# Exact bosonization in arbitrary dimensions

@article{Chen2019ExactBI, title={Exact bosonization in arbitrary dimensions}, author={Yu-An Chen}, journal={arXiv: Strongly Correlated Electrons}, year={2019} }

We extend the previous results of exact bosonization, mapping from fermionic operators to Pauli matrices, in 2d and 3d to arbitrary dimensions. This bosonization map gives a duality between any fermionic system in arbitrary $n$ spatial dimensions and a new class of $(n-1)$-form $\mathbb{Z}_2$ gauge theories in $n$ dimensions with a modified Gauss's law. This map preserves locality and has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the manifold…

## Figures from this paper

## 21 Citations

Constraints of kinematic bosonization in two and higher dimensions

- Physics
- 2020

Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They…

Model of bosonization by flux attachment on hamiltonian lattices of arbitrary dimension

- Physics, Mathematics
- 2020

We present and prove the correctness of a bosonization prescription for fermionic lattice models in arbitrary dimensions. Our bosonized model is subject to constraints, which are interpreted in the…

Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension: Emergent fermions in fracton topological order

- Physics, MathematicsPhysical Review Research
- 2020

Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions, we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians…

Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories

- PhysicsPhysical Review D
- 2021

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing…

Geometrically Interpreting Higher Cup Products, and Application to Combinatorial Pin Structures

- Physics, Mathematics
- 2020

We provide a geometric interpretation of the formulas for Steenrod's $\cup_i$ products, giving an explicit construction for a conjecture of Thorngren. We construct from a simplex and a branching…

GEOMETRICALLY INTERPRETING HIGHER CUP PRODUCTS,

- 2020

We provide a geometric interpretation of the formulas for Steenrod’s ∪i products, giving an explicit construction for a conjecture of Thorngren. We construct from a simplex and a branching structure…

Commuting projector models for (
3+1
)-dimensional topological superconductors via a string net of (
1+1
)-dimensional topological superconductors

- Physics
- 2020

We discuss a way to construct a commuting projector Hamiltonian model for a ($3+1$)-dimensional topological superconductor in class DIII. The wave function is given by a sort of string net of the…

Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions

- Physics
- 2020

We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology. A central benefit of our construction is that…

Equivalence between fermion-to-qubit mappings in two spatial dimensions

- Physics, Mathematics
- 2022

Yu-An Chen (陳昱安) 2, ∗ and Yijia Xu (许逸葭) 3, † Department of Physics, Joint Quantum Institute, and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park,…

Bosonization of Majorana modes and edge states

- Physics
- 2021

We present a bosonization procedure which replaces fermions with generalized spin variables subject to local constraints. It requires that the number of Majorana modes per lattice site matches the…

## References

SHOWING 1-10 OF 15 REFERENCES

Exact bosonization in two spatial dimensions and a new class of lattice gauge theories

- PhysicsAnnals of Physics
- 2018

We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When…

Bosonization in three spatial dimensions and a 2-form gauge theory

- Physics
- 2019

We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form Z_2 gauge theory with an unusual Gauss law. An important…

Fermion decoration construction of symmetry-protected trivial order for fermion systems with any symmetry and in any dimension

- Physics
- 2019

We use higher dimensional bosonization and fermion decoration to construct exactly soluble interacting fermion models to realize fermionic symmetry protected trivial (SPT) orders (which are also…

Spin TQFTs and fermionic phases of matter

- Physics, Mathematics
- 2015

We study lattice constructions of gapped fermionic phases of matter. We show that the construction of fermionic Symmetry Protected Topological orders by Gu and Wen has a hidden dependence on a…

Fermionic SPT phases in higher dimensions and bosonization

- Physics
- 2017

A bstractWe discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological…

Fermions without fermion fields.

- Physics, MedicinePhysical review letters
- 2005

The generality of these results suggests that the observation of Fermion excitations in nature does not demand that anticommuting Fermions fields be fundamental, and extra conserved degrees of freedom are introduced.

Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions

- Physics, Mathematics
- 2017

We propose a generic construction of exactly soluble \emph{local bosonic models} that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble…

Mapping local Hamiltonians of fermions to local Hamiltonians of spins

- Physics
- 2005

We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which…

An introduction to lattice gauge theory and spin systems

- Physics
- 1979

This article is an interdisciplinary review of lattice gauge theory and spin systems. It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models of…

Fermionic Quantum Computation

- Physics
- 2000

We define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs…