Quantum fluctuations in the two-dimensional XY model: Variational approach

Journal Article · Wed Jan 01 00:00:00 EST 1992 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.45.819· OSTI ID:5080515

Ariosa, D; Beck, H ^[1]

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1. Institut de Physique, Universite de Neuchatel, Rue A.-L. Breguet 1 CH-2000 Neuchatel (Switzerland)

Due to the small self-capacitance of individual junctions, two-dimensional arrays of ultrasmall Josephson junctions are sensitive to charging effects. Identifying the charging energy term with the kinetic part of a quantum Hamiltonian for a two-dimensional {ital XY} spin system, we study the effects of quantum fluctuations on the equilibrium thermodynamics of such a system. The study is based on a self-consistent evaluation of the free energy of the system, with both effective couplings {ital K} and angular thermal averages {l angle}{theta}{r angle} as variational parameters. In the weakly fluctuating regime (high values of {ital K}), we use the self-consistent harmonic approximation for an array of coupled quantum harmonic oscillators. In the strong fluctuating regime (small values of {ital K}), the coupling term is treated as a perturbation of the free-planar-rotator system. The calculation is then performed to second order in the coupling constant {ital K}. When plotted versus {ital K}, this free energy shows a double-well structure that evolves with the temperature as well as the capacitance, leading to a first-order phase transition at low temperatures. Sensitivity to charging effects is found to be considerably enhanced in fully frustrated systems (i.e., when the array is placed in a transverse magnetic field with half a flux quantum per plaquette). Furthermore, in the fully frustrated case we found an unusual coherent phase at very low temperatures. Our results are in good qualitative agreement with those obtained by Jacobs {ital et} {ital al}. with quantum Monte Carlo simulations.

• OSTI ID: 5080515
• Journal Information: Physical Review, B: Condensed Matter; (United States), Vol. 45:2; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
JOSEPHSON JUNCTIONS
FLUCTUATIONS
CRYSTAL MODELS
DENSITY MATRIX
FREE ENERGY
HAMILTONIANS
PHASE TRANSFORMATIONS
VARIATIONAL METHODS
ENERGY
JUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRICES
PHYSICAL PROPERTIES
QUANTUM OPERATORS
SUPERCONDUCTING JUNCTIONS
THERMODYNAMIC PROPERTIES
VARIATIONS
665000* - Physics of Condensed Matter- (1992-)