Confinement of spinons in the CPM-1 model (original) (raw)
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Quantum antiferromagnet at finite temperature: A gauge-field approach
Physical review. B, Condensed matter, 1994
Starting from the CP N−1 model description of the thermally disordered phase of the D = 2 quantum antiferromagnet, we examine the interaction of the Schwinger-boson spin-1/2 mean-field excitations with the generated gauge (chirality) fluctuations in the framework of the 1/N expansion. This interaction dramatically supresses the one-particle motion, but enhances the staggered static susceptibility. This means that actual excitations in the system are represented by the collective spin-1 excitations , whereas one-particle excitations disappear from the problem. We also show that massive fluctuations of the constraint field are significant for the susceptibility calculations. A connection with the problem of a particle in random magnetic field is discussed.
Physical Review B, 2004
The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a twodimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Qi = 1 on each lattice site i , which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, ξ(T ) ∝ exp(a J/T ) , come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T . This drawback, which is caused by overdamping, is overcome in a 'minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths λ > ξ and in the short-range-order regime at λ < ξ . We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.
Model with propagating spinons beyond one dimension
Physical Review B, 2003
For the model of frustrated spin-1/2 Heisenberg magnet described in A. A. Nersesyan and A. M. Tsvelik, (Phys. Rev. B67, 024422 (2003)) we calculate correlation functions of staggered magnetization and dimerization. The model is formulated as a collection of antiferromagnetic chains weakly coupled by a frustrated exchange interaction. The calculation done for the case of four chains demonstrates that these functions do not vanish. Since the correlation functions in question factorize into a product of correlation functions of spinon creation and annihilation operators, this constitutes a proof that spinons in this model propagate in the direction perpendicular to the chains.
Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field
The European Physical Journal B, 2000
We simulated the field-dependent magnetization m(H, T ) and the uniform susceptibility χ(H, T ) of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of χ(H, T ) at small T, H: limT→0 limH→0 χ(H, T ) = 1/(2J0)(1 − 1/D) and limH→0 limT→0 χ(H, T ) = 1/(2J0), where D = 3 is the number of spin components, J0 = zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results (D.A. Garanin, J. Stat. Phys. 83, 907 (1996)).
Universal properties of frustrated spin systems: 1/N-expansion and renormalization group approaches
Nuclear Physics B, 2009
We consider a quantum two-dimensional O(N ) ⊗ O(2)/O(N − 2) ⊗ O(2) diag nonlinear sigma model for frustrated spin systems and formulate its 1/N -expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions, respectively. The ground state phase diagram of this model is obtained within the 1/N -expansion and 2+ε renormalization group approaches. The temperature dependence of correlation length in the renormalized classical and quantum critical regimes is discussed. In the region ρ in < ρ out , χ in < χ out of the symmetry broken ground state (ρ in,out and χ in,out are the in-and out-of-plane spin stiffnesses and susceptibilities), where the mass M µ of the vector field can be arbitrarily small, physical properties at finite temperatures are universal functions of ρ in,out , χ in,out , and temperature T . For small M µ these properties show a crossover from low-to high temperature regime at T ∼ M µ . For ρ in > ρ out or χ in > χ out finite-temperature properties are universal functions only at sufficiently large M µ . The high-energy behaviour in the latter regime is similar to the Landau-pole dependence of the physical charge e on the momentum scale in quantum electrodynamics, with mass M µ playing a role of e −1 . The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.
Schwinger Bosons Approaches to Quantum Antiferromagnetism
Introduction to Frustrated Magnetism, 2011
The use of large N approximations to treat strongly interacting quantum systems been very extensive in the last decade. The approach originated in elementary particles theory, but has found many applications in condensed matter physics. Initially, the large N expansion was developed for the Kondo and Anderson models of magnetic impurities in metals. Soon thereafter it was extended to the Kondo and Anderson lattice models for mixed valence and heavy fermions phenomena in rare earth compounds .
1/N expansion for critical exponents of magnetic phase transitions in the CPN-1 model for 2<d<4
Physical Review B, 1996
Critical exponents in the CP N−1 model, which describes localized-moment ferro-and antiferromagnets (N = 2 in the Heisenberg model), are calculated from two-particle Green's functions to first order in 1/N . For d = 2 + ε the results agree with earlier renormalization group calculations. For d = 3 the leading 1/N -corrections turn out to be very large at N = 2. For d = 4 − ε the 1/N -corrections are small at any N and insufficient to describe correctly the magnetic phase transition.
Bound state models for fermion Regge poles
Nuclear Physics B, 1974
Trajectories of fermion Regge poles are calculated in a model in which a spln ~-parficle is bound to a spin 0 core. The leading trajectory with parity (-1)/-~ is much like the boson trajectory generated by similar interactions. The opposite parity trajectory satisfies the constraints of MacDowell symmetry, yet is totally distinct for s > 0. The model produces a trajectory which above the elastic threshold has a small negative Im a and an increasing Re a. Such a trajectory produces poles on the physical sheet of the energy plane.
Localized-versus-extended spin fluctuations in quantum antiferromagnets
Physical Review B, 1991
A recently devised trial wave function for the Heisenberg-Ising model is tested against linear spin waves in the whole anisotropic region. The above wave function is asymptotically exact in the limit of high anisotropy, and is constructed using locah'zed spin fluctuations over Neel states. The structure of this trial state is compared with the one presented by the zero-point state of the linear-spinwave theory. Striking similarities are found between both, despite that spin waves represent Auctuations that encompass the whole system. A crossover between both approaches near the isotropic point is attributed to a delocalization of spin fluctuations. We present results for one and two dimensions, and compare with exact results or numerical simulations.