Amplitude Mode in Quantum Magnets via Dimensional Crossover

Zhou, Chengkang; Yan, Zheng; Wu, Han‐Qing; Sun, Kai; Starykh, Oleg A.; Meng, Zi Yang

doi:10.1103/physrevlett.126.227201

Cited by 34 publications

(23 citation statements)

References 39 publications

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“…All these ESs have two gapless modes, a weak one at (0, 0) and a strong one at (π, π). The spectral properties of ES closely resemble the magnon dispersion of the edge system, that is, Goldstone modes of the antiferromagnetic Heisenberg model on square lattice [60,62]. As far as we are aware of, these results serve as the first demonstration in 2d entangling region, that ES is the spectra of the entanglement Hamiltonian, corresponding to a physical system living effectively on the edges of the partitioned bulk [18,20].…”

mentioning

confidence: 52%

“…Now that we can access L = 100, the ES in Fig. We find it is interesting that for all the three cases, ES have two gapless modes with a strong one at (π,π) and a weak one at (0,0), closely resembling those the Goldstone modes in square antiferromagnetic Heisenberg model [60,62,85]. We therefore fit all the three ESs in Fig.…”

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confidence: 97%

“…Motivated by these recent developments, in this paper, we develop a protocol to efficiently compute the ES in quantum Monte Carlo simulation for entangling region with long boundaries and in higher dimensions. As in the computation of EE [51,53,54], we construct a general partition function live in the manifold with replicas, where the entangling region are connected in the replica imaginary time axis and the rest of the system (the environment) are independent (a so-called "Qiu Ku" geometry [55]) We first compute the replica time correlation functions along the imaginary axis, and then employ the stochastic analytic continuation (SAC) technique [56][57][58][59][60][61][62] to obtain ES in real frequency. We note similar efforts have been tried in the interacting fermion systems [35][36][37], although the entangling region therein is still (quasi) 1d and the overall system sizes are limited due to the heavy computational complexity in determinant QMC.…”

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confidence: 99%

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Relating entanglement spectra and energy spectra via path-integral on replica manifold

Zheng¹,

Meng²

2021

Preprint

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Low-lying entanglement spectrum provide the quintessential fingerprint to identify the highly entangled quantum matter with topological and conformal field-theoretical properties. However, when the entangling region acquires long boundary with the environment, such as that between long coupled chains or in two or higher dimensions, there unfortunately exists no universal yet practical method to compute the entanglement spectra with affordable computational cost. Here we develop a new algorithm to overcome such difficulty and successfully extract the low-lying entanglement spectrum from quantum Monte Carlo simulation combined with stochastic analytic continuation. We demonstrate the strength and reliability of our method on long coupled spin chains and bilayer antiferromagnetic Heisenberg model which experiences (2 + 1)d O(3) quantum phase transition. Our simulation results, with unprecedentedly large system sizes, establish the practical computation scheme of entanglement spectrum in quantum many-body systems at higher dimensions and with long boundaries.

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confidence: 52%

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confidence: 97%

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confidence: 99%

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Relating entanglement spectra and energy spectra via path-integral on replica manifold

Zheng¹,

Meng²

2021

Preprint

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“…In addition to specific heat, critical fluctuations and non-Fermi-liquid behavior generate other experimental signatures as well, such as transport, spectroscopy, X-ray/neutron scatterings, magnetic resonance, etc. In QMC simulations, these physical observables can all be measured, utilizing analytic continuations to convert imaginary time and real Matsubara frequencies to real time and frequencies [31,43,44]. Such calculations will be performed in future studies, which can provide important guidance and insights for experimental studies in variety of quantum magnets, such as UGe 2 [4], URhGe [5], UCoGe [6] and YbNi 4 P 2 [7] and CeRh 6 Ge 4 [8,9].…”

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confidence: 99%

The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study

Liu,

Jiang,

Klein

et al. 2021

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We consider the effect of the coupling between 2D quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions. A common belief is that near a q = 0 ferromagnetic transition, fermions induce an Ω/𝑞 Landau damping of rotors (i.e., the dynamical critical exponent is 𝑧 = 3) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy Σ ∝ 𝜔 2/3 . This behavior has been confirmed in previous quantum Monte Carlo studies. Here we show that for the XY case the behavior is different. We report the results of large scale quantum Monte Carlo simulations, which clearly show that at small frequencies 𝑧 = 2 and Σ ∝ 𝜔 1/2 . We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces 1/𝑞 in the Landau damping by a constant. We discuss the implication of these results to experiments.

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“…Below the ordering temperature, the dipolar interaction generates a finite staggered field, H st [85,86]. It produces a confining potential that increases linearly with the distance between both spinons, opens the gap in the spectrum, ∆ 1 = (J * H 2 st ) 1/3 and splits the spectrum into a series of modes.…”

Section: Theoretical Descriptionmentioning

confidence: 99%

Low-energy spin dynamics in rare-earth perovskite oxides

Podlesnyak,

Nikitin,

Ehlers

2021

Preprint

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We review recent studies of spin dynamics in rare-earth orthorhombic perovskite oxides of the type RM O 3 , where R is a rare-earth ion and M is a transition-metal ion, using single-crystal inelastic neutron scattering (INS). After a short introduction to the magnetic INS technique in general, the results of INS experiments on both transition-metal and rare-earth subsystems for four selected compounds (YbFeO 3 , TmFeO 3 , YFeO 3 , YbAlO 3 ) are presented. We show that the spectrum of magnetic excitations consists of two types of collective modes that are well separated in energy: gapped magnons with a typical bandwidth of <70 meV, associated with the antiferromagnetically (AFM) ordered transition-metal subsystem, and AFM fluctuations of <5 meV within the rareearth subsystem, with no hybridization of those modes. We discuss the highenergy conventional magnon excitations of the 3d subsystem only briefly, and focus in more detail on the spectacular dynamics of the rare-earth sublattice in these materials. We observe that the nature of the ground state and the lowenergy excitation strongly depends on the identity of the rare-earth ion. In the case of non-Kramers ions, the low-symmetry crystal field completely eliminates the degeneracy of the multiplet state, creating a rich magnetic field-temperature phase diagram. In the case of Kramers ions, the resulting ground state is at least a doublet, which can be viewed as an effective quantum spin-1/2. Equally important is the fact that in Yb-based materials the nearest-neighbor exchange interaction dominates in one direction, despite the three-dimensional nature of the orthoperovskite crystal structure. The observation of a fractional spinon continuum and quantum criticality in YbAlO 3 demonstrates that Kramers rareearth based magnets can provide realizations of various aspects of quantum lowdimensional physics.

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Amplitude Mode in Quantum Magnets via Dimensional Crossover

Cited by 34 publications

References 39 publications

Relating entanglement spectra and energy spectra via path-integral on replica manifold

Relating entanglement spectra and energy spectra via path-integral on replica manifold

The dynamical exponent of a quantum critical itinerant ferromagnet: a Monte Carlo study

Low-energy spin dynamics in rare-earth perovskite oxides

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