Questions, Controversies and Frustration in Quantum Antiferromagnetism

Chandra, Premala; Coleman, Piers; Ritchey, I.

doi:10.1142/s0217979291000122

Cited by 17 publications

(14 citation statements)

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“…This fact was interpreted as a strong failure of the SBMFT. 32,33 Motivated by this observation, we demonstrate in this paper that the LSWT result for the dynamical spin susceptibility is recovered in large-S limit upon adding a 1/N correction to the SP or SBMFT. For simplicity, we focus on the triangular lattice Heisenberg antiferromagnet with a 120 • Néel ground state ordering, whose quantum (S = 1/2) magnetic excitation spectrum is very different from the semiclassical (S → ∞ ) limit.…”

Section: Introductionmentioning

confidence: 61%

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Large- S limit of the large- N theory for the triangular antiferromagnet

et al. 2019

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Large-S and large-N theories (spin value S and spinor component number N ) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-S spin-wave theory captures the correct semiclassical behavior, large-N theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the non-trivial recovery of the semiclassical magnetic excitations within a large-N approach, we compute the large-S limit of the dynamic spin structure of the triangular lattice Heisenberg antiferromagnet within a Schwinger boson spin representation. We demonstrate that, only after the incorporation of Gaussian (1/N ) corrections to the saddle-point (N = ∞) approximation, we are able to exactly reproduce the linear spin wave theory results in the large-S limit. The key observation is that the effect of 1/N corrections is to cancel out exactly the main contribution of the saddle-point solution; while the collective modes (magnons) consist of two spinon bound states arising from the poles of the RPA propagator. This result implies that it is essential to consider the interaction of the spinons with the emergent gauge fields and that the magnon dispersion relation should not be identified with that of the saddle-point spinons. arXiv:1905.10689v1 [cond-mat.str-el]

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Section: Introductionmentioning

confidence: 61%

“…At the SP level, the magnetic susceptibility is obtained by an analytic continuation iω n → ω + i0 + of χ sp I µν (q, iω n ) given in Eq. (32), which corresponds to the diagram shown in Fig. 4 (a).…”

Section: Dynamical Spin Structure Factormentioning

confidence: 99%

Large- S limit of the large- N theory for the triangular antiferromagnet

et al. 2019

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“…This "pathology" of the particular case α = 0 led the community to believe that the SP level of the SBT is enough to obtain the true collective modes of magnetically ordered states. While this generalized belief was questioned after noticing the impossibility of recovering the correct large-S limit with the SP result [76,77], the origin of this failure was not properly understood. As we have demonstrated here, the identity between the single-spinon and single-magnon dispersions is not true for general decoupling schemes (α = 0).…”

Section: Discussionmentioning

confidence: 99%

“…The correct identification of the true collective modes allowed us to recover the linear SWT result by taking the large-S limit of the SBT [39]. This identification also explains the failed attempts of recovering the correct large-S limit at the SP level of the SBT [76,77]. Unfortunately, this negative result was misinterpreted as an important shortcoming of the SBT that discouraged the use of this formalism for modelling the excitation spectrum of ordered magnets.…”

Section: Introductionmentioning

confidence: 98%

Schwinger boson theory of ordered magnets

Zhang,

Ghioldi,

Manuel

et al. 2021

Preprint

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The Schwinger boson theory (SBT) provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the 1/N expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in 1/N, which must be accounted to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.

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“…The question of the quantum ground state of these systems arose very early in the study of frustrated quantum magnetism [80][81][82], but the answers remain at present only partial. The spin-…”

Section: Vbcs or Rvb Spin Liquids On Kagomé And Pyrochlore Lattices?mentioning

confidence: 99%

Introduction to Quantum Spin Liquids

Lhuillier

Misguich

2010

Introduction to Frustrated Magnetism

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In SU(2)-invariant spin models with frustrated interactions and low spin quantum number, long-ranged magnetic order and breaking of the SU(2) symmetry is not the most general situation, especially in low dimensions. Many such systems are, loosely speaking, "quantum paramagnets" down to zero temperature, states conveniently represented in terms of spins paired into rotationally invariant singlets, or "valence bonds" (VBs). In this large family of states, at least two very different physical phases should be distinguished, valence bond crystals (or solids) and resonating-valence-bond (RVB) liquids.This chapter provides a basic introduction to the concept of short-range resonating-valence-bond (srRVB) states, and emphasizes the qualitative differences between VB crystals and RVB liquids. We explain in simple terms why the former sustain only integer-spin excitations while the latter possess spin-1 2 excitations (the property of fractionalization). We then elaborate qualitatively on the notion of macroscopic quantum resonances, which are behind the 'R' of the RVB spin liquid, to motivate the idea that spin liquids are not disordered systems but possess instead hidden quantum order parameters. After giving a brief list of models and materials of current interest as candidate spin liquids, we conclude by mentioning the role of the parity of the net spin in the unit cell (half-odd-integer or integer) in spin-liquid formation, by recalling the contrasting results for kagomé and pyrochlore lattices. IntroductionIn isotropic (SU(2)-invariant) Heisenberg spin systems, frustration of individual bond energies, arising due to competing interactions and/or lattice topology, and extreme quantum fluctuations, due to low spin values and low coordination numbers, can prevent T D 0 magnetic ordering (defined as the existence of a non-zero on-site magnetization, hs i i > 0). These factors lead instead to a large variety of quantum phases, sometimes given the misleading name "spin liquids." We begin the task of categorizing this large zoo of phases by excluding those which do possess an order parameter, but merely one more complex than an on-site magnetization, 23 24 C. Lhuillier and G. Misguich such as a quadrupolar moment or a spin current [1][2][3]). These exotic forms of complex order break SU(2) symmetry and support Goldstone modes, and hence can be understood by semiclassical (spin-wave-like) approximations.However, quantum effects may generate more radical situations where SU(2) symmetry is not broken in the ground state. One of the most common ways of achieving this is that the spins are paired in rotationally invariant singlets, or valence bonds (VBs). Such states are by definition non-magnetic, and thus qualify as "quantum paramagnets".1 This requirement on the ground-state wave function is insufficient to characterize the physics of an extended system, its low-energy excitations and the long-distance behavior of its correlation functions. In this large family of quantum paramagnets, a crucial distinction should be i...

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Questions, Controversies and Frustration in Quantum Antiferromagnetism

Abstract: The search for a gapless spin liquid phase has raised many issues in quantum antiferromagnetism. Here we review recent developments in this field, and in particular address questions and controversies surrounding a proposed “spin nematic” state.

Cited by 17 publications

References 0 publications

Large- S limit of the large- N theory for the triangular antiferromagnet

Large- S limit of the large- N theory for the triangular antiferromagnet

Schwinger boson theory of ordered magnets

Introduction to Quantum Spin Liquids

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