Related papers: Symmetry enriched U(1) quantum spin liquids
We derive a selection rule among the $(1+1)$-dimensional SU(2) Wess-Zumino-Witten theories, based on the global anomaly of the discrete $\mathbb{Z}_2$ symmetry found by Gepner and Witten. In the presence of both the SU(2) and $\mathbb{Z}_2$…
Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group…
The properties of stable Luttinger liquid phases in models with a non-conserved number of particles are investigated. We study the Luttinger liquid phases in one-dimensional models of hard-core boson and spinless fermion chains where…
We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer…
We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a…
The local Lie algebra of the Standard Model (SM) is $su(3)\times su(2) \times u(1)$, yet its global gauge group, $G_{{\rm SM}_{\rm q}}=$SU(3)$\times$SU(2)$\times$U(1)/$\mathbb{Z}_{\rm q}$, q$=1,2,3,6$ remains undetermined. Building on…
We use the projective symmetry group analysis to classify the quantum spin liquids on the $S=1/2$ pyrochlore magnet with a breathing anisotropy. We find 40 $\mathbb{Z}_2$ spin liquids and 16 $U(1)$ spin liquids that respect the $F\bar{4}3m$…
Spin liquids are exotic quantum states characterized by the existence of fractional and deconfined quasiparticle excitations, referred to as spinons and visons. Their fractional nature establishes topological properties such as a protected…
Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here, we consider a gapless U(1) spin liquid with spinon Fermi pockets in…
Symmetry protected topological (SPT) phases of bosons in $d$ spatial dimensions have been characterized by the action of the protecting global symmetry $G$ on their boundary. The symmetry acts on the boundary in a way that would be…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…
We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We…
We study two-dimensional bosonic symmetry protected topological (SPT) phases which are protected by reflection symmetry and local symmetry [$Z_N\rtimes R$, $Z_N\times R$, U(1)$\rtimes R$, or U(1)$\times R$], in the search for…
This chapter is intended as a brief overview of some of the quantum spin liquid phases with unbroken SU(2) spin symmetry available in one dimension. The main characteristics of these phases are discussed by means of the bosonization…
Recently, it was realized that quantum states of matter can be classified as long-range entangled (LRE) states (i.e. with non-trivial topological order) and short-range entangled (SRE) states (\ie with trivial topological order). We can use…
Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal…
Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are…
We consider compact $U^\kappa(1)$ gauge theory in 3+1D with the $2\pi$-quantized topological term ${\sum_{I, J =1}^\kappa\frac{K_{IJ}}{4\pi}\int_{M^4}F^I\wedge F^J}$. At energies below the gauge charges' gaps but above the monopoles' gaps,…
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well-established numerically, a controlled theoretical path from the lattice model leading to a low energy topological field theory…