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Quantum correlations in spin chains at finite temperatures and quantum phase transitions
T Werlang1, C Trippe, G A P Ribeiro
1Departamento de Física, Universidade Federal de São Carlos, São Carlos, SP 13565-905, Brazil.
Physical Review Letters
|September 28, 2010
Summary
Quantum discord (QD) highlights quantum phase transitions (QPT) in spin chains at finite temperatures, unlike entanglement. This finding aids experimental QPT detection when low temperatures are inaccessible.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- Statistical Mechanics
Background:
- The Heisenberg model (XXZ Hamiltonian) describes interacting spin-1/2 qubits.
- Quantum phase transitions (QPT) are fundamental changes in quantum systems at absolute zero.
- Characterizing QPTs at finite temperatures remains a significant challenge.
Purpose of the Study:
- To compute quantum discord (QD) and entanglement (EOF) for nearest-neighbor qubits in an infinite XXZ spin chain at finite temperatures.
- To investigate the behavior of QD and EOF near quantum critical points.
- To determine if QD can serve as a robust indicator of QPTs at non-zero temperatures.
Main Methods:
- Utilizing the canonical ensemble to model the spin chain thermalized with a reservoir at temperature T.
- Calculating quantum discord and entanglement measures for spin-1/2 qubits in the thermodynamic limit.
- Analyzing the behavior of these quantum correlations across different temperature regimes.
Main Results:
- Quantum discord (QD) effectively identifies critical points associated with quantum phase transitions (QPT) in the XXZ model, even at finite temperatures.
- Entanglement (EOF) and other thermodynamic quantities do not exhibit the same sensitivity to QPT critical points at finite T.
- QD demonstrates a remarkable ability to spotlight QPTs where traditional methods may fail due to thermal effects.
Conclusions:
- Quantum discord is a superior indicator for detecting quantum phase transitions in spin systems at finite temperatures compared to entanglement.
- The findings suggest that QD can be experimentally valuable for characterizing QPTs in regimes where extremely low temperatures are not achievable.
- This work provides a new perspective on using quantum correlations for understanding and identifying critical phenomena in quantum many-body systems.
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