Massively parallel approaches to frustrated quantum magnets

Frustration, or the competition between interacting components of a network, is often responsible for the emergent complexity of many-body systems. For instance, frustrated magnetism is a hallmark of poorly understood systems such as quantum spin liquids, spin glasses, and spin ices, whose ground states can be massively degenerate and carry high degrees of quantum entanglement. Here, we engineer frustrated antiferromagnetic interactions between spins stored in a crystal of up to 16 trapped (171)Yb(+) atoms. We control the amount of frustration by continuously tuning the range of interaction and directly measure spin correlation functions and their coherent dynamics. This prototypical quantum simulation points the way toward a new probe of frustrated quantum magnetism and perhaps the design of new quantum materials.Frustration, or the competition between interacting components of a network, is often responsible for the emergent complexity of many-body systems. For instance, frustrated magnetism is a hallmark of poorly understood systems such as quantum spin liquids, spin glasses, and spin ices, whose ground states can be massively degenerate and carry high degrees of quantum entanglement. Here, we engineer frustrated antiferromagnetic interactions between spins stored in a crystal of up to 16 trapped (171)Yb(+) atoms. We control the amount of frustration by continuously tuning the range of interaction and directly measure spin correlation functions and their coherent dynamics. This prototypical quantum simulation points the way toward a new probe of frustrated quantum magnetism and perhaps the design of new quantum materials.

arXiv:1210.0142ScienceMay 2, 2013451 citations

QUANTUM FRUSTRATED MAGNETS: FROM THEORY TO EXPERIMENTS

Frédéric Mila

Recent Progress in Many-Body TheoriesDec 1, 20020 citations

SU(N) evolution of a frustrated spin ladder

M. J. Bhaseen, Alexei M. Tsvelik

Recent studies indicate that the weakly coupled, ${J}_{\ensuremath{\perp}}\ensuremath{\ll}J,$ spin-1/2 Heisenberg antiferromagnet with next-nearest-neighbor frustration, ${J}_{\ifmmode\times\else\texttimes\fi{}},$ supports massive spinons for ${J}_{\ifmmode\times\else\texttimes\fi{}}{=J}_{\ensuremath{\perp}}/2.$ The straightforward $\mathrm{SU}(N)$ generalization of the low-energy ladder Hamiltonian yields two independent $\mathrm{SU}(N)$ Thirring models with $N\ensuremath{-}1$ multiplets of massive ``spinon'' excitations. We study the evolution of the complete set of low energy dynamical structure factors using form factors. Those corresponding to the smooth (staggered) magnetizations are qualitatively different (the same) in the $N=2$ and $N>2$ cases. The absence of single-particle peaks preserves the notion of spinons stabilized by frustration. In contrast to the ladder, we note that the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit of the four chain model is not a trivial free theory.Recent studies indicate that the weakly coupled, ${J}_{\ensuremath{\perp}}\ensuremath{\ll}J,$ spin-1/2 Heisenberg antiferromagnet with next-nearest-neighbor frustration, ${J}_{\ifmmode\times\else\texttimes\fi{}},$ supports massive spinons for ${J}_{\ifmmode\times\else\texttimes\fi{}}{=J}_{\ensuremath{\perp}}/2.$ The straightforward $\mathrm{SU}(N)$ generalization of the low-energy ladder Hamiltonian yields two independent $\mathrm{SU}(N)$ Thirring models with $N\ensuremath{-}1$ multiplets of massive ``spinon'' excitations. We study the evolution of the complete set of low energy dynamical structure factors using form factors. Those corresponding to the smooth (staggered) magnetizations are qualitatively different (the same) in the $N=2$ and $N>2$ cases. The absence of single-particle peaks preserves the notion of spinons stabilized by frustration. In contrast to the ladder, we note that the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit of the four chain model is not a trivial free theory.

arXiv:cond-mat/0305194Physical review. B, Condensed matterSep 5, 200310 citations

Frustrated Quantum Magnets

C. Lhuillier, Grégoire Misguich

arXiv:cond-mat/0109146Lecture notes in physicsJan 1, 200291 citations

Low-Dimensional Frustrated Quantum Magnets: A Playground for Novel Phases

Wen Jin

Nov 21, 20191 citation

Universal emergence of the one-third plateau in the magnetization process of frustrated quantum spin chains

Fabian Heidrich‐Meisner, I. A. Sergienko, Adrian E. Feiguin +1 more

We present a numerical study of the magnetization process of frustrated quantum spin- $S$ chains with $S=1,3∕2,2$ as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin- $S$ chains with $S>1∕2$ . Similar to the case of $S=1∕2$ , this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin- $S=1$ , $3∕2$ , and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin- $3∕2$ chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin- $3∕2$ chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin $S$ increases.We present a numerical study of the magnetization process of frustrated quantum spin-$S$ chains with $S=1,3∕2,2$ as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-$S$ chains with $S>1∕2$. Similar to the case of $S=1∕2$, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin-$S=1$, $3∕2$, and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin-$3∕2$ chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin-$3∕2$ chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin $S$ increases.

arXiv:cond-mat/0609555Physical Review BFeb 12, 200745 citations

\mathrm{SU}(N)

generalization of the low-energy ladder Hamiltonian yields two independent

\mathrm{SU}(N)

Thirring models with $N\ensuremath{-}1$ multiplets of massive ``spinon'' excitations. We study the evolution of the complete set of low energy dynamical structure factors using form factors. Those corresponding to the smooth (staggered) magnetizations are qualitatively different (the same) in the

N=2

and

N>2

cases. The absence of single-particle peaks preserves the notion of spinons stabilized by frustration. In contrast to the ladder, we note that the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit of the four chain model is not a trivial free theory.

We present a numerical study of the magnetization process of frustrated quantum spin-

S

chains with

S=1,3∕2,2

as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-

S

chains with

S>1∕2

. Similar to the case of

S=1∕2

, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin-

S=1

3∕2

, and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin-

3∕2

chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin-

3∕2

chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin

S

increases.