Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0003274 · Journal of Physics and Chemistry of Solids

Spin-gap states of a periodic mixed spin chain

Ken’ichi Takano

Published Jan 1, 2001• 2 citations
arXivHTMLPDF
DOI
10.1016/s0022-3697(00)00169-4

Related papers

Ground State Properties of Alternating Spin Chains

Takuma Nishimura, M. Katsumura, T. Morita +3 more

Abstracts of the meeting of the Physical Society of Japan. Sectional meeting•Sep 13, 1996•0 citations

Disordered Phases in Mixed Quantum Spin Chains

Ken'ichi Takano

Mixed quantum spin chains with periodicity are transformed into a nonlinear σ model (NLSM). The NLSM deduces a general formula which determines whether the system has a spin gap or not. The formula is applied to some concrete systems and their ground-state phase diagrams are derived. The odd period case is generally discussed.

Progress of Theoretical Physics Supplement•Jan 1, 2002•0 citations

C−P−T anomaly matching in bosonic quantum field theory and spin chains

Tin Sulejmanpašić, Yuya Tanizaki

We consider the $O(3)$ nonlinear sigma model with the $\ensuremath{\theta}$ term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any $\ensuremath{\theta}$, and enjoys the periodicity in $\ensuremath{\theta}\ensuremath{\rightarrow}\ensuremath{\theta}+2\ensuremath{\pi}$. At $\ensuremath{\theta}=0,\ensuremath{\pi}$ it also has a charge-conjugation $C$ symmetry. Gauging the discrete space-time reflection symmetries is interpreted as putting the theory on the nonorientable $\mathbb{R}{P}^{2}$ manifold, after which the $2\ensuremath{\pi}$ periodicity of $\ensuremath{\theta}$ and the $C$ symmetry at $\ensuremath{\theta}=\ensuremath{\pi}$ are lost. We interpret this observation as a mixed 't Hooft anomaly among charge-conjugation $C$, parity $P$, and time-reversal $T$ symmetries when $\ensuremath{\theta}=\ensuremath{\pi}$. Anomaly matching implies that in this case the ground state cannot be trivially gapped, as long as $C,P$, and $T$ are all good symmetries of the theory. We make several consistency checks with various semiclassical regimes, and with the exactly solvable XYZ model. We interpret this anomaly as an anomaly of the corresponding spin-half chains with translational symmetry, parity, and time reversal [but not involving the SO(3)-spin symmetry], requiring that the ground state is never trivially gapped, even if SO(3) spin symmetry is explicitly and completely broken. We also consider generalizations to $\mathbb{C}{P}^{N\ensuremath{-}1}$ models and show that the $C\text{\ensuremath{-}}P\text{\ensuremath{-}}T$ anomaly exists for even $N$.

arXiv:1802.02153•Physical review. B./Physical review. B•Apr 9, 2018•54 citations

Topological phases in quasi-periodic spin chains

Yifei Liu, Léa Ferreira dos Santos, Emil V. Prodan

Bulletin of the American Physical Society•Mar 19, 2021•0 citations

A Quantum Monte Carlo Study on Mixed-Spin Chains of 1/2-1/2-1-1 and 3/2-3/2-1-1

Zhaoxin Xu, Jun Zhang, Ying He-Ping

The ground-state and thermodynamic properties of quantum mixed-spin chains of 1/2-1/2-1-1 and 3/2-3/2-1-1 are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameter .

Communications in Theoretical Physics•Nov 15, 2003•1 citation

The spectral gap for some spin chains with discrete symmetry breaking

Bruno Nachtergaele

arXiv:cond-mat/9410110•Communications in Mathematical Physics•Feb 1, 1996•105 citations
We consider the O(3)O(3)O(3) nonlinear sigma model with the $\ensuremath{\theta}$ term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any $\ensuremath{\theta}$, and enjoys the periodicity in $\ensuremath{\theta}\ensuremath{\rightarrow}\ensuremath{\theta}+2\ensuremath{\pi}$. At $\ensuremath{\theta}=0,\ensuremath{\pi}$ it also has a charge-conjugation CCC symmetry. Gauging the discrete space-time reflection symmetries is interpreted as putting the theory on the nonorientable RP2\mathbb{R}{P}^{2}RP2 manifold, after which the $2\ensuremath{\pi}$ periodicity of $\ensuremath{\theta}$ and the CCC symmetry at $\ensuremath{\theta}=\ensuremath{\pi}$ are lost. We interpret this observation as a mixed 't Hooft anomaly among charge-conjugation CCC, parity PPP, and time-reversal TTT symmetries when $\ensuremath{\theta}=\ensuremath{\pi}$. Anomaly matching implies that in this case the ground state cannot be trivially gapped, as long as C,PC,PC,P, and TTT are all good symmetries of the theory. We make several consistency checks with various semiclassical regimes, and with the exactly solvable XYZ model. We interpret this anomaly as an anomaly of the corresponding spin-half chains with translational symmetry, parity, and time reversal [but not involving the SO(3)-spin symmetry], requiring that the ground state is never trivially gapped, even if SO(3) spin symmetry is explicitly and completely broken. We also consider generalizations to $\mathbb{C}{P}^{N\ensuremath{-}1}$ models and show that the $C\text{\ensuremath{-}}P\text{\ensuremath{-}}T$ anomaly exists for even NNN.
The ground-state and thermodynamic properties of quantum mixed-spin chains of 1/2-1/2-1-1 and 3/2-3/2-1-1 are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameter .