Fermionization of the spin-S Uimin–Lai–Sutherland model: generalisation of the supersymmetric t–J model to spin-S

Ambjørn, J.; Karakhanyan, D.; Mirumyan, M.; Sedrakyan, A.

doi:10.1016/s0550-3213(00)00757-4

Cited by 22 publications

(36 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The local Hilbert state basis is therefore given by a triple of states |1 ≡ |↑ , |2 ≡ |0 , |3 ≡ |↓ , which can be interpreted as three different particle species; respectively, as spin-up particles, holes, and spin-down particles. The model then becomes equivalent to the so-called supersymmetric t-J model [26]. Lai-Sutherland chain is a multi-component quantum model and we may associate with it a skew-symmetric tensor of particle currents, with two-site density…”

Section: Open Lai-sutherland Model Far From Equilibriummentioning

confidence: 99%

“…Theorem 2. A possible irreducible explicit representation of Lie algebra g (26) satisfying (27) is given as…”

Section: Matrix Product Solutionmentioning

confidence: 99%

“…have been defined. Note that, due to (33), b x = iεs 3 x = −b x for ε ∈ R. The last two lines of (26) indicate that pairs of auxiliary operators (t + , t − ) and (u + , u − ) span the Weyl-Heisenberg algebra. In conjunction with the highest weight conditions (27) this fixes (uniquely, up to unitary transformations) the representation of (t + , t − ) and (u + , u − ) to be that of a Fock space of two canonical bosonic (oscillator) modes, specified by creation/annihilation operators,…”

Section: Matrix Product Solutionmentioning

confidence: 99%

See 2 more Smart Citations

Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

Ilievski

Prosen

2014

Nuclear Physics B

View full text Add to dashboard Cite

We present an explicit construction of a family of steady state density matrices for an open integrable spin-1 chain with bilinear and biquadratic interactions, also known as the Lai-Sutherland model, driven far from equilibrium by means of two oppositely polarizing Markovian dissipation channels localized at the boundary. The steady state solution exhibits n + 1 fold degeneracy, for a chain of length n, due to existence of (strong) Liouvillian U(1) symmetry. The latter can be exploited to introduce a chemical potential and define a grand canonical nonequilibrium steady state ensemble. The matrix product form of the solution entails an infinitely-dimensional representation of a non-trivial Lie algebra (semidirect product of sl 2 and a non-nilpotent radical) and hints to a novel Yang-Baxter integrability structure.

show abstract

Section: Open Lai-sutherland Model Far From Equilibriummentioning

confidence: 99%

“…Theorem 2. A possible irreducible explicit representation of Lie algebra g (26) satisfying (27) is given as…”

Section: Matrix Product Solutionmentioning

confidence: 99%

Section: Matrix Product Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

Ilievski

Prosen

2014

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…On the one hand, the realization of angular momentum algebra has been of interest for a long time. Besides the well-known Schwinger representation [11] and the Holstein-Primakoff representation [2], there are many other schemes, including the realization of su (2) algebra [3,4,12,13,14], and the realization of su q (2) and su q (n) algebra [15,16]. On the other hand, the spin wave plays an important role in magnetic problems [17,18].…”

Section: Introductionmentioning

confidence: 99%

Intermediate-statistics spin waves

Dai

Xie²

2009

J. Stat. Mech.

View full text Add to dashboard Cite

In this paper, we show that spin waves, the elementary excitation of the Heisenberg magnetic system, obey a kind of intermediate statistics with a finite maximum occupation number n. We construct an operator realization for the intermediate statistics obeyed by magnons, the quantized spin waves, and then construct a corresponding intermediate-statistics realization for the angular momentum algebra in terms of the creation and annihilation operators of the magnons. In other words, instead of the Holstein–Primakoff representation, a bosonic representation subject to a constraint on the occupation number, we present an intermediate-statistics representation with no constraints. In this realization, the maximum occupation number is naturally embodied in the commutation relation of creation and annihilation operators, while the Holstein–Primakoff representation is a bosonic operator relation with an additional putting-in-by-hand restriction on the occupation number. We deduce the intermediate-statistics distribution function for magnons from the intermediate-statistics commutation relation of the creation and annihilation operators directly, which is a modified Bose–Einstein distribution. On the basis of these results, we calculate the dispersion relations for ferromagnetic and antiferromagnetic spin waves. The relations between the intermediate statistics that magnons obey and the other two important kinds of intermediate statistics, Haldane–Wu statistics and the fractional statistics of anyons, are discussed. We also compare the spectrum of the intermediate-statistics spin wave with the exact solution of the one-dimensional s = 1/2 Heisenberg model, which is obtained by the Bethe ansatz method. For ferromagnets, we take the contributions from the interaction between magnons (the quartic contribution), the next-to-nearest-neighbor interaction, and the dipolar interaction into account for comparison with the experiment.

show abstract

“…The developed theory utilizes the graded R operator formalism 26,27,28,29,30 and allows the generalization to other integrable models, which is demonstrated in this work by operating with rather general R operator.…”

Section: Introductionmentioning

confidence: 99%

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Khachatryan

Sedrakyan

2009

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and XY Z model, which is simple to apply for calculation of various correlation functions. We calculate the partition function of 2DIM and XY model within the developed framework. Determinant representation of spin-spin correlation functions is derived using fermionic realization for the Boltzmann weights. The approach also allows formulation of the partition function of 2DIM in the presence of an external magnetic field.

show abstract

Fermionization of the spin-S Uimin–Lai–Sutherland model: generalisation of the supersymmetric t–J model to spin-S

Cited by 22 publications

References 36 publications

Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

Intermediate-statistics spin waves

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Contact Info

Product

Resources

About