Contributor info: Mr Chunxiao Liu

Chunxiao Liu, Weicheng Ye

SciPost Phys. 18, 161 (2025) · published 20 May 2025 | Toggle abstract · pdf

We compute the mod-2 cohomology ring for three-dimensional (3D) space groups and establish a connection between them and the lattice structure of crystals with space group symmetry. This connection allows us to obtain a complete set of Lieb-Schultz-Mattis constraints, specifying the conditions under which a unique, symmetric, gapped ground state cannot exist in 3D lattice magnets. We associate each of these constraints with an element in the third mod-2 cohomology of the space group, when the internal symmetry acts on-site and its projective representations are classified by powers of $\mathbb{Z}_2$. We demonstrate the relevance of our results to the study of $U(1)$ quantum spin liquids on the 3D pyrochlore lattice. We determine, through anomaly matching, the symmetry fractionalization patterns of both electric and magnetic charges, extending previous results from projective symmetry group classifications.

Chunxiao Liu, Pengfei Zhang, Xiao Chen

SciPost Phys. 10, 048 (2021) · published 23 February 2021 | Toggle abstract · pdf

We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large $N$ limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

Pengfei Zhang, Chunxiao Liu, Xiao Chen

SciPost Phys. 8, 094 (2020) · published 26 June 2020 | Toggle abstract · pdf

The Sachdev-Ye-Kitaev model is an $N$-modes fermionic model with infinite range random interactions. In this work, we study the thermal R\'enyi entropy for a subsystem of the SYK model using the path-integral formalism in the large-$N$ limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size $M\leq N/2$. We also consider generalizations of the SYK model with quadratic random hopping term or $U(1)$ charge conservation.