Fourfold degenerate columnar-dimer ground state in square lattice antiferromagnets

Kumar, Rakesh; Kumar, Brijesh

doi:10.1103/physrevb.77.144413

Cited by 11 publications

(25 citation statements)

References 40 publications

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“…In particular, stimulated by the recent discussion of deconfined quantum criticality in two-dimensional spin systems, 40,41 a renewed interest in the nature of the phase transition between the semiclassical Néel phase and the quantum paramagnetic phase has emerged. 27,30,42,43 However, in spite of numerous intensive efforts focused on the transition between the Néel and the quantum paramagnetic phases in the J 1 -J 2 squarelattice antiferromagnet and some other candidate models, [44][45][46][47][48][49] this field remains still highly controversial. For completeness we mention that the classical square-lattice J 1 -J 2 model ͑s → ϱ͒ exhibits a direct first-order transition between Néel state and collinear state at J 2 / J 1 =1/ 2.…”

Section: Introductionmentioning

confidence: 99%

Ground state phases of the spin-1/2J1–J2Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Darradi¹,

Derzhko

Zinke³

et al. 2008

Phys. Rev. B

192

295

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Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 J 1 -J 2 frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the Néel and collinear orders are J 2 c1 Ϸ͑0.44Ϯ 0.01͒J 1 and J 2 c2 Ϸ͑0.59Ϯ 0.01͒J 1 , respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by ͓Sirker et al. Phys. Rev. B 73, 184420 ͑2006͔͒, our data do not provide evidence for the transition from the Néel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

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Section: Introductionmentioning

confidence: 99%

Ground state phases of the spin-1/2J1–J2Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Darradi¹,

Derzhko

Zinke³

et al. 2008

Phys. Rev. B

192

295

View full text Add to dashboard Cite

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“…A spin-gapped state consisting of the product of plaquettes has also been proposed earlier in the intermediate region   a 0.7 0.9 [15][16][17], and very recently it is confirmed by OPEN ACCESS RECEIVED high-pressure inelastic neutron scattering experiments [18]. These two important models have been generalized further [19][20][21][22] and inspired many other interesting exactly solvable constructions [23,24]. In most generic models, an exact dimer ground state is elusive.…”

Section: Introductionmentioning

confidence: 57%

“…A triplon mean-field theory is developed with respect to a quantum paramagnetic state in which spin-singlets are 'frozen' on some lattice units (for example, dimers or plaquettes) [23,24,26,[42][43][44]. Generally we consider homogeneity of spin-singlet objects in a quantum paramagnetic state, although, in principle, heterogeneous spin-singlet objects can also be taken.…”

Section: Triplon Mean-field Theorymentioning

confidence: 99%

“…Thus, triplet excitations ('triplons') disperse in the singlet background and are responsible for a phase transition between a quantum paramagnetic phase and a magnetically ordered phase. In the following two subsections, we formulate two kinds of triplon mean-field theories for Hamiltonian : dimer triplon mean-field theory [23,24,26,43] and plaquette triplon mean-field theory [42,44]. These are devised by choosing a suitable dimerization and plaquettization on a lattice, respectively.…”

Section: Triplon Mean-field Theorymentioning

confidence: 99%

“…They describe it not in terms of the usual order parameters as required in the Landau-Ginzburg theory but using the 'deconfined' quantum criticality notion in which the free spinons at the quantum critical point act as the essential degrees of freedom. With inspiring by this remarkable suggestion, many quantum spin models have been constructed and investigated to check this scenario [23,24,[39][40][41]. The signatures of such a deconfined quantum critical transition seem to have been observed in a spin-1 2 multiple-spin exchange model on the square lattice [40].…”

Section: Introductionmentioning

confidence: 99%

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Triplon mean-field analysis of an antiferromagnet with degenerate Shastry–Sutherland ground states

Kumar¹,

Kumar²

2017

J. Phys. Commun.

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We look into the quantum phase diagram of a spin-1 2 antiferromagnet on the square lattice with degenerate Shastry-Sutherland ground states, for which only a schematic phase diagram is known so far. Many exotic phases were proposed in the schematic phase diagram by the use of exact diagonalization on very small system sizes. In our present work, an important extension of this antiferromagnet is introduced and investigated in the thermodynamic limit using triplon mean-field theory. Remarkably, this antiferromagnet shows a stable plaquette spin-gapped phase like the original Shastry-Sutherland antiferromagnet, although both of these antiferromagnets differ in the Hamiltonian construction and ground state degeneracy. We propose a sublattice columnar dimer phase which is stabilized by the second and third neighbor antiferromagnetic Heisenberg exchange interactions. There are also some commensurate and incommensurate magnetically ordered phases, and other spin-gapped phases which find their places in the quantum phase diagram. Mean-field results suggest that there is always a level-crossing phase transition between two spin-gapped phases, whereas in other situations, either a level-crossing or a continuous phase transition happens. s where L is the total number of lattice sites, = + J J K 2 2 4 3 , = + J J K 3 3 2 3 1 , z = J J 2 and plot eigenenergies of the Hamiltonian  p in figure 7. If z < 1 3 (equivalently, < J J 2 1 1 2 ), the two lowest eigenvalues -+ J J 2 1 1 2 2 and -+ J J 2 -+ -+ + J J J J J J 1 , z = J J 2 . 1 , d = J J 3

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K -edge and L3 -edge RIXS study of columnar and staggered quantum dimer phases of the square lattice Heisenberg model

He¹,

Datta²,

Yao³

2020

Phys. Rev. B

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We compute the K and L 3 -edge resonant inelastic x-ray scattering (RIXS) spectrum of the columnar and the staggered quantum dimer states accessible to the square lattice Heisenberg magnet. Utilizing a bond operator representation mean field theory we investigate the RIXS features of the one-and two-triplon excitation spectrum supported by the quantum dimer model in the background of condensed singlet excitation. We find that the two-triplon excitation boundary lies within a 124 (78) meV to 414 (345) meV energy range for the columnar (staggered) phase. We estimated the two-triplon gap to be 124 (78) meV for the columnar (staggered) dimer phase. The highest intensity of the K -edge RIXS spectrum is centralized approximately around the (π/2, π/2) point for both the columnar and the staggered phases. At the L 3 -edge we study the one-and two-triplon signal considering experimental scattering geometry, polarization restriction, and experimental resolution effects. Our calculations find an additional contribution to the two-triplon RIXS signal, not previously reported in the literature, that originates from the local hard-core dimer constraint. This leads to a finite non-zero signal at the (0,0) momentum transfer which can offer an explanation for the existing ladder RIXS experiments and also predicts a non-zero signal for the two-dimensional quantum dimer system. We find that the L 3 edge RIXS response of the one-and two-triplon signal could exist in antiphase rung modulation for zero and π as found in inelastic neutron scattering. We also consider static crystal twinning at the L 3 -edge RIXS signal to mimic realistic crystal effects. Since the disordered phase has the potential to harbor a variety of quantum paramagnetic states, our RIXS calculations provide useful signatures to identify the true nature of the ordering pattern. PACS number(s): 78.70. Ck, 75.10.Jm

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Fourfold degenerate columnar-dimer ground state in square lattice antiferromagnets

Cited by 11 publications

References 40 publications

Ground state phases of the spin-1/2J1–J2Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Ground state phases of the spin-1/2J1–J2Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Triplon mean-field analysis of an antiferromagnet with degenerate Shastry–Sutherland ground states

K -edge and L3 -edge RIXS study of columnar and staggered quantum dimer phases of the square lattice Heisenberg model

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