Related papers: An index for two-dimensional SPT states
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain…
We study several aspects of the realization of global symmetries in highly entangled phases of quantum matter. Examples include gapped topological ordered phases, gapless quantum spin liquids and non-fermi liquid phases. An insightful…
We construct an exactly sovable commuting projector Hamiltonian for (2+1)D bosonic topological insulator which is one of symmetry-protected topological (SPT) phases protected by U(1) and time-reversal $\mathbb{Z}_2^T$ symmetry, where the…
We propose a class of pure states of two-dimensional lattice systems realizing topological order associated with unitary rational vertex operator algebras. We show that the states are well-defined in the thermodynamic limit and have…
We study two-dimensional bosonic symmetry protected topological (SPT) phases which are protected by reflection symmetry and local symmetry [$Z_N\rtimes R$, $Z_N\times R$, U(1)$\rtimes R$, or U(1)$\times R$], in the search for…
Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting…
We explicitly realize the Rep($Q_8$) non-invertible symmetry-protected topological (SPT) state as a 1+1d cluster state on a tensor product Hilbert space of qubits. Using the Kramers-Wannier operator, we construct the lattice models for the…
A method of using partial symmetries to distinguish two dimensional symmetry protected topological (SPT) phases of on-site, unitary symmetries is proposed. This novel order parameter takes a wavefunction, such as a ground state of a lattice…
We consider symmetry protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases. We show that such phases can be understood in terms of lower-dimensional topological phases with on-site…
It has been shown that the L-type bosonic symmetry-protected-trivial (SPT) phases with pure gauge anomalous boundary can all be realized via non-linear $\sigma$-models (NL$\sigma$Ms) of the symmetry group $G$ with various topological terms.…
A grand-canonical system of interacting bosons is considered to study phase transitions of ultracold atoms in an optical lattice. The phase diagram is discussed in terms of a matrix-like order parameter, representing a symmetric phase (Mott…
Symmetry Protected Topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper we describe the classification and properties of such phases for three dimensional(3D)…
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac,…
We study $S=1$ quantum spin systems on the infinite chain with short ranged Hamiltonians which have certain rotational and discrete symmetry. We define a $\mathbb{Z}_2$ index for any gapped unique ground state, and prove that it is…
We describe a systematic procedure for determining the identity of a 2D bosonic symmetry protected topological (SPT) phase from the properties of its edge excitations. Our approach applies to general bosonic SPT phases with either unitary…
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 an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase…
We employ index theoretic methods to study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. This allows us to compare singly quantized $hc/2e$ and doubly quantized $hc/e$ vortices, the…
We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence…
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…