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Finite-size scaling at first-order quantum transitions
Massimo Campostrini1, Jacopo Nespolo1, Andrea Pelissetto2
1Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.
Physical Review Letters
|August 30, 2014
Summary
Finite-size effects in first-order quantum transitions (FOQTs) exhibit predictable scaling behavior. This behavior is governed by the ratio of transition-driving energy to the finite-size energy gap, offering insights into quantum systems.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- First-order quantum transitions (FOQTs) are critical phenomena in quantum systems.
- Understanding finite-size effects is crucial for characterizing quantum phase transitions in realistic, finite systems.
Purpose of the Study:
- To investigate and characterize finite-size effects at first-order quantum transitions (FOQTs).
- To establish a finite-size scaling (FSS) behavior for the low-energy properties near FOQTs.
- To provide a theoretical framework applicable to a broad range of FOQTs.
Main Methods:
- Developing a theoretical framework for finite-size scaling (FSS) at FOQTs.
- Identifying the key scaling variable as the ratio of perturbation energy to the finite-size energy gap.
- Utilizing a phenomenological two-level theory for systems with crossing low-energy states.
- Performing numerical simulations on the quantum Ising chain in various magnetic fields.
Main Results:
- Demonstrated that low-energy properties near FOQTs follow a finite-size scaling (FSS) behavior.
- Showed that the scaling variable depends on the ratio of perturbation energy to the finite-size energy gap.
- Confirmed that the gap's size dependence, influenced by boundary conditions, dictates the scaling variable's behavior.
- Validated the theoretical framework with numerical results from the quantum Ising chain.
Conclusions:
- The study provides a general framework for understanding finite-size effects in FOQTs.
- The derived scaling laws are broadly applicable, particularly to systems with specific low-energy state degeneracies.
- Numerical evidence supports the proposed FSS ansatz, confirming its validity for quantum systems like the Ising chain.
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