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

Chen, Yu-An; Kapustin, Anton

doi:10.1103/physrevb.100.245127

Cited by 61 publications

(84 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The variation involves introducing ancilla degrees of freedom at the boundary. These are bosonic ancillas, but we will think of them as fermions f coupled to a lattice Z f 2 gauge field, similar to the way the spin degrees of freedom in Kitaev's honeycomb model can be thought of as fermions coupled to a Z f 2 gauge field [15,[34][35][36]. We now proceed as before, but make the domain walls topologically trivial by condensing a bilinear between f and one of the 3-fermion anyons -such a particle is a boson, and can be condensed everywhere on the domain wall.…”

Section: Topologically Ordered Boundarymentioning

confidence: 99%

Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase

2020

View full text Add to dashboard Cite

We construct an exactly solvable commuting projector model for a 4 + 1 dimensional Z 2 symmetry-protected topological phase (SPT) which is outside the cohomology classification of SPTs. The model is described by a decorated domain wall construction, with "threefermion" Walker-Wang phases on the domain walls. We describe the anomalous nature of the phase in several ways. One interesting feature is that, in contrast to in-cohomology phases, the effective Z 2 symmetry on a 3 + 1 dimensional boundary cannot be described by a quantum circuit and instead is a nontrivial quantum cellular automaton (QCA). A related property is that a codimension-two defect (for example, the termination of a Z 2 domain wall at a trivial boundary) will carry nontrivial chiral central charge 4 mod 8. We also construct a gapped symmetric topologically-ordered boundary state for our model, which constitutes an anomalous symmetry enriched topological phase outside of the classification of Ref.[1], and define a corresponding anomaly indicator.(⇒) If U acts as a QCA by conjugation, β(X i ) is supported near spin i for a spin Pauli operator X i at i. Hence, since this operator must commute with X j for j far from i, not only is (V z+i ) † V z an operator on the material supported near spin i, it is equal to (V z+i+j ) † V z+j for any j far from i. In words, (V z+i ) † V z depends only on spins near i.Note that U dis acting by conjugation as a QCA is a stronger requirement than just that U mat z acts by conjugation as a QCA as it also imposes locality requirements on the spin degrees of freedom. Heuristically, it means that changing z locally will only change the action of U mat z locally.Following [13], we believe that if one restricts U mat z to just the material degrees of freedom in the domain wall manifold M z , then it is nontrivial, i.e., it cannot be written as a quantum circuit

show abstract

Section: Topologically Ordered Boundarymentioning

confidence: 99%

Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase

2020

View full text Add to dashboard Cite

show abstract

“…We will always work with an arbitrary triangulation of a closed simply connected n-dimensional manifold M n equipped with a branching structure (orientations on edges without forming a loop in any triangle). 2 The vertices, edges, faces, and tetrahedra are denoted v, e, f , t, respectively. The general d simplex is denoted as d .…”

Section: Chains Cochains and Higher Cup Productsmentioning

confidence: 99%

“…We defined this as the + tetrahedron, the directions of faces 012 and 023 are inward (blue) while the directions of faces 123 and 013 are outward (red). The directions of faces are reversed in the -tetrahedron (mirror image of this tetrahedron) [2].…”

Section: Chains Cochains and Higher Cup Productsmentioning

confidence: 99%

“…We begin by reviewing the duality between fermions and Z 2 lattice gauge theory in both two spatial dimensions [1] and three spatial dimensions [2]. On each face f of the 2-manifold M 2 , we place a single pair of fermionic creation-annihilation operators c f , c † f , or equivalently a pair of Majorana fermions:…”

Section: Review Of Boson-fermion Duality In (2+1)d and (3+1)dmentioning

confidence: 99%

“…The 2D duality is also kinematic. This approach has been generalized to 3D [2]. Every fermionic lattice system in 3D is dual to a Z 2 2-form gauge theory with an unusual Gauss's law.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact bosonization in arbitrary dimensions

Chen

2020

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

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 class of (n − 1)-form 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 spatial manifold. A formula for Stiefel-Whitney homology classes on lattices is derived. In the Euclidean path integral, this exact bosonization map is equivalent to introducing a topological Steenrod square term to the space-time action.

show abstract

Hydrodynamics, anomaly inflow and bosonic effective field theory

Abanov,

Cappelli

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the action formulation of hydrodynamics at zero temperature is reconsidered and shown to be equal to standard field-theory bosonization. Furthermore, it can be derived from a topological gauge theory in one extra dimension, which identifies the fluid variables through the anomaly inflow relations. Extending this framework to 3+1 dimensions yields an effective field theory/hydrodynamics model, capable of elucidating the mixed axial-vector and axial-gravitational anomalies of Dirac fermions. This formulation provides a platform for bosonization in higher dimensions. Moreover, the connection with 4+1 dimensional topological theories suggests some generalizations of fluid dynamics involving additional degrees of freedom.

show abstract

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

Cited by 61 publications

References 15 publications

Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase

Exactly solvable model for a 4+1D beyond-cohomology symmetry-protected topological phase

Exact bosonization in arbitrary dimensions

Hydrodynamics, anomaly inflow and bosonic effective field theory

Contact Info

Product

Resources

About