Related papers: Hidden Symmetry in 1D Localization
We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this work we use symmetry as a guide to map…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
A disordered solid, such as an athermal jammed packing of soft spheres, exists in a rugged potential-energy landscape in which there are a myriad of stable configurations that defy easy enumeration and characterization. Nevertheless, in…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
A fermionic disordered one dimensional wire in the presence of attractive interactions is known to have two distinct phases: A localized and a superconducting one depending on the strength of interaction and disorder. The localized region…
As the dimensionality is reduced, the world becomes more and more interesting; novel and fascinating phenomena show up which call for understanding. Physics in one dimension is a fascinating topic for theory and experiment: for the former…
We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems.…
We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
It has been widely believed that almost all states in one-dimensional (1d) disordered systems with short-range hopping and uncorrelated random potential are localized. Here, we consider the fate of these localized states by coupling between…
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity…
From the perfect radial symmetries of radiolarian mineral skeletons to the broken symmetry of homochirality, the logic of Nature's regularities has fascinated scientists for centuries. Some of Nature's symmetries are clearly visible in…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we investigate the boundary supersymmetry of one-dimensional…
We study numerically and analytically the moments of the dimensionless level curvature for one-dimensional disordered rings of the circumference L pierced by a magnetic flux. The negative moments of the curvature distribution can be…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder…
We investigate nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such "random-field" disorder is known to have…