Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons

Journal Article · Sat May 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.052118· OSTI ID:21408777

Giorgi, Gian Luca; Galve, Fernando ^[1]; Paganelli, Simone ^[2]

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1. Instituto de Fisica Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca (Spain)
2. Grup de Fisica Teorica, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Spain)

It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here we show how it is possible to build a model representing a spin chain interacting with bosons that is exactly solvable. The exact spectrum of the model at zero temperature and the ground-state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent a useful resource for phase transition detection since a measure of the phonon can give information about the phase of the spin system. A finite-temperature phase diagram is also given in the adiabatic regime.

• OSTI ID: 21408777
• Journal Information: Physical Review. A, Vol. 81, Issue 5; Other Information: DOI: 10.1103/PhysRevA.81.052118; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
36 MATERIALS SCIENCE
BOSONS
COUPLING
ENERGY SPECTRA
EXACT SOLUTIONS
EXCITATION
GROUND STATES
IONS
MAGNETIZATION
MANY-BODY PROBLEM
ORDER PARAMETERS
PHASE DIAGRAMS
PHASE TRANSFORMATIONS
PHONONS
POPULATIONS
SIMULATION
SPIN
TRAPS
ANGULAR MOMENTUM
CHARGED PARTICLES
DIAGRAMS
DIMENSIONLESS NUMBERS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
INFORMATION
MATHEMATICAL SOLUTIONS
PARTICLE PROPERTIES
QUASI PARTICLES
SPECTRA