3,124 research outputs found
On the Structure of Covers of Sofic Shifts
A canonical cover generalizing the left Fischer cover to arbitrary sofic
shifts is introduced and used to prove that the left Krieger cover and the past
set cover of a sofic shift can be divided into natural layers. These results
are used to find the range of a flow-invariant and to investigate the ideal
structure of the universal C*-algebra associated to a sofic shift space.Comment: To appear in Documenta Mathematica. Section 2 has been shortened.
Three sections concerning the layered structure of the left Krieger cover and
the past set cover have been merged and rewritten. Non-essential examples
have been omitted. 21 pages, 8 figure
Energy as an Entanglement Witness for Quantum Many-Body Systems
We investigate quantum many-body systems where all low-energy states are
entangled. As a tool for quantifying such systems, we introduce the concept of
the entanglement gap, which is the difference in energy between the
ground-state energy and the minimum energy that a separable (unentangled) state
may attain. If the energy of the system lies within the entanglement gap, the
state of the system is guaranteed to be entangled. We find Hamiltonians that
have the largest possible entanglement gap; for a system consisting of two
interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such
example. We also introduce a related concept, the entanglement-gap temperature:
the temperature below which the thermal state is certainly entangled, as
witnessed by its energy. We give an example of a bipartite Hamiltonian with an
arbitrarily high entanglement-gap temperature for fixed total energy range. For
bipartite spin lattices we prove a theorem demonstrating that the entanglement
gap necessarily decreases as the coordination number is increased. We
investigate frustrated lattices and quantum phase transitions as physical
phenomena that affect the entanglement gap.Comment: 16 pages, 3 figures, published versio
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