Solvable Lattice Hamiltonians with Fractional Hall Conductivity

Abstract

We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem and is generalizable.

24 pages, published version

References in corpus (3)

• Generalized Global Symmetries
• Topological boundary conditions in abelian Chern-Simons theory
• A Commuting Projector Model with a Non-zero Quantized Hall conductance

Cited by in corpus (4)

• Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Models of interacting bosons with exact ground states: a unified approach
• Hamiltonian Lattice Formulation of Compact Maxwell-Chern-Simons Theory