Multiple-spin exchange interaction in two-dimensional quantum solid

$^{3}\mathrm{He}$ adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins $S=\frac{1}{2}$ is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of $^{3}\mathrm{He}$ on graphite preplated by one layer of $^{4}\mathrm{He}$ . By adding controlled amounts of $^{4}\mathrm{He}$ , $^{3}\mathrm{He}$ atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.$^{3}\mathrm{He}$ adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins $S=\frac{1}{2}$ is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of $^{3}\mathrm{He}$ on graphite preplated by one layer of $^{4}\mathrm{He}$. By adding controlled amounts of $^{4}\mathrm{He}$, $^{3}\mathrm{He}$ atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.

Physical Review BMar 23, 20068 citations

Dynamics of Two-Dimensional Quantum Spin Systems

M. S. Makivić, Mark Jarrell

Springer proceedings in physicsJan 1, 19930 citations

Numerical Studies of Two-Dimensional Quantum Spin Systems

Eric S. Swanson

Jan 1, 19900 citations

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

Serge I. Doronin, I. I. Maksimov, Edward B. Fel’dman

Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.

Journal of Experimental and Theoretical PhysicsSep 1, 200078 citations

Quantum Communication in Spin Chain with Multiple Spin Exchange Interaction

Hao Xiang, Zhu Shi-Qun

The transmission of quantum states in the anisotropic Heisenberg XXZ chain model with three-spin exchange interaction is studied. The average fidelity is used to evaluate the state transfer. It is found that quantum communication can be enhanced by the anisotropic coupling and multiple spin interaction. Such spin model can reduce the time required for the perfect state transmission where the fidelity is unity. The maximally entangled Bell states can be generated and separated from the whole quantum systems.The transmission of quantum states in the anisotropic Heisenberg XXZ chain model with three-spin exchange interaction is studied. The average fidelity is used to evaluate the state transfer. It is found that quantum communication can be enhanced by the anisotropic coupling and multiple spin interaction. Such spin model can reduce the time required for the perfect state transmission where the fidelity is unity. The maximally entangled Bell states can be generated and separated from the whole quantum systems.

Communications in Theoretical PhysicsJun 1, 20109 citations

Experimental studies of one-dimensional quantum spin systems

K. Katsumata

Journal of Magnetism and Magnetic MaterialsFeb 1, 199524 citations

^{3}\mathrm{He}

adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins

S=\frac{1}{2}

is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of

^{3}\mathrm{He}

on graphite preplated by one layer of

^{4}\mathrm{He}

. By adding controlled amounts of

^{4}\mathrm{He}

^{3}\mathrm{He}

atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.