• Corpus ID: 235390875

Higher cup products on hypercubic lattices: application to lattice models of topological phases

  title={Higher cup products on hypercubic lattices: application to lattice models of topological phases},
  author={Yu-An Chen and Sri Ramya Tata},
In this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation on the simplicial complexes. We illustrate how this formalism can elucidate lattice constructions on hypercubic lattices for various models and deriving them from spacetime actions. In particular, we demonstrate explicitly that the (3+1)D SPT S = 12 ∫ w 22 + w 41 (where w 1 and w 2 are the first and second Stiefel-Whitney classes) is dual to the… 

Modified Villain formulation of abelian Chern-Simons theory

We formulate $U(1)_k$ Chern-Simons theory on a Euclidean spacetime lattice using the modified Villain approach. Various familiar aspects of continuum Chern-Simons theory such as level quantization,

Towards topological fixed-point models beyond gappable boundaries

We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of

Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies

We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four

Comments on foliated gauge theories and dualities in 3+1d

We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent

Fermionic defects of topological phases and logical gates

We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a

Long-range entanglement from measuring symmetry-protected topological phases

A fundamental distinction between many-body quantum states are those with shortand longrange entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the

Loops in 4+1d Topological Phases

Xie Chen, Arpit Dua, Po-Shen Hsin, Chao-Ming Jian, Wilbur Shirley, Cenke Xu 1 Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA



The Low-Energy TQFT of the Generalized Double Semion Model

  • A. Debray
  • Mathematics
    Communications in Mathematical Physics
  • 2019
The generalized double semion (GDS) model, introduced by Freedman and Hastings, is a lattice system similar to the toric code, with a gapped Hamiltonian whose definition depends on a triangulation of

Double Semions in Arbitrary Dimension

We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of $${d-1}$$d-1 dimensional surfaces in a d dimensional ambient space. We construct

A formula for Stiefel-Whitney homology classes

The purpose of this paper is to define for mod 2 Euler spaces a formula which enables one to compute the Stiefel-Whitney homology classes in the original triangulation without passing to the first

Exactly soluble model of a three-dimensional symmetry-protected topological phase of bosons with surface topological order

We construct an exactly soluble Hamiltonian on the D=3 cubic lattice, whose ground state is a topological phase of bosons protected by time-reversal symmetry, i.e., a symmetry-protected topological

String-net condensation: A physical mechanism for topological phases

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''

Topological Field Theory on a Lattice, Discrete Theta-Angles and Confinement

We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite

Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory

Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the

Exact bosonization in arbitrary dimensions

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