Quantum theory of one-dimensional spin systems

The $T=0$ dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the $T=0$ dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at $T=0$ .The $T=0$ dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the $T=0$ dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at $T=0$.

Physical review. B, Condensed matterAug 1, 198329 citations

New methods in the theory of quantum spin systems

V Ulyanov

Physics ReportsJul 1, 1992167 citations

Holographic Dual of Quantum Spin Chain as Chern-Simons-Scalar Theory

Naoto Yokoi, Yasuyuki Oikawa, Eiji Saitoh

We construct a holographic dual theory of one-dimensional anisotropic Heisenberg spin chain, which includes two Chern-Simons gauge fields and a charged scalar field. Thermodynamic quantities of the spin chain at low temperatures, which are exactly calculated from the integrability, are completely reproduced by the dual theory on three-dimensional black hole backgrounds and the exact matching of the parameters between the dual theory and the spin chain is obtained. The holographic dual theory provides a new theoretical framework to analyze the quantum spin chain and one-dimensional quantum many-body systems.We construct a holographic dual theory of one-dimensional anisotropic Heisenberg spin chain, which includes two Chern-Simons gauge fields and a charged scalar field. Thermodynamic quantities of the spin chain at low temperatures, which are exactly calculated from the integrability, are completely reproduced by the dual theory on three-dimensional black hole backgrounds and the exact matching of the parameters between the dual theory and the spin chain is obtained. The holographic dual theory provides a new theoretical framework to analyze the quantum spin chain and one-dimensional quantum many-body systems.

arXiv:2310.01890Oct 3, 20230 citations

Holographic dual of a quantum spin chain as a Chern-Simons-scalar theory

Naoto Yokoi, Yasuyuki Oikawa, Eiji Saitoh

We construct a holographic dual theory of one-dimensional anisotropic Heisenberg spin chain, which includes two Chern-Simons gauge fields and a charged scalar field. Thermodynamic quantities of the spin chain at low temperatures, which are exactly calculated from the integrability, are completely reproduced by the dual theory on three-dimensional black hole backgrounds and the exact matching of the parameters between the dual theory and the spin chain is obtained. The holographic dual theory provides a new theoretical framework to analyze the quantum spin chain and one-dimensional quantum many-body systems. Published by the American Physical Society 2024We construct a holographic dual theory of one-dimensional anisotropic Heisenberg spin chain, which includes two Chern-Simons gauge fields and a charged scalar field. Thermodynamic quantities of the spin chain at low temperatures, which are exactly calculated from the integrability, are completely reproduced by the dual theory on three-dimensional black hole backgrounds and the exact matching of the parameters between the dual theory and the spin chain is obtained. The holographic dual theory provides a new theoretical framework to analyze the quantum spin chain and one-dimensional quantum many-body systems. Published by the American Physical Society 2024

Physical review. D/Physical review. D.Apr 25, 20240 citations

One-Dimensional Quantum Spin System with Two Kinds of Spins

Takashi Tonegawa, Makoto Kaburagi, S. Miyashita

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

The

T=0

dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the

T=0

dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at

T=0