Abstract The spectra of N -boson systems with arbitrary nonzero spin f have been studied. Firstly, only the singlet pairing interaction is considered, a set of exact eigenstates together with the eigenenergies are analytically obtained. The completeness of this set is proved. The analytical expression allows us to see clearly the spin textures of various states different in N and/or f , and to find out the similarity and relationship lying among them. Secondly, the effect of other interactions is evaluated via exact numerical calculations on the systems with a smaller N . Some features and notable phenomena that might emerge in high- f systems, say, the ground band might have extremely high level density, have been discussed.Abstract The spectra of N -boson systems with arbitrary nonzero spin f have been studied. Firstly, only the singlet pairing interaction is considered, a set of exact eigenstates together with the eigenenergies are analytically obtained. The completeness of this set is proved. The analytical expression allows us to see clearly the spin textures of various states different in N and/or f , and to find out the similarity and relationship lying among them. Secondly, the effect of other interactions is evaluated via exact numerical calculations on the systems with a smaller N . Some features and notable phenomena that might emerge in high- f systems, say, the ground band might have extremely high level density, have been discussed.

arXiv:2112.07885Physica ScriptaMar 3, 20223 citations

Ground states of quantum spin systems

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Communications in Mathematical PhysicsDec 1, 197816 citations

Behavior of entanglement and Cooper pairs under relativistic boosts

Veiko Palge, Vlatko Vedral, Jacob Dunningham

Recent work [J. A. Dunningham, V. Palge, and V. Vedral, Phys. Rev. A 80, 044302 (2009)] has shown how single-particle entangled states are transformed when boosted in relativistic frames for certain restricted geometries. Here we extend that work to consider completely general inertial boosts. We then apply our single-particle results to multiparticle entanglements by focusing on Cooper pairs of electrons. We show that a standard Cooper pair state consisting of a spin-singlet acquires spin-triplet components in a relativistically boosted inertial frame, regardless of the geometry. We also show that, if we start with a spin-triplet pair, two out of the three triplet states acquire a singlet component, the size of which depends on the geometry. This transformation between the different singlet and triplet superconducting pairs may lead to a better understanding of unconventional superconductivity.Recent work [J. A. Dunningham, V. Palge, and V. Vedral, Phys. Rev. A 80, 044302 (2009)] has shown how single-particle entangled states are transformed when boosted in relativistic frames for certain restricted geometries. Here we extend that work to consider completely general inertial boosts. We then apply our single-particle results to multiparticle entanglements by focusing on Cooper pairs of electrons. We show that a standard Cooper pair state consisting of a spin-singlet acquires spin-triplet components in a relativistically boosted inertial frame, regardless of the geometry. We also show that, if we start with a spin-triplet pair, two out of the three triplet states acquire a singlet component, the size of which depends on the geometry. This transformation between the different singlet and triplet superconducting pairs may lead to a better understanding of unconventional superconductivity.

arXiv:1109.5972Physical Review AOct 14, 201122 citations

Study of two-spin entanglement in singlet states

Muzaffar Qadir Lone, Amit Dey, Sreenija Yarlagadda

arXiv:1205.5667Solid State CommunicationsNov 16, 20142 citations

Overcomplete Bases for S = 1 Spin Liquids

Zheng-Xin Liu

For a $S=1$ system with even number of spins, the product states of two-body singlets, called the singlet pair states (SPSs), are overcomplete bases for the Hilbert space of many-body singlets. If the system contains odd number of spins, a singlet state can be decomposed as a superposition of all of the following configurations, in each configuration three of the spins form a three-body singlet and the remaining form two-body singlet pairs. This indicates that a $S=1$ spin liquid is especially a resonating-valence bond state. Although this conclusion is no longer valid for $SO(3)$ symmetric $S>1$ systems, it can be generalized to an integer spin- $S$ system if it has an enlarged $SO(2S+1)$ symmetry. Similar results can also be obtained for systems with $SU(n)$ symmetry.For a $S=1$ system with even number of spins, the product states of two-body singlets, called the singlet pair states (SPSs), are overcomplete bases for the Hilbert space of many-body singlets. If the system contains odd number of spins, a singlet state can be decomposed as a superposition of all of the following configurations, in each configuration three of the spins form a three-body singlet and the remaining form two-body singlet pairs. This indicates that a $S=1$ spin liquid is especially a resonating-valence bond state. Although this conclusion is no longer valid for $SO(3)$ symmetric $S>1$ systems, it can be generalized to an integer spin-$S$ system if it has an enlarged $SO(2S+1)$ symmetry. Similar results can also be obtained for systems with $SU(n)$ symmetry.

arXiv:1411.0754Nov 4, 20140 citations

Basics of Quantum Spin Systems

Hal Tasaki

Graduate texts in physicsJan 1, 20200 citations

For a

S=1

system with even number of spins, the product states of two-body singlets, called the singlet pair states (SPSs), are overcomplete bases for the Hilbert space of many-body singlets. If the system contains odd number of spins, a singlet state can be decomposed as a superposition of all of the following configurations, in each configuration three of the spins form a three-body singlet and the remaining form two-body singlet pairs. This indicates that a

S=1

spin liquid is especially a resonating-valence bond state. Although this conclusion is no longer valid for

SO(3)

symmetric

S>1

systems, it can be generalized to an integer spin-

S

system if it has an enlarged

SO(2S+1)

symmetry. Similar results can also be obtained for systems with

SU(n)

symmetry.