Fractionalization as an alternate to charge ordering in electronic insulators

Abstract

Incompressible insulating phases of electronic systems at partial filling of a lattice are often associated with charge ordering that breaks lattice symmetry. The resulting phases have an enlarged unit cell with an effective integer filling. Here we explore the possibility of insulating states - which we dub "Quantum Charge Liquids" (QCL) - at partial lattice filling that preserve lattice translation symmetry. Such QCL phases must necessarily either have gapped fractionally charged excitations and associated topological order or have gapless neutral excitations. We establish some general constraints on gapped fermionic QCL phases that restrict the nature of their topological order. We prove a number of results on the minimal topological order that is consistent with the lattice filling. In particular we show that at rational fillings $\nu =p/q$ with $q$ an even integer the minimal ground state degeneracy on a torus of the fermionic QCL is $4q^2$, 4 times larger than that of the bosonic QCL at the same filling. We comment on models and physical systems which may host fermionic QCL phases and discuss the phenomenology of these phases.

30 pages, 6 figures; updated upon journal acceptance

References in corpus (50)

• Anyons in an exactly solved model and beyond
• Quantum Spin Liquids
• Quantum Spin Liquids
• Optical detection of Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices
• Magic continuum in twisted bilayer WSe2
• Observation of Fractionally Quantized Anomalous Hall Effect
• Lieb-Schultz-Mattis in Higher Dimensions
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Abundance of correlated insulating states at fractional fillings of WSe${}_2$/WS${}_2$ moiré superlattices
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Fractionalized Fermi liquids
• Quantum orders in an exact soluble model
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Interacting fermionic topological insulators/superconductors in three dimensions
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Anyon condensation and its applications
• Dual Order Parameter for the Nodal Liquid
• Putting competing orders in their place near the Mott transition
• Exotic order in simple models of bosonic systems
• Orthogonal Metals: The simplest non-Fermi liquids
• Microscopic models for fractionalized phases in strongly correlated systems
• Magnetization plateaus of SrCu_2(BO_3)_2 from a Chern-Simons theory
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Quantum Confinement Transition in a d-wave Superconductor
• Composite fermion duality for half-filled multicomponent Landau Levels
• Fermionic symmetry fractionalization in (2+1)D
• Realizing topological surface states in a lower-dimensional flat band
• Symmetry enriched U(1) quantum spin liquids
• Correlated Fermions on a Checkerboard Lattice
• Bosonic model with $Z_3$ fractionalization
• Hall conductance and the statistics of flux insertions in gapped interacting lattice systems
• A study of time reversal symmetry of abelian anyons
• Theory of a continuous bandwidth-tuned Wigner-Mott transition
• Anomaly cascade in (2+1)D fermionic topological phases
• Metal-Insulator Transition with Charge Fractionalization
• Gauging Lie group symmetry in (2+1)d topological phases
• Anomaly indicators for topological orders with $U(1)$ and time-reversal symmetry
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems
• Non-Abelian spin Hall insulator
• Filling constraints on fermionic topological order in zero magnetic field
• Resonating Valence Bond States in an Electron-Phonon System
• Fermionic quantum dimer and fully-packed loop models on the square lattice
• Metal to Wigner-Mott insulator transition in two-leg ladders
• Continuous Wigner-Mott transition at $\nu =1/5$

Cited by in corpus (4)

• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Ordering the topological order in the fractional quantum Hall effect
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges