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Boundary entropy of one-dimensional quantum systems at low temperature
Daniel Friedan1, Anatoly Konechny
1Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854-8019, USA. friedan@physics.rutgers.edu
Physical Review Letters
|August 25, 2004
Summary
Researchers derived a gradient formula for the boundary beta function in one-dimensional quantum systems. This formula confirms that boundary entropy decreases under renormalization, validating a long-standing conjecture on ground-state degeneracy.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- The renormalization group describes critical phenomena in quantum systems.
- Systems with boundaries exhibit unique behaviors not present in bulk systems.
- Understanding boundary criticality is crucial for classifying universality classes.
Purpose of the Study:
- To derive a gradient formula for the boundary beta function.
- To investigate the behavior of boundary entropy under renormalization.
- To prove the conjecture regarding ground-state degeneracy at critical points.
Main Methods:
- Derivation of a gradient formula for the boundary beta function.
- Expressing the boundary beta function as the gradient of boundary entropy.
- Analysis of boundary entropy behavior at fixed nonzero temperature.
Main Results:
- The boundary beta function is shown to be the gradient of boundary entropy.
- Boundary entropy decreases under renormalization, except at critical points.
- The number exp(s) is confirmed as ground-state degeneracy, decreasing with renormalization.
Conclusions:
- The study proves the conjecture that ground-state degeneracy decreases under renormalization.
- Boundary entropy's dependence on temperature is clarified, showing decrease except at critical points.
- The boundedness of boundary entropy remains an open question.