Abstract This chapter provides a brief introduction to the terminology and basic concepts of quantum spin systems, which are widely used in QIS and QC. The quantum spin of an elementary particle is an example of a qubit and can be visually represented as a spinning top. The vector direction of spin in state space, however, is different from the direction in physical space. Quantum spin-1/2 systems have two orthogonal states: spin-up and spin-down. The distinction between state space angles and physical space angles is emphasized. Because spin is a qubit, the quantum gates from Chapter 6 can be applied to spin-1/2 quantum states with predictable results.Abstract This chapter provides a brief introduction to the terminology and basic concepts of quantum spin systems, which are widely used in QIS and QC. The quantum spin of an elementary particle is an example of a qubit and can be visually represented as a spinning top. The vector direction of spin in state space, however, is different from the direction in physical space. Quantum spin-1/2 systems have two orthogonal states: spin-up and spin-down. The distinction between state space angles and physical space angles is emphasized. Because spin is a qubit, the quantum gates from Chapter 6 can be applied to spin-1/2 quantum states with predictable results.

Apr 15, 20220 citations

Exactly solved quantum spin ladders

M. Maslen

Jan 1, 20020 citations

Spin analogs of superconductivity and integer quantum Hall effect in an array of spin chains

Daniel Hill, Se Kwon Kim, Yaroslav Tserkovnyak

Motivated by the successful idea of using weakly coupled quantum electronic wires to realize the quantum Hall effects and the quantum spin Hall effects, we theoretically study two systems composed of weakly coupled quantum spin chains within the mean-field approximations, which can exhibit spin analogs of superconductivity and the integer quantum Hall effect. First, a certain bilayer of two arrays of interacting spin chains is mapped, via the Jordan-Wigner transformation, to an attractive Hubbard model that exhibits fermionic superconductivity, which corresponds to spin superconductivity in the original spin Hamiltonian. Secondly, an array of spin-orbit-coupled spin chains in the presence of a suitable external magnetic field is transformed to an array of quantum wires that exhibits the integer quantum Hall effect, which translates into its spin analog in the spin Hamiltonian. The resultant spin superconductivity and spin integer quantum Hall effect can be characterized by their ability to transport spin without any resistance.Motivated by the successful idea of using weakly coupled quantum electronic wires to realize the quantum Hall effects and the quantum spin Hall effects, we theoretically study two systems composed of weakly coupled quantum spin chains within the mean-field approximations, which can exhibit spin analogs of superconductivity and the integer quantum Hall effect. First, a certain bilayer of two arrays of interacting spin chains is mapped, via the Jordan-Wigner transformation, to an attractive Hubbard model that exhibits fermionic superconductivity, which corresponds to spin superconductivity in the original spin Hamiltonian. Secondly, an array of spin-orbit-coupled spin chains in the presence of a suitable external magnetic field is transformed to an array of quantum wires that exhibits the integer quantum Hall effect, which translates into its spin analog in the spin Hamiltonian. The resultant spin superconductivity and spin integer quantum Hall effect can be characterized by their ability to transport spin without any resistance.

arXiv:1701.01509Physical review. B./Physical review. BMay 24, 20173 citations

Two-step spin flop transition in quantum spin ladders

Tôru Sakai, Kiyomi Okamoto

Bulletin of the American Physical SocietyMar 13, 20080 citations

Bond-operator analysis of the magnetization of spin chains

Hanting Wang, Hua Lin, Jue-Lian Shen

A bond operator representation of quantum $S=1$ spins is developed along the same line to the bond operator representation of quantum $S=\frac{1}{2}$ spins. The two representations are then applied to investigate the magnetization of the isotropic spin- $1$ antiferromagnetic chains and the spin- $\frac{1}{2}$ and spin- $1$ spin ladders. With the appropriate quantum states projected out, the spin- $1$ chains and the spin- $\frac{1}{2}$ and spin- $1$ spin ladders can be mapped to effective Hamiltonians of the $\mathcal{S}=\frac{1}{2}$ pseudospins in the effective external magnetic fields. The magnetization features of the spin- $1$ chains and the spin- $\frac{1}{2}$ and spin- $1$ spin ladders are then analyzed with the use of the existing rigorous results of the spin- $\frac{1}{2}$ $\mathrm{XXZ}$ spin chains. For spin- $1$ chains, the dependences of the magnetization on the applied magnetic fields are obtained. The $m=\frac{1}{4}$ plateau appearing in the magnetization of the spin- $\frac{1}{2}$ spin ladders and the $m=\frac{1}{4},$ $\frac{1}{2},$ and $\frac{3}{4}$ plateaus in the magnetization of the spin- $1$ spin ladders are studied. The effects of the single-ion anisotropy and the related experiments on spin- $1$ spin ladders are discussed also.A bond operator representation of quantum $S=1$ spins is developed along the same line to the bond operator representation of quantum $S=\frac{1}{2}$ spins. The two representations are then applied to investigate the magnetization of the isotropic spin-$1$ antiferromagnetic chains and the spin-$\frac{1}{2}$ and spin-$1$ spin ladders. With the appropriate quantum states projected out, the spin-$1$ chains and the spin-$\frac{1}{2}$ and spin-$1$ spin ladders can be mapped to effective Hamiltonians of the $\mathcal{S}=\frac{1}{2}$ pseudospins in the effective external magnetic fields. The magnetization features of the spin-$1$ chains and the spin-$\frac{1}{2}$ and spin-$1$ spin ladders are then analyzed with the use of the existing rigorous results of the spin-$\frac{1}{2}$ $\mathrm{XXZ}$ spin chains. For spin-$1$ chains, the dependences of the magnetization on the applied magnetic fields are obtained. The $m=\frac{1}{4}$ plateau appearing in the magnetization of the spin-$\frac{1}{2}$ spin ladders and the $m=\frac{1}{4},$ $\frac{1}{2},$ and $\frac{3}{4}$ plateaus in the magnetization of the spin-$1$ spin ladders are studied. The effects of the single-ion anisotropy and the related experiments on spin-$1$ spin ladders are discussed also.

Physical review. B, Condensed matterFeb 1, 200025 citations

Monte Carlo Simulation of s=1/2 Quantum Spin Ladders

Takafumi Momose, Takafumi Suzuki, Yuhei Natsume

Abstracts of the meeting of the Physical Society of Japan. Sectional meetingSep 13, 19960 citations

A bond operator representation of quantum

S=1

spins is developed along the same line to the bond operator representation of quantum

S=\frac{1}{2}

spins. The two representations are then applied to investigate the magnetization of the isotropic spin-

1

antiferromagnetic chains and the spin-

\frac{1}{2}

and spin-

1

spin ladders. With the appropriate quantum states projected out, the spin-

1

chains and the spin-

\frac{1}{2}

and spin-

1

spin ladders can be mapped to effective Hamiltonians of the

\mathcal{S}=\frac{1}{2}

pseudospins in the effective external magnetic fields. The magnetization features of the spin-

1

chains and the spin-

\frac{1}{2}

and spin-

1

spin ladders are then analyzed with the use of the existing rigorous results of the spin-

\frac{1}{2}

\mathrm{XXZ}

spin chains. For spin-

1

chains, the dependences of the magnetization on the applied magnetic fields are obtained. The

m=\frac{1}{4}

plateau appearing in the magnetization of the spin-

\frac{1}{2}

spin ladders and the

m=\frac{1}{4},

\frac{1}{2},

and

\frac{3}{4}

plateaus in the magnetization of the spin-

1

spin ladders are studied. The effects of the single-ion anisotropy and the related experiments on spin-

1

spin ladders are discussed also.