String Picture for a Model of Frustrated Quantum Magnets and Dimers

Jiang, Ying; Emig, Thorsten

doi:10.1103/physrevlett.94.110604

Cited by 17 publications

(30 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with b q = p b p e −iq·rp (r p is the position vector for the site p), we find diffusive lines in S(q) consistent with the directional order. This "locking transition" is suggested to be induced by the interlayer coupling, similar to the Ising model on the stacked triangular layers [32][33][34][35][36][37][38]. Coming back to the consideration of the energetics (iii), the two b p in a R cube not included in a buckled hexagon [b pa and b p b in the inset of Fig.…”

Section: Ground Statementioning

confidence: 74%

Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

et al. 2017

View full text Add to dashboard Cite

Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a threedimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent Z2 degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic -the flux configuration is subextensively degenerate while showing a directional order with broken C3 rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for the thermodynamics. arXiv:1707.02794v4 [cond-mat.str-el]

show abstract

Section: Ground Statementioning

confidence: 74%

Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Geometric frustration arises on various triangle-based lattices such as one-dimensional (1D) trestle lattice, two-dimensional (2D) triangular and kagome lattices and three-dimensional (3D) B-site spinel and pyrochlore lattices, and are typically investigated in spin systems 1 2 3 . It has become well known that the introduction of quantum fluctuations in geometrically frustrated magnets gives rise to a rich variety of interesting quantum phases 3 4 5 , as discussed with both the transverse Ising models 6 7 8 9 and Heisenberg models 10 11 . Especially, exotic quantum spin liquids (QSLs), characterized by either gapped or gapless itinerant excitations 3 4 , have been theoretically predicted to show extremely intriguing phenomena.…”

mentioning

confidence: 99%

Quantum electric-dipole liquid on a triangular lattice

Shen

Song

et al. 2016

Nat Commun

View full text Add to dashboard Cite

Geometric frustration and quantum fluctuations may prohibit the formation of long-range ordering even at the lowest temperature, and therefore liquid-like ground states could be expected. A good example is the quantum spin liquid in frustrated magnets. Geometric frustration and quantum fluctuations can happen beyond magnetic systems. Here we propose that quantum electric-dipole liquids, analogues of quantum spin liquids, could emerge in frustrated dielectrics where antiferroelectrically coupled electric dipoles reside on a triangular lattice. The quantum paraelectric hexaferrite BaFe12O19 with geometric frustration represents a promising candidate for the proposed electric-dipole liquid. We present a series of experimental lines of evidence, including dielectric permittivity, heat capacity and thermal conductivity measured down to 66 mK, to reveal the existence of an unusual liquid-like quantum phase in BaFe12O19, characterized by itinerant low-energy excitations with a small gap. The possible quantum liquids of electric dipoles in frustrated dielectrics open up a fresh playground for fundamental physics.

show abstract

“…For instance, a vertical 3D stacking of TLIMs produces a low-T partially disordered antiferromagnetic (PDA) phase consisting of two ordered sublattices with opposite magnetizations and the third one that remains disordered [10][11][12][13][14][15]. By adding a transverse field, we obtain the quantum Ising model (QIM) that also contains a low-T PDA phase stabilized by quantum fluctuations [16][17][18].…”

mentioning

confidence: 99%

Stiffness from Disorder in Triangular-Lattice Ising Thin Films

et al. 2014

View full text Add to dashboard Cite

We study the triangular lattice Ising model with a finite number of vertically stacked layers and demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions, which results in an extended disordered regime down to T = 0. Numerical results are complemented with the derivation of an effective low-temperature dimer theory. Contrary to order by disorder, we present a new scenario for fluctuation-induced ordering in frustrated spin systems. While short-range spin-spin correlations are enhanced by fluctuations, quasi-long-range ordering is precluded at low enough temperatures by proliferation of topological defects.PACS numbers: 64.60.F-, 05.50.+qIntroduction.-The antiferromagnetic triangular lattice Ising model (TLIM) is the paradigmatic example of geometric frustration [1][2][3]. Despite its simplicity, the TLIM exhibits all the defining features of a highly frustrated magnet. The extensive degeneracy of its ground state or Wannier manifold, which comprises any state without three parallel spins on the same triangle, leads to a residual entropy density S ≈ 0.323k B . This property makes the system very sensitive to perturbations, as is manifested in the algebraic spin-spin correlations. Simple perturbations, such as further-neighbor couplings, relieve the frustration and induce long-range order (LRO) or quasi-LRO [4][5][6][7][8]. The ground state degeneracy can also be lifted via the order by disorder mechanism [9]. For instance, a vertical 3D stacking of TLIMs produces a low-T partially disordered antiferromagnetic (PDA) phase consisting of two ordered sublattices with opposite magnetizations and the third one that remains disordered [10][11][12][13][14][15]. By adding a transverse field, we obtain the quantum Ising model (QIM) that also contains a low-T PDA phase stabilized by quantum fluctuations [16][17][18].In this Letter, we show an exotic classical spin liquid phase with unusual pseudocritical correlations in a simple generalization of the TLIM, namely, a vertically stacked finite number N z of triangular layers. This new phase consists of a line of pseudocritical disordered states. Surprisingly, spins become more correlated at short distances with increasing temperature: the spin correlation falls off like ∼r −η(T ) e −r/ξ with the exponentially large correlation length, ln ξ ∝ J/T , and the short-distance effective power law decay becomes slower at higher T (dη/dT < 0) [19]. This is similar to Villain's order by disorder [9]. However, while thermal fluctuations increase short-distance spin-spin correlations, hence the stiffness of the effective field theory, quasi-LRO sets in only when the stiffness reaches a critical value necessary to suppress the proliferation of topological defects.Our study is in part motivated by recent advances in filmgrowth techniques [20,21] and fabrication of artificial spin systems [22]. The model Hamiltonian is

show abstract

String Picture for a Model of Frustrated Quantum Magnets and Dimers

Cited by 17 publications

References 36 publications

Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

Chiral spin liquids at finite temperature in a three-dimensional Kitaev model

Quantum electric-dipole liquid on a triangular lattice

Stiffness from Disorder in Triangular-Lattice Ising Thin Films

Contact Info

Product

Resources

About