Finite-size scaling at first-order quantum transitions

Abstract

We study finite-size effects at first-order quantum transitions (FOQTs). We show that the low-energy properties show a finite-size scaling (FSS) behavior, the relevant scaling variable being the ratio of the energy associated with the perturbation driving the transition and the finite-size energy gap at the FOQT point. The size dependence of the scaling variable is therefore essentially determined by the size dependence of the gap at the transition, which in turn depends on the boundary conditions. Our results have broad validity and, in particular, apply to any FOQT characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. In this case, a phenomenological two-level theory provides exact expressions for the scaling functions. Numerical results for the quantum Ising chain in transverse and parallel magnetic fields support the FSS ansatzes.

5 pages

References in corpus (4)

• Many-Body Physics with Ultracold Gases
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Antiferromagnetic criticality at a heavy-fermion quantum phase transition
• Sharp phase transitions in a small frustrated network of trapped ion spins

Cited by in corpus (11)

• Quantum transitions driven by one-bond defects in quantum Ising rings
• Dynamic off-equilibrium transition in systems slowly driven across thermal first-order phase transitions
• Finite-size scaling at the first-order quantum transitions of quantum Potts chains
• Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases
• Quantum critical systems with dissipative boundaries
• Renormalization-group theory for cooling first-order phase transitions in Potts models
• Dynamic finite-size scaling at first-order transitions
• Scaling of decoherence and energy flow in interacting quantum spin systems
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Critical crossover phenomena driven by symmetry-breaking defects at quantum transitions
• Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model