Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase

Doretto, R. L.; Vojta, Matthias

doi:10.1103/physrevb.85.104416

Cited by 14 publications

(32 citation statements)

References 43 publications

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“…44, provides reasonable results for the excitation spectra (see below) without the discontinuities and logarithmic singularities reported in Ref. 46.…”

Section: Cubic-quartic Approximationsupporting

confidence: 80%

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Plaquette valence-bond solid in the square-latticeJ1-J2antiferromagnet Heisenberg model: A bond operator approach

Doretto

2014

Phys. Rev. B

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We study the plaquette valence-bond solid phase of the spin-1/2 J1-J2 antiferromagnet Heisenberg model on the square lattice within the bond-operator theory. We start by considering four S = 1/2 spins on a single plaquette and determine the bond operator representation for the spin operators in terms of singlet, triplet, and quintet boson operators. The formalism is then applied to the J1-J2 model and an effective interacting boson model in terms of singlets and triplets is derived. The effective model is analyzed within the harmonic approximation and the previous results of Zhitomirsky and Ueda [Phys. Rev. B 54, 9007 (1996)] are recovered. By perturbatively including cubic (triplet-triplet-triplet and singlet-triplet-triplet) and quartic interactions, we find that the plaquette valence-bond solid phase is stable within the parameter region 0.34 < J2/J1 < 0.59, which is narrower than the harmonic one. Differently from the harmonic approximation, the excitation gap vanishes at both critical couplings J2 = 0.34 J1 and J2 = 0.59 J1. Interestingly, for J2 < 0.48 J1, the excitation gap corresponds to a singlet-triplet excitation at the Γ point while, for J2 > 0.48 J1, it is related to a singlet-singlet excitation at the X = (π/2, 0) point of the tetramerized Brillouin zone.

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“…44, provides reasonable results for the excitation spectra (see below) without the discontinuities and logarithmic singularities reported in Ref. 46.…”

Section: Cubic-quartic Approximationsupporting

confidence: 80%

“…The above equation is solved within the on-shell approximation, 44,46 where the self-energy is evaluated at the bare (harmonic) single-particle energy:…”

Section: Cubic-quartic Approximationmentioning

confidence: 99%

Plaquette valence-bond solid in the square-latticeJ1-J2antiferromagnet Heisenberg model: A bond operator approach

Doretto

2014

Phys. Rev. B

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“…It has further been shown that the geometric frustration plays an important role in the physics of non-Fermi liquid of doped Mott insulators and high-Tc superconductors [2][3][4][5][6] . Typically, frustrated magnetic systems show extensive degeneracy of their ground states in the classical limit, which can be lifted by addition of thermal or quantum fluctuations, or perturbations such as spin-orbit interactions, spin-lattice couplings, further neglected exchange terms and impurities.…”

Section: Introductionmentioning

confidence: 99%

Emergence of string valence-bond-solid state in the frustrated J1−J2 transverse field Ising model on the square lattice

et al. 2016

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We investigate the ground state nature of the transverse field Ising model on the J1 − J2 square lattice at the highly frustrated point J2/J1 = 0.5. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for non-zero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (COA) with multi-spin cluster type fluctuations above a non-magnetic cluster ordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the Hellmann-Feynman theorem. However, the stringtype anharmonic fluctuations of COA are able to lift the degeneracy toward a string-valence bond solid (VBS) state, which is obtained from an effective theory consistent with the Hellmann-Feynman theorem as well. Our results are further confirmed by implementing numerical tree tensor network simulation. The emergent non-magnetic string-VBS phase is gapped and breaks lattice rotational symmetry with only two-fold degeneracy, which bears a continuous quantum phase transition at Γ/J1 ∼ = 0.50 to the quantum paramagnet phase of high fields. The critical behavior is characterized by ν ∼ = 1.0 and γ ∼ = 0.33 exponents.

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“…These systems provide excellent experimental setups to probe quantum critical behavior through field-and pressuretuning, and have motivated some notable theoretical works based on bond-operator techniques [21][22][23][24].…”

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confidence: 99%

“…1), where J 0 J 1 > J 2 > 0. The mapping of the dimerized quantum antiferromagnet to a model of hard-core bosons is achieved by expressing the spin operators of each dimer in terms of singlet and triplet bond operators [21][22][23][24],…”

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confidence: 99%

Bose and Mott glass phases in dimerized quantum antiferromagnets

Thomson

Krüger

2015

Phys. Rev. B

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We examine the effects of disorder on dimerized quantum antiferromagnets in a magnetic field, using the mapping to a lattice gas of hard-core bosons with finite-range interactions. Combining a strong-coupling expansion, the replica method, and a one-loop renormalization group analysis, we investigate the nature of the glass phases formed. We find that away from the tips of the Mott lobes, the transition is from a Mott insulator to a compressible Bose glass, however the compressibility at the tips is strongly suppressed. We identify this finding with the presence of a rare Mott glass phase not previously described by any analytic theory for this model and demonstrate that the inclusion of replica symmetry breaking is vital to correctly describe the glassy phases. This result suggests that the formation of Bose and Mott glass phases is not simply a weak localization phenomenon but is indicative of much richer physics. We discuss our results in the context of both ultracold atomic gases and spin-dimer materials. The disordered Bose-Hubbard model is an ideal system for the thorough study of the effects of disorder on strongly interacting quantum systems. Ultracold atoms in optical lattices [1][2][3][4][5] perhaps offer the most direct experimental system in which to realize Bose-Hubbard physics, however the small system sizes and destructive nature of many measurements limit the efficacy of experiments. Dimerized quantum antiferromagnets present a compelling alternative environment due to an exact mapping to a lattice gas of bosons with hard-core repulsion [6][7][8]. These systems consist of lattices of pairs of spins (dimers) which, in the ground state, are all in a singlet configuration. This state can be viewed as an 'empty' lattice while a local triplet excitation can be thought of as a site occupied by a spin-1 boson ('triplon').Condensation of these bosons corresponds to exotic magnetically ordered states seen in materials such as [18][19][20]. These systems provide excellent experimental setups to probe quantum critical behavior through field-and pressuretuning, and have motivated some notable theoretical works based on bond-operator techniques [21][22][23][24].Recent experiments on disordered quantum antiferromagnets have seen evidence for novel glassy phases, particularly in bromine-doped dichloro-tetrakis-thioureanickel (DTN) [25] where both Bose and Mott glass phases of bosonic quasiparticles have been observed. Such phases have also been seen in other materials [26][27][28][29] and in quantum Monte Carlo simulations [30][31][32][33][34].Motivated by these experimements, in this Letter we present an analytic treatment of dimerized quantum antiferromagnets with weak intra-dimer bond disorder us- ing the hard-core boson formalism. We perform a strong coupling expansion [35,36] combined with a replica disorder average to derive an effective field theory. From a renormalization group (RG) analysis we obtain the phase boundaries between the gapped magnetic states -or in boson language, incompressible Mott ins...

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Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase

Cited by 14 publications

References 43 publications

Plaquette valence-bond solid in the square-latticeJ1-J2antiferromagnet Heisenberg model: A bond operator approach

Plaquette valence-bond solid in the square-latticeJ1-J2antiferromagnet Heisenberg model: A bond operator approach

Emergence of string valence-bond-solid state in the frustrated J1−J2 transverse field Ising model on the square lattice

Bose and Mott glass phases in dimerized quantum antiferromagnets

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