Topological disorder parameter: A many-body invariant to characterize gapped quantum phases

Entropic topological invariant for a gapped one-dimensional system

We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well-defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, sug...

Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry

Recent vigorous investigations of topological order have not only discovered new topological states of matter but also shed new light to “already known” topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking but most typically manifest ...

Topological phases and quantum computation

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being ‘in the same phase’ if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on s ∈ [0, 1], such that for each s, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectivel...

Identifying phases of quantum many-body systems that are universal for quantum computation.

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possess...