Spin-Peierls, valence-bond solid, and Néel ground states of low-dimensional quantum antiferromagnets

Read, N.; Sachdev, Subir

doi:10.1103/physrevb.42.4568

Cited by 515 publications

(765 citation statements)

References 64 publications

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“…After substituting the bare values of Eq. (18), this is in a perfect agreement with the spin wave calculation, while the theory of Ref. 36 yields the same velocity v = 1 for all three modes.…”

Section: Effective Low-energy Field Theory For the Sp(n ) Heisenbsupporting

confidence: 78%

“…18 The Sp(N ) symmetry of the Hamiltonian is enlarged to SU (N ) at the point J = 0, where the two-site Hamiltonian becomes a permutation operator of two Ncomponent objects. Since the lattice is bipartite, the enlargement of symmetry to SU (N ) happens also at J ′ = 0 point.…”

Section: Effective Low-energy Field Theory For the Sp(n ) Heisenbmentioning

confidence: 99%

“…(18) In particular, note the different signs of g 1 and g 2 . The first two terms in the action (17) constitute the familiar action of the CP N −1 model, [23][24][25][26][27] that has been extensively studied as an effective theory for SU (N ) antiferromagnets 18,22 .…”

Section: Effective Low-energy Field Theory For the Sp(n ) Heisenbmentioning

confidence: 99%

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Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

Kolezhuk¹,

Vekua²

2011

Phys. Rev. B

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We study the magnetic phase diagram of spin-3 2 fermions in a spatially anisotropic square optical lattice at quarter filling (corresponding to one particle per lattice site). In the limit of the large onsite repulsion the system can be mapped to the so-called Sp(N ) Heisenberg spin model with N = 4. We analyze the Sp(N ) spin model with the help of the large-N field-theoretical approach and show that the effective theory corresponds to the Sp(N ) extension of the CP N−1 model, with the Lorentz invariance generically broken. We obtain the renormalization flow of the model couplings and show that although the Sp(N ) terms are seemingly irrelevant, their presence leads to a renormalization of the CP N−1 part of the action, driving a phase transition. We further consider the influence of the external magnetic field (the quadratic Zeeman effect), and present the qualitative analysis of the ground state phase diagram.

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Section: Effective Low-energy Field Theory For the Sp(n ) Heisenbsupporting

confidence: 78%

Section: Effective Low-energy Field Theory For the Sp(n ) Heisenbmentioning

confidence: 99%

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Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

Kolezhuk¹,

Vekua²

2011

Phys. Rev. B

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“…The Berry's phases associated with the instantons lead to columnar spin-Peierls order [24,8] (equivalent to dimer order) as indicated in figure 4. The dimerization pattern induced in the decoupled chain phase is similar to that found by White and Affleck [21] for a pair of chains with zigzag coupling.…”

Section: Incommensurate Phasesmentioning

confidence: 99%

Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs₂CuCl₄and to the layered organic superconductors κ-(BEDT-TTF)₂X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)

Chung

Marston

McKenzie

2001

J. Phys.: Condens. Matter

107

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We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials κ-(BEDT-TTF)2X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs2CuCl4. We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite-N are also discussed. For parameters relevant to Cs2CuCl4 the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap. A metal-insulator transition occurs at intermediate values of the interaction strength.

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“…Now add further neighbor exchange couplings until magnetic order is lost and a spin gap appears. We will show that the ground state undergoes a novel, second-order quantum phase transition to a state with bond order: translational symmetry is spontaneously broken [19,20] so that the resulting lattice structure has an even number of S = 1/2 spins per unit cell. So aspects of the non-zero spin excitations in this paramagnet are very similar to the "dimerized" systems considered in Section 2, and experimentally they will appear to be almost identical.…”

Section: Introductionmentioning

confidence: 99%

Quantum phases and phase transitions of Mott insulators

Sachdev

2004

Quantum Magnetism

Self Cite

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Summary. This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S = 1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S = 1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S = 1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-GinzburgWilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.

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Spin-Peierls, valence-bond solid, and Néel ground states of low-dimensional quantum antiferromagnets

Cited by 515 publications

References 64 publications

Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs₂CuCl₄and to the layered organic superconductors κ-(BEDT-TTF)₂X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)

Quantum phases and phase transitions of Mott insulators

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Spin-Peierls, valence-bond solid, and Néel ground states of low-dimensional quantum antiferromagnets

Cited by 515 publications

References 64 publications

Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

Magnetic phases of spin-32fermions on a spatially anisotropic square lattice

Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4and to the layered organic superconductors κ-(BEDT-TTF)2X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)

Quantum phases and phase transitions of Mott insulators

Contact Info

Product

Resources

About

Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs₂CuCl₄and to the layered organic superconductors κ-(BEDT-TTF)₂X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)