SciPost Phys. 11, 024 (2021) ·
published 6 August 2021

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We propose and prove a family of generalized LiebSchultzMattis (LSM)
theorems for symmetry protected topological (SPT) phases on boson/spin models
in any dimensions. The "conventional" LSM theorem, applicable to e.g. any
translation invariant system with an odd number of spin1/2 particles per unit
cell, forbids a symmetric shortrangeentangled ground state in such a system.
Here we focus on systems with no LSM anomaly, where global/crystalline
symmetries and fractional spins within the unit cell ensure that any symmetric
SRE ground state must be a nontrivial SPT phase with anomalous boundary
excitations. Depending on models, they can be either strong or "higherorder"
crystalline SPT phases, characterized by nontrivial surface/hinge/corner
states. Furthermore, given the symmetry group and the spatial assignment of
fractional spins, we are able to determine all possible SPT phases for a
symmetric ground state, using the real space construction for SPT phases based
on the spectral sequence of cohomology theory. We provide examples in one, two
and three spatial dimensions, and discuss possible physical realization of
these SPT phases based on condensation of topological excitations in
fractionalized phases.
Shenghan Jiang, Panjin Kim, Jung Hoon Han, Ying Ran
SciPost Phys. 7, 006 (2019) ·
published 9 July 2019

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The properties of ground state of spin$\frac{1}{2}$ kagome antiferromagnetic
Heisenberg (KAFH) model have attracted considerable interest in the past few
decades, and recent numerical simulations reported a spin liquid phase. The
nature of the spin liquid phase remains unclear. For instance, the interplay
between symmetries and $Z_2$ topological order leads to different types of
$Z_2$ spin liquid phases. In this paper, we develop a numerical simulation
method based on symmetric projected entangledpair states (PEPS), which is
generally applicable to strongly correlated model systems in two spatial
dimensions. We then apply this method to study the nature of the ground state
of the KAFH model. Our results are consistent with that the ground state is a
$U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.
Dr Jiang: "We appreciate the positive rem..."
in Submissions  report on Generalized LiebSchultzMattis theorem on bosonic symmetry protected topological phases