scholarly journals Thermodynamic limit of the two-spinon form factors for the zero field XXX chain

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Nikolai Kitanine ◽  
Giridhar V. Kulkarni
Keyword(s):  
Bethe Ansatz ◽  
Thermodynamic Limit ◽  
Vertex Operator ◽  
Form Factors ◽  
Quantum Spin ◽  
Spin Chains ◽  
Zero Field ◽  
Heisenberg Chain ◽  
Quantum Spin Chains ◽  
Operator Approach

In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in particular the formula for the two-spinon form factors for the isotropic XXX Heisenberg chain obtained initially in the framework of the q-vertex operator approach.

ENHANCED TELEPORTATION THROUGH ANISOTROPIC HEISENBERG QUANTUM SPIN CHAINS

2008 ◽  
Vol 22 (01) ◽  
pp. 17-23 ◽  
Author(s):  
XIANG HAO ◽  
SHIQUN ZHU
Keyword(s):  
Thermal Equilibrium ◽  
Quantum Spin ◽  
Spin Chains ◽  
Equilibrium States ◽  
Heisenberg Chain ◽  
Quantum Spin Chains ◽  
Critical Temperatures ◽  
Average Fidelity ◽  
Entanglement Teleportation

The teleportation via the channel of the thermal equilibrium states in anisotropic Heisenberg XYZ chains is analyzed. It is found that there are the critical temperatures below which entanglement teleportation can be realized. Entanglement teleportation is enhanced through anisotropic XYZ chains in contrast to the isotropic Heisenberg one. Anisotropic spin exchanges can increase these critical temperatures for the teleportation. Entanglement can be transferred in the ferromagnetic anisotropic Heisenberg chain while it cannot be done in the ferromagnetic isotropic one. The average fidelity of the teleportation can be improved in the antiferromagnetic chains.

RENORMALIZATION-GROUP INVESTIGATION OF THE S = 1 RANDOM ANTIFERROMAGNETIC HEISENBERG CHAIN

2006 ◽  
Vol 17 (12) ◽  
pp. 1739-1753 ◽  
Author(s):  
PÉTER LAJKÓ
Keyword(s):  
Phase Diagram ◽  
Renormalization Group ◽  
Density Matrix ◽  
Energy Scale ◽  
Quantum Spin ◽  
Spin Chains ◽  
Density Matrix Renormalization Group ◽  
Heisenberg Chain ◽  
Quantum Spin Chains ◽  
Density Matrix Renormalization

We introduce variants of the Ma-Dasgupta renormalization-group (RG) approach for random quantum spin chains, in which the energy-scale is reduced by decimation built on either perturbative or non-perturbative principles. In one non-perturbative version of the method, we require the exact invariance of the lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques, different decimation rules are utilized. For the S = 1 random antiferromagnetic Heisenberg chain, both type of methods provide the same type of disorder dependent phase diagram, which is in agreement with density-matrix renormalization-group calculations and previous studies.

scholarly journals Yang-Baxter integrable Lindblad equations

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Aleksandra A. Ziolkowska ◽  
Fabian Essler
Keyword(s):  
Bethe Ansatz ◽  
Quantum Spin ◽  
Spin Chains ◽  
Integrable Models ◽  
Late Time ◽  
Quantum Spin Chains ◽  
Operator Formalism ◽  
One Dimensional ◽  
Time Dynamics

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.

scholarly journals BETHE ANSATZ SOLUTIONS FOR TEMPERLEY–LIEB QUANTUM SPIN CHAINS

2000 ◽  
Vol 15 (21) ◽  
pp. 3395-3425 ◽  
Author(s):  
R. C. T. GHIOTTO ◽  
A. L. MALVEZZI
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Quantum Group ◽  
Bethe Ansatz ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Free Boundary Conditions

We solve the spectrum of quantum spin chains based on representations of the Temperley–Lieb algebra associated with the quantum groups [Formula: see text] for Xn=A1, Bn, Cn and Dn. The tool is a modified version of the coordinate Bethe ansatz through a suitable choice of the Bethe states which give to all models the same status relative to their diagonalization. All these models have equivalent spectra up to degeneracies and the spectra of the lower-dimensional representations are contained in the higher-dimensional ones. Periodic boundary conditions, free boundary conditions and closed nonlocal boundary conditions are considered. Periodic boundary conditions, unlike free boundary conditions, break quantum group invariance. For closed nonlocal cases the models are quantum group invariant as well as periodic in a certain sense.

Introduction to Integrable Many-Body Systems II

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Ladislav Šamaj
Keyword(s):  
Bethe Ansatz ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Scattering Method ◽  
Heisenberg Chain ◽  
Many Body ◽  
Xxz Model ◽  
The Subject ◽  
Many Body Systems

Introduction to Integrable Many-Body Systems IIThis is the second part of a three-volume introductory course about integrable systems of interacting bodies. The models of interest are quantum spin chains with nearest-neighbor interactions between spin operators, in particular Heisenberg spin-1/2 models. The Ising model in a transverse field, expressible as a quadratic fermion form by using the Jordan-Wigner transformation, is the subject of Sect. 12. The derivation of the coordinate Bethe ansatz for the XXZ Heisenberg chain and the determination of its absolute ground state in various regions of the anisotropy parameter are presented in Sect. 13. The magnetic properties of the ground state are explained in Sect. 14. Sect. 15 concerns excited states and the zero-temperature thermodynamics of the XXZ model. The thermodynamics of the XXZ Heisenberg chain is derived on the basis of the string hypothesis in Sect. 16; the thermodynamic Bethe ansatz equations are analyzed in high-temperature and low-temperature limits. An alternative derivation of the thermodynamics without using strings, leading to a non-linear integral equation determining the free energy, is the subject of Sect. 17. A nontrivial application of the Quantum Inverse Scattering method to the fully anisotropic XYZ Heisenberg chain is described in Sect. 18. Sect. 19 deals with integrable cases of isotropic spin chains with an arbitrary spin.

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