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Modern Physics Letters B

SU(2) TO U(1) MICROSCOPIC TRANSITION IN THE HEISENBERG CHAIN

J. M. P. Carmelo, H. Q. Lin

Published Sep 10, 1993• 2 citations
Publisher

Abstract

We find that the nature of the gapless low-energy excitations of the spin 1/2 isotropic Heisenberg chain with J < 0 (antiferromagnetic chain at magnetic field H = 0) is different in the usual SU(2) "phase" and in the finite-magnetic field "phase" of symmetry U(1). This is shown to have relevant consequences for the microscopic description of the low-energy physics, which is different from the usual "spinon" two-kink picture. The use of the until now hidden "Landau-liquid" character of the model reveals a number of unexpected aspects of its physics and deepens the microscopic understanding of this fundamental quantum system.

DOI
10.1142/s0217984993001430

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We find that the nature of the gapless low-energy excitations of the spin 1/2 isotropic Heisenberg chain with J < 0 (antiferromagnetic chain at magnetic field H = 0) is different in the usual SU(2) "phase" and in the finite-magnetic field "phase" of symmetry U(1). This is shown to have relevant consequences for the microscopic description of the low-energy physics, which is different from the usual "spinon" two-kink picture. The use of the until now hidden "Landau-liquid" character of the model reveals a number of unexpected aspects of its physics and deepens the microscopic understanding of this fundamental quantum system.
We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains (spin ladder). It is shown that the system always has a spectral gap and the lower lying excitations are triplets. For the case of identical chains the model in the continuous limit is shown to be equivalent to four decoupled noncritical Ising models with the Z2{\mathit{Z}}_{2}Z2​\ifmmode\times\else\texttimes\fi{}SU(2) symmetry. For this case we obtain the exact expressions for asymptotics of spin-spin correlation functions. It is shown that when the chains have different exchange integrals J1{\mathit{J}}_{1}J1​\ensuremath{\gg}J2{\mathit{J}}_{2}J2​ the spectrum at low energies is described by the O(3)-nonlinear \ensuremath{\sigma} model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility. \textcopyright{} 1996 The American Physical Society.
We explore the nature of the quantum phase transition between a magnetically ordered state with collinear spin pattern and a gapless Z2{Z}_{2}Z2​ spin liquid in the Heisenberg-Kitaev model. We construct a slave particle mean-field theory for the Heisenberg-Kitaev model in terms of complex fermionic spinons. It is shown that this theory, formulated in the appropriate basis, is capable of describing the Kitaev spin liquid as well as the transition between the gapless Z2{Z}_{2}Z2​ spin liquid and the so-called stripy antiferromagnet. Within our mean-field theory, we find a discontinuous transition from the Z2{Z}_{2}Z2​ spin liquid to the stripy antiferromagnet. We argue that subtle spinon confinement effects, associated with the instability of gapped U(1)U(1)U(1) spin liquid in two spatial dimensions, play an important role at this transition. The possibility of an exotic continuous transition is briefly addressed.
Motivated by recent experiments on the Heisenberg S=1/2S=1/2S=1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled antiferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.
We perform a detailed study on the consequences of the nonsymmorphic symmetries in the Luttinger phase of the one-dimensional (1D) spin-12\frac{1}{2}21​ Kitaev-Heisenberg-Gamma model with an antiferromagnetic Kitaev interaction. Although the low-energy Hamiltonian has an emergent U(1) symmetry, the bosonization formulas for the spin operators contain ten nonuniversal coefficients which only respect the discrete nonsymmorphic symmetries and can be determined by our density matrix renormalization group simulations to a high degree of accuracy. Using the nonsymmorphic bosonization formulas, the response to weak magnetic field is analyzed, and the zigzag phase in the 2D Kitaev-Heisenberg-Gamma model is recovered by weakly coupling an infinite number of 1D chains. Furthermore, we find a line of critical points with an emergent SU(2)1\mathrm{SU}{(2)}_{1}SU(2)1​ conformal symmetry located on the boundary of the Luttinger liquid phase. Our work reveals the rich physics related to nonsymmorphic symmetries in strongly correlated quantum magnetic models, and demonstrates the usefulness of 1D analysis for understanding the 2D Kitaev physics.
The U(1)U(1)U(1) Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in 2+12+12+1 dimensions, where gapless modes exist but spinons and gauge fields are strongly coupled. Its existence was proposed in frustrated Heisenberg models in the presence of frustrating superexchange interactions by the (Abrikosov) fermionic representation of the spin operators [Wen, Phys. Rev. B 65, 165113 (2002)], supplemented by the Gutzwiller projection. Here, we construct charge-QQQ monopole excitations in the Heisenberg model on the triangular lattice with nearest-neighbor (J1{J}_{1}J1​) and next-nearest-neighbor (J2{J}_{2}J2​) couplings. In the highly frustrated regime, singlet and triplet monopoles with Q=1Q=1Q=1 become gapless in the thermodynamic limit; in addition, the energies for generic QQQ agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic $\ensuremath{\pi}$ fluxes are concentrated in the triangular plaquettes (in analogy with Z2{\mathbb{Z}}_{2}Z2​ visons), showing that these kinds of states do not play a relevant role at low energies. All our findings lend support to a stable U(1)U(1)U(1) Dirac spin liquid in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the triangular lattice.