Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets

Sun, Guang Yu; Wang, Yan-Cheng; Fang, Chen; Qi, Yang; Cheng, Meng; Meng, Zi Yang

doi:10.1103/physrevlett.121.077201

Cited by 62 publications

(79 citation statements)

References 50 publications

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“…Such calculations provide experimentally accessible signatures of exotic states of matter where emergent gauge fields, fractionalized excitations, can be traced. Similar attempts have recently been applied to the deconfined quantum critical point in pure spin model [69], emergent Z 2 spin liquid at (2+1)D [81] and U(1) spin liquid at (3+1)D [82] and the Z 2 counterpart of our model [18]. In the present cQED 3 model, dynamical measurements in the QMC simulation plus state-ofart analytical continuation [81,83,84] can help to reveal more fundamental physical understanding of these exotic quantum phase transitions.…”

Section: Discussionmentioning

confidence: 56%

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Zhang

et al. 2019

Phys. Rev. X

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101

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The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact U(1) lattice gauge theory coupled to fermionic matter in (2 + 1)D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are incarnation of an exotic states of matter, i.e. the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, N f = 4, our data suggests a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

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Section: Discussionmentioning

confidence: 56%

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Zhang

et al. 2019

Phys. Rev. X

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101

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“…Since S (q, ω) can be accessed directly by INS and nuclear magnetic resonance (NMR) experiments, the most favorable evidence for the validity of the QMC-SAC method is that the calculated S (q, ω) results are in good agreement with the existing experimental results [19]. As an effective numerical method for calculating the complete spectra, the QMC-SAC method has recently been used in some interesting work, such as the spin excitation spectrum of the random singlet state [20], quantum spin liquids [13], the dynamical signature of fractionalization at a deconfined quantum critical point [12], and the dynamics of the Higgs mode in spin systems [21,22]. However, unlike the results given by analytical studies, the effects of various modes of spin excitation are intermingled in the results obtained with QMC-SAC.…”

Section: Introductionmentioning

confidence: 79%

Spin excitation spectra of the two-dimensional S=12 Heisenberg model with a checkerboard structure

Xiong

et al. 2019

Phys. Rev. B

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We study the spin excitation spectra of the two-dimensional spin-1/2 Heisenberg model with a checkerboard structures using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearestneighbor interactions J 1 and J 2 , and the tuning parameter g is defined as J 2 /J 1 . The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When g is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the 3×3 checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when g is small. The gapless branch in this case can be regarded as a spin wave in Néel order formed by a "block spin" in each 3 × 3 plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.arXiv:1811.12753v2 [cond-mat.str-el]

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“…The resulting spectra will be collected as an ensemble average of the Metropolis process within the configurational space of {a i , ω i }, as explained in Refs. [33,[48][49][50][51][52].…”

Section: Model and Methodsmentioning

confidence: 99%

“…One first measures the imaginary time correlation functions with good statistics, then performs analytic continuation to convert the correlation from imaginary to real frequencies. The recent developments of stochastic analytic continuation (SAC) scheme [48] is proven to be more reliable and could reveal non-trivial results in both unfrustrated and frustrated magnetic systems in 2D and 3D [33,[49][50][51][52]. Therefore the techniques for investigating the dynamical properties of the QED 3 -GN transitions are available.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of compact quantum electrodynamics at large fermion flavor

Wang

et al. 2019

Phys. Rev. B

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Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor (N f ) and the strength of gauge fluctuations is mapped out [1]. Here we focus on the large fermion flavor case (N f = 8) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED 3 -Gross-Neveu chiral O(2) universality whose properties still largely unknown.

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Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets

Cited by 62 publications

References 50 publications

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Spin excitation spectra of the two-dimensional S=12 Heisenberg model with a checkerboard structure

Dynamics of compact quantum electrodynamics at large fermion flavor

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