Related papers: Boundary-obstructed topological phases
Symmetry-protected topological (SPT) phases in interacting bosonic systems have been widely explored, yet most realizations rely on fine-tuned interactions or enlarged symmetries. Here we show that a qualitatively simpler mechanism--parity…
Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases --symmetry-protected topological (SPT) phases in particular--defined in one dimensional lattices. On the other hand, it is natural to…
This thesis studies a pair of symmetry protected topological (SPT) phases which arise when considering one-dimensional quantum spin systems possessing a natural orthogonal group symmetry. Particular attention is given to a family of exactly…
We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand,…
In this paper we systematically classify and describe bosonic symmetry protected topological (SPT) phases in all physical spatial dimensions using semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases on a…
Generalised charge pumps are topological obstructions to trivialising loops in the space of symmetric gapped Hamiltonians. We show that given mild conditions on such pumps, the associated loop has high-symmetry points which must be in…
In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry…
The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels.…
Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup $\mathbb{Z}_N \times \mathbb{Z}_N$) with $N>2$. The unique feature of these symmetry…
We study $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases in one-dimensional spin systems with $Z_3 \times Z_3$ symmetry. We construct ground-state wave functions of the matrix product form for nontrivial $\mathbb{Z}_3$ phases and…
While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological…
We study the interplay of duality and stacking of bosonic and fermionic symmetry-protected topological phases in one spatial dimension. In general the classifications of bosonic and fermionic phases have different group structures under the…
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 (SPT) phase. In this model anyonic…
Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of topological insulators, have attracted enormous theoretical interest in the last few years. Although BSPT states have been classified by various approaches, there…
In 2+1D, topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries. Additionally, they support topologically protected spin-1 edge states,…
Sub-symmetry (SubSy) protected topological states represent a concept that goes beyond the conventional framework of symmetry-protected topological (SPT) phases, demonstrating that topological boundary states can remain robust even when the…
Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Target model in this study is an extended version of the cluster model in one dimension with $Z_2\otimes Z_2$ symmetry,…
A platform for constructing microscopic Hamiltonians describing bosonic symmetry-protected topological (SPT) states is presented. The Hamiltonians we consider are examples of frustration-free Rokhsar-Kivelson models, which are known to be…
We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all…
Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting…