We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sublattices), such that the scattering phases are constants: Particles of the same type scatter as free fermions, whereas the interparticle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sublattice entanglement by numerical means.We introduce an integrable spin ladder model and study its exact solution, correlation functions, and entanglement properties. The model supports two particle types (corresponding to the even and odd sublattices), such that the scattering phases are constants: Particles of the same type scatter as free fermions, whereas the interparticle phase shift is a constant tuned by an interaction parameter. Therefore, the spin ladder bears similarities with anyonic models. We present exact results for the spectrum and correlation functions, and we study the sublattice entanglement by numerical means.

Physical review. EOct 14, 20228 citations

EXACT SOLUTIONS IN A SPATIALLY ANISOTROPIC QUANTUM SPIN LADDER MODEL HAVING TWO- AND FOUR-SPIN EXCHANGE INTERACTIONS

Jeremiah H. Barry, J. D. COHEN, Mark W. Meisel

We consider a two-leg S=1/2 quantum spin ladder model with two-spin (intra-rung) and four-spin (inter-rung) Heisenberg exchange interactions and a uniform magnetic field. Exact mappings are derived connecting the partition function and correlations in the three-parameter quantum model to those known in a two-parameter Ising chain. The quantum phase diagram of the ladder magnet is determined. Static correlations provide pertinent correlation lengths and underlie spatial fluctuation behaviors at arbitrary temperatures, including quantum fluctuations at absolute zero. Dynamic correlations in zero field are used to obtain an exact solution for the inelastic neutron scattering function Sxx(q, ω) at all temperatures, explicitly yielding the elementary excitation spectrum.We consider a two-leg S=1/2 quantum spin ladder model with two-spin (intra-rung) and four-spin (inter-rung) Heisenberg exchange interactions and a uniform magnetic field. Exact mappings are derived connecting the partition function and correlations in the three-parameter quantum model to those known in a two-parameter Ising chain. The quantum phase diagram of the ladder magnet is determined. Static correlations provide pertinent correlation lengths and underlie spatial fluctuation behaviors at arbitrary temperatures, including quantum fluctuations at absolute zero. Dynamic correlations in zero field are used to obtain an exact solution for the inelastic neutron scattering function Sxx(q, ω) at all temperatures, explicitly yielding the elementary excitation spectrum.

International Journal of Modern Physics BMar 30, 20091 citation

Integrable spin ladder systems

Angela Foerster, Arlei Prestes Tonel

We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings.The model is exactly solvable by means of the Bethe ansatz method.We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram.Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters.We also investigate the thermodynamics of the model.Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically.The influence of this anisotropy parameter on these physical curves is determined explicitly.A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.We present an integrable spin ladder model which possesses a free parameter besides the rung and leg couplings.The model is exactly solvable by means of the Bethe ansatz method.We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram.Finally, we show that the model is a special case of a more general Hamiltonian with six free parameters.We also investigate the thermodynamics of the model.Specifically, the magnetic susceptibility as a function of the temperature is obtained numerically.The influence of this anisotropy parameter on these physical curves is determined explicitly.A comparsion between the spin gap obtained from the susceptibility curve and that one obtained from the Bethe ansatz equations is performed and a good agreement is found.

Workshop on Integrable Theories, Solitons and DualityDec 1, 20020 citations

Phase transitions on a ladder of braided non-Abelian anyons

Babatunde M. Ayeni, Robert N. C. Pfeifer, Gavin K. Brennen

Non-Abelian anyons can exist as pointlike particles in two-dimensional systems and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian braid statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest-neighbor Heisenberg interactions among anyons. We study two of the most prominent non-Abelian anyon models: the Fibonacci and Ising types. We discover rich phase diagrams for both anyon models and show the different roles of their fusion and braid statistics.Non-Abelian anyons can exist as pointlike particles in two-dimensional systems and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian braid statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest-neighbor Heisenberg interactions among anyons. We study two of the most prominent non-Abelian anyon models: the Fibonacci and Ising types. We discover rich phase diagrams for both anyon models and show the different roles of their fusion and braid statistics.

arXiv:1712.04179Physical review. B./Physical review. BJul 30, 20185 citations

Quantum spin ladders of non-Abelian anyons

Didier Poilblanc, Andreas W. W. Ludwig, Simon Trebst +1 more

Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including ${p}_{x}+i{p}_{y}$ superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd and even effects with the ladder width, and elementary ``magnon'' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom. In general, two-dimensional systems of interacting localized non-Abelian anyons are anyonic generalizations of two-dimensional quantum magnets.Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including ${p}_{x}+i{p}_{y}$ superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd and even effects with the ladder width, and elementary ``magnon'' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom. In general, two-dimensional systems of interacting localized non-Abelian anyons are anyonic generalizations of two-dimensional quantum magnets.

arXiv:1101.1186Physical Review BApr 29, 201122 citations

Exact solutions in a S=12 quantum spin ladder model with pair and quartic interactions

Jeremiah H. Barry, Mark W. Meisel

The effects of multispin interactions upon quantum spin ladders are investigated theoretically. A two-leg $S=\frac{1}{2}$ quantum spin ladder is taken to have intrarung (inter-rung) quadratic (biquadratic) Heisenberg exchange-type interactions and is placed in a uniform magnetic field. Due to the commutability properties of the Hamiltonian, the magnetic canonical partition function of the model is exactly calculable by a method of rung transfer matrix. Exact solutions are then derived for thermodynamic quantities like free and internal energies, magnetization, and magnetic susceptibilities (initial and nonlinear). The zero-temperature results comprise exact solutions in the complete interaction parameter space for the ground-state energy and degeneracy, zero-field spin gap, loci of quantum phase transitions, and the critical magnetic field.The effects of multispin interactions upon quantum spin ladders are investigated theoretically. A two-leg $S=\frac{1}{2}$ quantum spin ladder is taken to have intrarung (inter-rung) quadratic (biquadratic) Heisenberg exchange-type interactions and is placed in a uniform magnetic field. Due to the commutability properties of the Hamiltonian, the magnetic canonical partition function of the model is exactly calculable by a method of rung transfer matrix. Exact solutions are then derived for thermodynamic quantities like free and internal energies, magnetization, and magnetic susceptibilities (initial and nonlinear). The zero-temperature results comprise exact solutions in the complete interaction parameter space for the ground-state energy and degeneracy, zero-field spin gap, loci of quantum phase transitions, and the critical magnetic field.

Physical review. B, Condensed matterAug 1, 19983 citations

{p}_{x}+i{p}_{y}

superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensates. Here we use a combination of exact diagonalization and conformal field theory to determine the phase diagrams of ladders with up to four chains. We discuss how phenomena familiar from ordinary SU(2) spin ladders are generalized in their anyonic counterparts, such as gapless and gapped phases, odd and even effects with the ladder width, and elementary ``magnon'' excitations. Other features are entirely due to the topological nature of the anyonic degrees of freedom. In general, two-dimensional systems of interacting localized non-Abelian anyons are anyonic generalizations of two-dimensional quantum magnets.

The effects of multispin interactions upon quantum spin ladders are investigated theoretically. A two-leg

S=\frac{1}{2}

quantum spin ladder is taken to have intrarung (inter-rung) quadratic (biquadratic) Heisenberg exchange-type interactions and is placed in a uniform magnetic field. Due to the commutability properties of the Hamiltonian, the magnetic canonical partition function of the model is exactly calculable by a method of rung transfer matrix. Exact solutions are then derived for thermodynamic quantities like free and internal energies, magnetization, and magnetic susceptibilities (initial and nonlinear). The zero-temperature results comprise exact solutions in the complete interaction parameter space for the ground-state energy and degeneracy, zero-field spin gap, loci of quantum phase transitions, and the critical magnetic field.