A expandable series of non-linear σ models with instantons

D’Adda, A.; Lüscher, Martin; Vecchia, P. Di

doi:10.1016/0550-3213(78)90432-7

Cited by 736 publications

(477 citation statements)

References 12 publications

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“…Different behavior occurs for m in the range −2 < m ≤ 0. In both the spin chains/vertex models and sigma models, the exponents in the critical theories are independent of n for each m. For m > 2 there are arguments that the transition is first order, as originally found using the 1/m expansion [30]. We refer to Ref.…”

Section: Spin Chains and Sigma Modelsmentioning

confidence: 81%

ExactS-matrices for supersymmetric sigma models and the Potts model

Fendley

Read

2002

J. Phys. A: Math. Gen.

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We study the algebraic formulation of exact factorizable S-matrices for integrable twodimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie "supersymmetry" algebras sl(m + n|n) (m = 1, 2, n > 0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These Smatrices represent the perturbation of the conformal theory at θ = π by a small change in the topological angle θ. The m = 1, n = 1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for θ = 0 and θ = π, in certain other supersymmetric sigma models.

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Section: Spin Chains and Sigma Modelsmentioning

confidence: 81%

ExactS-matrices for supersymmetric sigma models and the Potts model

Fendley

Read

2002

J. Phys. A: Math. Gen.

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“…In particular, we are interested in the Z 4 symmetry which rotates the four sublattices in Fig 9c into each other, as the values of X seem to distinguish between them. Let us consider the symmetry R n which rotates lattice anticlockwise by an angle nπ/2 about the direct lattice point at the center of a plaquette in Fig 9c, associated with the transformation in (53). It is easy to see that Z 1,4 remains invariant under R n provided we simultaneously rotate the angular variables ϑ:…”

Section: Berry Phasesmentioning

confidence: 99%

Quantum phases and phase transitions of Mott insulators

Sachdev

2004

Quantum Magnetism

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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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“…25,26 This critical value depends on N , and from the numerical work [28][29][30] it is known that the two-dimensional CP N −1 model on a square lattice is disordered for N/n c ≥ 5.…”

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

confidence: 99%

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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A expandable series of non-linear σ models with instantons

Cited by 736 publications

References 12 publications

ExactS-matrices for supersymmetric sigma models and the Potts model

ExactS-matrices for supersymmetric sigma models and the Potts model

Quantum phases and phase transitions of Mott insulators

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

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