Related papers: Entropic topological invariant for a gapped one-di…
We study topological order in a toric code in three spatial dimensions, or a 3+1D Z_2 gauge theory, at finite temperature. We compute exactly the topological entropy of the system, and show that it drops, for any infinitesimal temperature,…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
We introduce an entropic quantity for two-dimensional (2D) quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator…
The study of the (logarithm of the) {\em fidelity} i.e., of the overlap amplitude, between ground states of Hamiltonians corresponding to different coupling constants, provides a valuable insight on critical phenomena. When the parameters…
The criteria determining the sign of entropy change in the open system are formulated. The concepts of entrostat, degree of openness, critical level of ordering are entered. The opportunity of occurrence of entropy oscillations in a…
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a…
We introduce a novel approach, inspired from the theory of renewal processes, to determine the configurational entropy of ensembles of constrained configurations of particles on the one-dimensional lattice. The proposed method can deal with…
We demonstrate that hidden long range order is always present in the gapped phases of interacting fermionic systems on one dimensional lattices. It is captured by correlation functions of appropriate nonlocal charge and/or spin operators,…
The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our…
We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local…
Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…
Conformal transformations can be used to obtain the order parameter for two-dimensional systems at criticality in finite geometries with fixed boundary conditions on a connected boundary. To the known examples of this class (such as the…
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…