Nonlocal Order in Gapless Systems: Entanglement Spectrum in Spin Chains
- Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)
- Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States)
We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high 'entanglement energy' levels, from a flat band of levels with specific multiplicities defining the ground state, and remains finite in the thermodynamic limit. We pick the appropriate set of quantum numbers and partition the system in this space, corresponding to a nonlocal real-space cut. Despite the Laughlin state being bulk gapped while the antiferromagnetic spin chain state is bulk gapless, we show that the S=(1/2) Heisenberg antiferromagnet in one dimension has an entanglement spectrum almost identical to that of the Laughlin Fractional Quantum Hall state in two dimensions, revealing the similar field theory of their low-energy bulk and edge excitations, respectively. We also discuss the dimerization transition from entanglement gap scaling.
- OSTI ID:
- 21471011
- Journal Information:
- Physical Review Letters, Vol. 105, Issue 11; Other Information: DOI: 10.1103/PhysRevLett.105.116805; (c) 2010 American Institute of Physics; ISSN 0031-9007
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
ANTIFERROMAGNETISM
DIMERIZATION
EXCITATION
FIELD THEORIES
GROUND STATES
HALL EFFECT
HEISENBERG MODEL
MULTIPLICITY
QUANTUM ENTANGLEMENT
QUANTUM NUMBERS
SPACE
SPECTRA
SPIN
ANGULAR MOMENTUM
CHEMICAL REACTIONS
CRYSTAL MODELS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
MAGNETISM
MATHEMATICAL MODELS
PARTICLE PROPERTIES
POLYMERIZATION