillouin zone). The strong renormalization of the magnon branch (also including roton-like minima around the M points, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a non-trivial magnetic π-flux threading half of the triangular plaquettes. When increasing the frustrating ratio J2/J1, we detect a progessive softening of the magnon branch at M , which eventually becomes gapless within the spin-liquid phase. This feature is captured by the band structure of the unprojected wave function (with 2 Dirac points for each spin component). In addition, we observe an intense signal at low energies around the K points, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids. arXiv:1903.05691v3 [cond-mat.str-el]

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“…The Lehman representation can be evaluated explicitly with ED since we have a complete and exact representation of the Hamiltonian eigenstates, but this technique is limited to small clusters. To evaluate the Green's function for the cases not amenable to the exact diagonalization, we can use a method similar to the approach used to calculate the spin and charge dynamical structure factors by exhausting an important subspace of the Hilbert space for the excitations [24][25][26][27][28]. In this framework, the time evolutions by the Hamiltonian in the N − 1 particle sector for G h σ ðk; ωÞ [Eq.…”

Section: A Green's Functionmentioning

confidence: 99%

“…The recent formulation of the time-dependent variational Monte Carlo method based on the variational principle opened a way to study the long-time dynamics [21,22], but it has not been extensively applied yet to interacting fermion systems except for in a few examples [23]. Meanwhile, methods of calculating the spin and charge dynamical structure factors utilizing the variational wave functions for ground and excited states have been proposed recently [24][25][26][27][28]. Some attempts have been made to calculate the excitation spectrum on larger clusters of the t-J model [29,30].…”

Section: Introductionmentioning

confidence: 99%

Single-Particle Spectral Function Formulated and Calculated by Variational Monte Carlo Method with Application to d -Wave Superconducting State

Charlebois

Imada

2020

Phys. Rev. X

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A method to calculate the one-body Green's function for ground states of correlated electron materials is formulated by extending the variational Monte Carlo method. We benchmark against the exact diagonalization (ED) for the one-and two-dimensional Hubbard models of 16-site lattices, which proves high accuracy of the method. The application of the method to a larger-sized Hubbard model on the square lattice correctly reproduces the Mott insulating behavior at half-filling and gap structures of the d-wave superconducting state of the hole-doped Hubbard model in the ground state optimized by enforcing the charge uniformity, evidencing a wide applicability to strongly correlated electron systems. From the obtained d-wave superconducting gap of the charge-uniform state, we find that the gap amplitude at the antinodal point is several times larger than the experimental value when we employ a realistic parameter as a model of the cuprate superconductors. The effective attractive interaction of carriers in the d-wave superconducting state inferred for an optimized state of the Hubbard model is as large as the order of the nearest-neighbor transfer, which is far beyond the former expectation in the cuprates. We discuss the nature of the superconducting state of the Hubbard model in terms of the overestimate of the gap and the attractive interaction in comparison to the cuprates.

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Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice

Cited by 74 publications

References 44 publications

Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice

Dynamical Structure Factor of the J1−J2 Heisenberg Model on the Triangular Lattice: Magnons, Spinons, and Gauge Fields

Single-Particle Spectral Function Formulated and Calculated by Variational Monte Carlo Method with Application to d -Wave Superconducting State

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