Related papers: On the Phases of a Complex Matrix
We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground…
We study a one-dimensional ladder of two coupled XXZ spin chains and identify several distinct gapless symmetry-enriched critical phases. These have the same unbroken symmetries and long-wavelength description, but cannot be connected…
We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both…
A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The…
e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine…
We make extensive simulations over a spin chain model that combines the frustrated $J_1\textrm{-}J_2$ spin chain and the long-range nonfrustrated $(-1)^{(r-1)}r^{-\alpha}$ decay interactions through the variational matrix product state…
Given a star product with separation of variables on a pseudo-Kaehler manifold, we obtain a new formal (1,1)-form from its classifying form and call it the phase form of the star product. The cohomology class of a star product with…
We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological…
From known phase diagram regions of different model Hamiltonians describing strongly correlated systems we deduced new domains of the ground state phase diagram of the same model by an unitary transformation. Different types of extended…
The continuous phase transition, indicated by the macroscopic order parameter and the occurrence of the spontaneous symmetry breaking, is well illustrated based on the Ginzburg-Landau's paradigm. In systems described by one order parameter,…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…
The notion of the higher rank numerical range $\Lambda_{k}(L(\lambda))$ for matrix polynomials $L(\lambda)=A_{m}\lambda^{m}+...+A_{1}\lambda+A_{0}$ is introduced here and some fundamental geometrical properties are investigated. Further,…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics,…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study…
We investigate a unitary matrix model with a complex potential with Fisher-Hartwig singularities. We show that the model exhibits finite-$N$ phase transitions. The order of the phase transition is coupling-dependent. At large-$N$, these…