Related papers: Measuring Modular Matrices by Shearing Lattices
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
We study the topological phase in dipolar-coupled two-dimensional breathing square lattice of magnetic vortices. By evaluating the quantized Chern number and $\mathbb{Z}_{4}$ Berry phase, we obtain the phase diagram and identify that the…
We study the topology of the order parameter in the intermediate phase between the superconducting and time-reversal symmetry breaking transitions of a $p_x+ip_y$ superconductor under strain. The application of in-plane strain reduces the…
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
We study the transport and localization properties of scalar vibrations on a lattice with random bond strength by means of the transfer matrix method. This model has been recently suggested as a means to investigate the vibrations and heat…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
We study topological properties of families of Hamiltonians which may contain degenerate energy levels aka. band crossings. The primary tool are Chern classes, Berry phases and slicing by surfaces. To analyse the degenerate locus, we study…
We study the topological properties of Peierls transitions in a monovalent M\"{o}bius ladder. Along the transverse and longitudinal directions of the ladder, there exist plenty Peierls phases corresponding to various dimerization patterns.…
The effect of spatially modulated interaction on quantum phase transition in one-dimensional interacting spinless fermion system is theoretically investigated by exact diagonalization and density matrix renormalization group method. Our…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
Electronic charge order is a symmetry breaking state in high-$T_\mathrm{c}$ cuprate superconductors. In scanning tunneling microscopy, the detected charge-order-induced modulation is an electronic response of the charge order. For an…
We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite…
We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled qubits…
Topological models are characterized by a quantized topological invariant and provide a description of novel phases of matter that can exhibit localized edge states, corner modes, and chiral transport. We experimentally realize two 1-D…
Modular Berry transport associates a geometric phase to a zero mode ambiguity in a family of modular operators. In holographic settings, this phase was shown to encode nontrivial information about the emergent spacetime geometry. We…
Thouless charge pumping protocol provides an effective route for realizing topological particle transport. To date, the first-order and higher-order topological pumps, exhibiting transitions of edge-bulk-edge and corner-bulk-corner states,…
The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find…