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

Bulletin of the American Physical Society

Symmetry protected topological phases for 1-dimensional spin-1 antiferromagnets

Zheng-Xin Liu, Xie Chen, Xiao-Gang Wen

Published Feb 28, 2012• 0 citations
OpenAlex

Related papers

Realizing a symmetry-protected topological phase in the antiferromagnetic spin-1/2 Hubbard ladder

Sarah Hirthe, Pimonpan Sompet, Dominik Bourgund +9 more

Bulletin of the American Physical Society•Mar 17, 2021•0 citations

Three-dimensional symmetry-protected topological phase close to antiferromagnetic Néel order

Cenke Xu

It is well known that the Haldane phase of a one-dimensional spin-1 chain is a symmetry-protected topological (SPT) phase, which is described by a nonlinear sigma model (NLSM) with a $\ensuremath{\Theta}$ term at $\ensuremath{\Theta}=2\ensuremath{\pi}$. In this work we study a three-dimensional (3d) SPT phase of a SU(2$N$) antiferromagnetic spin system with a self-conjugate representation on every site. The spin-ordered N\'eel phase of this system has a ground state manifold $\mathcal{M}=\frac{\mathrm{U}(2N)}{\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(N)}$, and this system is described by a NLSM defined with manifold $\mathcal{M}$. Since the homotopy group ${\ensuremath{\pi}}_{4}[\mathcal{M}]=\mathbb{Z}$ for $N>1$, this NLSM can naturally have a $\ensuremath{\Theta}$ term. We will argue that when $\ensuremath{\Theta}=2\ensuremath{\pi}$ this NLSM describes a SPT phase. This SPT phase is protected by the SU(2$N$) spin symmetry, or its subgroup SU($N$)$\ifmmode\times\else\texttimes\fi{}$SU$(N)\ensuremath{\rtimes}{Z}_{2}$, without assuming any other discrete symmetry. We will also construct a trial SU(2$N$) spin state on a 3d lattice; we argue that the long-wavelength physics of this state is precisely described by the aforementioned NLSM with $\ensuremath{\Theta}=2\ensuremath{\pi}$.

arXiv:1209.4399•Physical Review B•Apr 25, 2013•39 citations

Symmetry protected topological phases in spin-1 ladders and their phase transitions

Ji-Yao Chen, Zheng-Xin Liu

arXiv:1503.05835•Annals of Physics•Sep 1, 2015•5 citations

Classification of symmetry protected topological phases in quantum spin chains

Yoshiko Ogata

We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems.SPT phases are gapped short-range-entangled quantum phases with a symmetry G.We explain that in one and two-dimensional quantum spin systems, there are H 2 (G, U (1))/ H 3 (G, U (1))-valued invariant, confirming a physicists conjecture.Contents 1. Symmetry protected topological phases 41 2. SPT-phases in 1-dimensional systems 63 3. SPT-phases in 2-dimensional systems 78

arXiv:2110.04671•Current Developments in Mathematics•Jan 1, 2020•15 citations

Classification of fermionic symmetry-protected topological phases

Qing-Rui Wang, Zheng‐Cheng Gu

Bulletin of the American Physical Society•Mar 4, 2019•0 citations

Bosonic symmetry-protected topological phases with reflection symmetry

Tsuneya Yoshida, Takahiro Morimoto, Akira Furusaki

We study two-dimensional bosonic symmetry-protected topological (SPT) phases that are protected by reflection symmetry and local symmetry [${Z}_{N}\ensuremath{\rtimes}R, {Z}_{N}\ifmmode\times\else\texttimes\fi{}R$, U(1)$\ensuremath{\rtimes}R$, or U(1)$\ifmmode\times\else\texttimes\fi{}R$], in the search for two-dimensional bosonic analogs of topological crystalline insulators in integer-$S$ spin systems with reflection and spin-rotation symmetries. To classify them, we employ a Chern-Simons approach and examine the stability of edge states against perturbations that preserve the assumed symmetries. We find that SPT phases protected by ${Z}_{N}\ensuremath{\rtimes}R$ symmetry are classified as ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ for even $N$ and 0 (no SPT phase) for odd $N$, while those protected by U(1)$\ensuremath{\rtimes}R$ symmetry are ${\mathbb{Z}}_{2}$. We point out that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state of $S=2$ spins on the square lattice is a ${\mathbb{Z}}_{2}$ SPT phase protected by reflection and $\ensuremath{\pi}$-rotation symmetries.

arXiv:1509.04395•Physical Review B•Dec 14, 2015•18 citations
It is well known that the Haldane phase of a one-dimensional spin-1 chain is a symmetry-protected topological (SPT) phase, which is described by a nonlinear sigma model (NLSM) with a $\ensuremath{\Theta}$ term at $\ensuremath{\Theta}=2\ensuremath{\pi}$. In this work we study a three-dimensional (3d) SPT phase of a SU(2NNN) antiferromagnetic spin system with a self-conjugate representation on every site. The spin-ordered N\'eel phase of this system has a ground state manifold $\mathcal{M}=\frac{\mathrm{U}(2N)}{\mathrm{U}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(N)}$, and this system is described by a NLSM defined with manifold M\mathcal{M}M. Since the homotopy group ${\ensuremath{\pi}}_{4}[\mathcal{M}]=\mathbb{Z}$ for N>1N>1N>1, this NLSM can naturally have a $\ensuremath{\Theta}$ term. We will argue that when $\ensuremath{\Theta}=2\ensuremath{\pi}$ this NLSM describes a SPT phase. This SPT phase is protected by the SU(2NNN) spin symmetry, or its subgroup SU(NNN)$\ifmmode\times\else\texttimes\fi{}$SU$(N)\ensuremath{\rtimes}{Z}_{2}$, without assuming any other discrete symmetry. We will also construct a trial SU(2NNN) spin state on a 3d lattice; we argue that the long-wavelength physics of this state is precisely described by the aforementioned NLSM with $\ensuremath{\Theta}=2\ensuremath{\pi}$.
We study two-dimensional bosonic symmetry-protected topological (SPT) phases that are protected by reflection symmetry and local symmetry [${Z}_{N}\ensuremath{\rtimes}R, {Z}_{N}\ifmmode\times\else\texttimes\fi{}R$, U(1)$\ensuremath{\rtimes}R$, or U(1)$\ifmmode\times\else\texttimes\fi{}R$], in the search for two-dimensional bosonic analogs of topological crystalline insulators in integer-SSS spin systems with reflection and spin-rotation symmetries. To classify them, we employ a Chern-Simons approach and examine the stability of edge states against perturbations that preserve the assumed symmetries. We find that SPT phases protected by ${Z}_{N}\ensuremath{\rtimes}R$ symmetry are classified as ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ for even NNN and 0 (no SPT phase) for odd NNN, while those protected by U(1)$\ensuremath{\rtimes}R$ symmetry are Z2{\mathbb{Z}}_{2}Z2​. We point out that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state of S=2S=2S=2 spins on the square lattice is a Z2{\mathbb{Z}}_{2}Z2​ SPT phase protected by reflection and $\ensuremath{\pi}$-rotation symmetries.