Quantum Integrals of Motion for the Heisenberg Spin Chain

Grabowski, Marek; Mathieu, Pierre

doi:10.1142/s0217732394002057

Cited by 54 publications

(80 citation statements)

References 14 publications

(19 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The current-current correlation function is to be evaluated in thermal equilibrium and poses the main problem of our work. However, as already pointed out in [8,[11][12][13][14][15]] the total thermal current operator J E commutes with the Hamiltonian H of the XXZ chain. Hence we find…”

Section: Introductionmentioning

confidence: 72%

“…For the XXZ chain as a quantum spin model (or alternatively as a lattice gas model) the spin transport (electrical transport) was investigated analytically [1] by use of a method suggested in [2] and numerically [3,4] with so far inconclusive results about the finite temperature Drude weight. In [5][6][7] the thermal conductivity of the quasi one-dimensional magnetic system (Sr,Ca) 14 Cu 24 O 41 was investigated showing anomalous transport properties along the chain directions. In [7] it was argued that the large thermal conductivity can not be explained in terms of phonons.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The thermal conductivity of the spin-½ XXZ chain at arbitrary temperature

Klümper

Sakai

2002

J. Phys. A: Math. Gen.

177

266

View full text Add to dashboard Cite

Motivated by recent investigations of transport properties of strongly correlated 1d models and thermal conductivity measurements of quasi 1d magnetic systems we present results for the integrable spin-1/2 XXZ chain. The thermal conductivity κ(ω) of this model has Re κ(ω) =κδ(ω), i.e. it is infinite for zero frequency ω. The weightκ of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low and high temperature limits are studied analytically.

show abstract

Section: Introductionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

The thermal conductivity of the spin-½ XXZ chain at arbitrary temperature

Klümper

Sakai

2002

J. Phys. A: Math. Gen.

177

266

View full text Add to dashboard Cite

show abstract

“…The eigenvalues of the charges q k define the complete set of quantum numbers parameterizing the eigenspectrum of the dilatation operator. Integrability imposes a nontrivial analytical structure of anomalous dimensions of Wilson operators and implies the double degeneracy of eigenvalues with the opposite parity [2,20,3]. To the lowest order of perturbation theory this property has been verified in Refs.…”

Section: • Planar Limitmentioning

confidence: 88%

Integrability of two-loop dilatation operator in gauge theories

Belitsky¹,

Korchemsky²,

Müller³

2006

Nuclear Physics B

View full text Add to dashboard Cite

We study the two-loop dilatation operator in the noncompact SL(2) sector of QCD and supersymmetric Yang-Mills theories with N = 1, 2, 4 supercharges. The analysis is performed for Wilson operators built from three quark/gaugino fields of the same helicity belonging to the fundamental/adjoint representation of the SU(3)/SU(N c ) gauge group and involving an arbitrary number of covariant derivatives projected onto the light-cone. To one-loop order, the dilatation operator inherits the conformal symmetry of the classical theory and is given in the multi-color limit by a local Hamiltonian of the Heisenberg magnet with the spin operators being generators of the collinear subgroup of full (super)conformal group. Starting from two loops, the dilatation operator depends on the representation of the gauge group and, in addition, receives corrections stemming from the violation of the conformal symmetry. We compute its eigenspectrum and demonstrate that to two-loop order integrability survives the conformal symmetry breaking in the aforementioned gauge theories, but it is violated in QCD by the contribution of nonplanar diagrams. In SYM theories with extended supersymmetry, the N −dependence of the two-loop dilatation operator can be factorized (modulo an additive normalization constant) into a multiplicative c-number. This property makes the eigenspectrum of the two-loop dilatation operator alike in all gauge theories including the maximally supersymmetric theory. Our analysis suggests that integrability is only tied to the planar limit and it is sensitive neither to conformal symmetry nor supersymmetry.

show abstract

“…In fact, up to a trivial scale and shift, the conserved current J (2) is identical to the r.h.s.of the upper equation, see also [51][52][53][54][55][56].…”

Section: Thermal Transportmentioning

confidence: 99%

Integrability of quantum chains: Theory and applications to the spin-1/2 XXZ chain

Klümper

2004

Quantum Magnetism

112

View full text Add to dashboard Cite

Summary. In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively we present the treatment of integrable quantum systems at finite temperature on the basis of a lattice path integral formulation and a suitable transfer matrix approach (quantum transfer matrix). The general method is carried out for the seminal model of the spin-1/2 XXZ chain for which thermodynamic properties like specific heat, magnetic susceptibility and the finite temperature Drude weight of the thermal conductivity are derived.

show abstract

Quantum Integrals of Motion for the Heisenberg Spin Chain

Cited by 54 publications

References 14 publications

The thermal conductivity of the spin-½ XXZ chain at arbitrary temperature

The thermal conductivity of the spin-½ XXZ chain at arbitrary temperature

Integrability of two-loop dilatation operator in gauge theories

Integrability of quantum chains: Theory and applications to the spin-1/2 XXZ chain

Contact Info

Product

Resources

About