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Nonlocal order in gapless systems: entanglement spectrum in spin chains
Ronny Thomale1, D P Arovas, B Andrei Bernevig
1Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review Letters
|September 28, 2010
Summary
We demonstrate that entanglement spectra reveal non-local order in gapless spin systems. This reveals a shared field theory between 1D spin chains and 2D Fractional Quantum Hall states.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Statistical Mechanics
Background:
- Non-local order is crucial for understanding exotic quantum phases.
- Entanglement properties offer new perspectives beyond traditional order parameters.
- Gapless spin systems and fractional quantum Hall states exhibit complex behaviors.
Purpose of the Study:
- To define and characterize non-local order in gapless spin systems using entanglement spectra.
- To explore the relationship between entanglement spectra of 1D spin chains and 2D fractional quantum Hall states.
- To investigate entanglement gap scaling near dimerization transitions.
Main Methods:
- Analysis of entanglement spectra in gapless spin systems.
- Comparison of entanglement spectra between 1D Heisenberg antiferromagnets and 2D Laughlin states.
- Utilizing quantum numbers to define non-local real-space cuts.
- Studying entanglement gap scaling across phase transitions.
Main Results:
- A finite entanglement gap separates high-energy levels from a ground state band in the thermodynamic limit.
- The entanglement spectrum of the S=1/2 Heisenberg antiferromagnet is nearly identical to that of the Laughlin state.
- This similarity indicates a shared underlying field theory for low-energy excitations.
Conclusions:
- Entanglement spectra provide a robust tool for defining non-local order in quantum systems.
- The study reveals deep connections between seemingly different quantum phases, like 1D spin chains and 2D fractional quantum Hall states.
- Entanglement gap scaling offers insights into quantum phase transitions, such as dimerization.
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