Related papers: Lattice model constructions for gapless domain wal…

Much of the dramatic growth in research on topological materials has focused on topologically protected surface states. While the domain walls of topological materials such as Weyl semimetals with broken inversion or time-reversal symmetry…

We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

We construct a one-dimensional local spin Hamiltonian with an intrinsically non-local, and therefore anomalous, global $\mathbb{Z}_2$ symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and…

We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show…

Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard…

We study the domain walls which form when Bose condensates acquire a double-well dispersion. Experiments have observed such domain walls in condensates driven across a $\mathbb{Z}_2$ symmetry-breaking phase transition in a shaken optical…

We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not…

Experiments in gated bilayer graphene with stacking domain walls present topological gapless states protected by no-valley mixing. Here we research these states under gate voltages using atomistic models, which allow us to elucidate their…

We study with lattice techniques the localisation of gauge fields on domain wall defects in 2+1 dimensions, following a scenario originally proposed by Dvali and Shifman for 3+1 dimensions, based on confining dynamics in the bulk. We find…

We study the mean-field BCS-BEC evolution of a uniform Fermi gas on a single-band triangular lattice, and construct its ground-state phase diagrams, showing a wealth of topological quantum phase transitions between gapped and gapless…

We construct fixed point lattice models for group supercohomology symmetry protected topological (SPT) phases of fermions in 2+1D. A key feature of our approach is to construct finite depth circuits of local unitaries that explicitly build…

In this work, the second paper of this series, we study the 2+1d version of a Hamiltonian model for topological phases based on higher lattice gauge theory. We construct the ribbon operators that produce the point-like excitations. These…

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 in any spacetime dimensions, whose…

We consider exactly solvable models in (3+1)d whose ground states are described by topological lattice gauge theories. Using simplicial arguments, we emphasize how the consistency condition of the unitary map performing a local change of…

We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands.…

The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. The ribbon operators and the classification of…

In recent work, we developed a method to construct invertible and non-invertible symmetries of finite-group gauge theories as topological domain walls on the lattice. In the present work, we consider abelian and non-abelian finite-group…

We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $\alpha$ over $G$. The detailed properties of the ground states are studied, and we find that the…

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…