Doped Heisenberg chains: Spin-S generalizations of the supersymmetric t-J model

Frahm, Holger

doi:10.1016/s0550-3213(99)00403-4

Cited by 26 publications

(25 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The spectrum of these states can be studied using the algebraic Bethe Ansatz. They are parameterized in terms of N h real numbers ν α and N h + N ↓ complex numbers λ j solving the Bethe Ansatz equations (BAE) [6,7]…”

Section: Bethe Ansatz For the Doped Spin-s Chainmentioning

confidence: 99%

“…In the limiting cases of the undoped (completely doped) model where the model reduces to the integrable spin-S (spin-(S − 1/2)) Takhtajan-Babujian spin chains, respectively, ǫ 2S (x) reduces to the massless spinon mode of these models which can be described by a SU(2) level-2S (level-(2S − 1)) WZW model. For arbitrary doping the contribution of the magnetic modes to the low temperature specific heat has been found to be [6,7]…”

Section: )mentioning

confidence: 99%

“…2S − 1 2 on sites i and j. In the DE model these hopping amplitudes favour the formation of a ferromagnetically ordered state, this feature is not shared by the integrable chains [6,7]. In terms of a microscopic model the electronic hopping has to be dressed by bilinears in the localized magnetic moments, similar to bond-charge type interactions considered in generalizations of the Hubbard model.…”

Section: Introductionmentioning

confidence: 99%

“…An important open question is the proper identification of effective field theories describing the low energy/low temperature behaviour of these systems [6,7,11,12]. In the limit of low hole concentration the low temperature specific heat indicates that the two gapless magnetic modes found for vanishing magnetic field can be described in terms of a level-2S SU(2) Wess-Zumino-Witten (WZW) model (which is the effective field theory of the undoped Takhtajan-Babujian spin-S chain [8][9][10]) and the minimal model M 2S+1 , respectively [6,7]. Upon variation of the doping a continous transition to a product SU(2) 2S−1 ⊗ SU(2) 1 satisfying a sum rule in the coefficients of the low temperature specific heat is observed [7].…”

Section: Introductionmentioning

confidence: 99%

“…In the limit of low hole concentration the low temperature specific heat indicates that the two gapless magnetic modes found for vanishing magnetic field can be described in terms of a level-2S SU(2) Wess-Zumino-Witten (WZW) model (which is the effective field theory of the undoped Takhtajan-Babujian spin-S chain [8][9][10]) and the minimal model M 2S+1 , respectively [6,7]. Upon variation of the doping a continous transition to a product SU(2) 2S−1 ⊗ SU(2) 1 satisfying a sum rule in the coefficients of the low temperature specific heat is observed [7]. For S = 1 a field theoretical description of these degrees of freedom has been proposed based on four Majorana fermions [6] (see also [11,12]).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Magnetic properties of doped Heisenberg chains

Frahm

Slavnov

2000

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

The magnetic susceptibility of systems from a class of integrable models for doped spin-S Heisenberg chains is calculated in the limit of vanishing magnetic field. For small concentrations x h of the mobile spin-(S − 1/2) charge carriers we find an explicit expression for the contribution of the gapless mode associated to the magnetic degrees of freedom of these holes to the susceptibility which exhibits a singularity for x h → 0 for sufficiently large S. We prove a sum rule for the contributions of the two gapless magnetic modes in the system to the susceptibility which holds for arbitrary hole concentration. This sum rule complements the one for the low temperature specific heat which has been obtained previously.

show abstract

Section: Bethe Ansatz For the Doped Spin-s Chainmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Magnetic properties of doped Heisenberg chains

Frahm

Slavnov

2000

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

show abstract

Dilatation operator in (super-)Yang–Mills theories on the light-cone

Belitsky

Derkachov

Korchemsky³

et al. 2005

Nuclear Physics B

115

View full text Add to dashboard Cite

The gauge/string correspondence hints that the dilatation operator in gauge theories with the superconformal SU(2, 2|N ) symmetry should possess universal integrability properties for different N . We provide further support for this conjecture by computing a one-loop dilatation operator in all (super)symmetric Yang-Mills theories on the light-cone ranging from gluodynamics all the way to the maximally supersymmetric N = 4 theory. We demonstrate that the dilatation operator takes a remarkably simple form when realized in the space spanned by single-trace products of superfields separated by light-like distances. The latter operators serve as generating functions for Wilson operators of the maximal Lorentz spin and the scale dependence of the two are in the one-to-one correspondence with each other. In the maximally supersymmetric, N = 4 theory all nonlocal light-cone operators are built from a single CPT self-conjugated superfield while for N = 0, 1, 2 one has to deal with two distinct superfields and distinguish three different types of such operators. We find that for the light-cone operators built from only one species of superfields, the one-loop dilatation operator takes the same, universal form in all SYM theories and it can be mapped in the multi-color limit into a Hamiltonian of the SL(2|N ) Heisenberg (super)spin chain of length equal to the number of superfields involved. For "mixed" light-cone operators involving both superfields the dilatation operator for N ≤ 2 receives an additional contribution from the exchange interaction between superfields on the light-cone which breaks its integrability symmetry and creates a mass gap in the spectrum of anomalous dimensions.

show abstract

Continuum limit of the integrable superspin chain

2005

Self Cite

View full text Add to dashboard Cite

By a combination of analytical and numerical techniques, we analyze the continuum limit of the integrable 3 ⊗3 ⊗ 3 ⊗3 . . . sl(2/1) superspin chain. We discover profoundly new features, including a continuous spectrum of conformal weights, whose numerical evidence is infinite degeneracies of the scaled gaps in the thermodynamic limit. This indicates that the corresponding conformal field theory has a non compact target space (even though our lattice model involves only finite dimensional representations). We argue that our results are compatible with this theory being the level k = 1, 'SU (2/1) WZW model' (whose precise definition requires some care). In doing so, we establish several new results for this model. With regard to potential applications to the spin quantum Hall effect, we conclude that the continuum limit of the 3 ⊗3 ⊗ 3 ⊗3 . . . sl(2/1) integrable superspin chain is not the same as (and is in fact very different from) the continuum limit of the corresponding chain with two-superspin interactions only, which is known to be a model for the spin quantum Hall effect. The study of possible RG flows between the two theories is left for further study.

show abstract

Doped Heisenberg chains: Spin-S generalizations of the supersymmetric t-J model

Cited by 26 publications

References 38 publications

Magnetic properties of doped Heisenberg chains

Magnetic properties of doped Heisenberg chains

Dilatation operator in (super-)Yang–Mills theories on the light-cone

Continuum limit of the integrable superspin chain

Contact Info

Product

Resources

About