Metastable quantum phase transitions in a periodic one-dimensional Bose gas. II. Many-body theory

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.023625· OSTI ID:21408297

Kanamoto, R ^[1]; Carr, L D ^[2]; Ueda, M ^[3]

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1. Division of Advanced Sciences, Ochadai Academic Production, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610 (Japan)
2. Department of Physics, Colorado School of Mines, Golden, Colorado, 80401 (United States)
3. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan)

We show that quantum solitons in the Lieb-Liniger Hamiltonian are precisely the yrast states. We identify such solutions with Lieb's type II excitations from weak to strong interactions, clarifying a long-standing question of the physical meaning of this excitation branch. We demonstrate that the metastable quantum phase transition previously found in mean-field analysis of the weakly interacting Lieb-Liniger Hamiltonian [Phys. Rev. A 79, 063616 (2009)] extends into the medium- to strongly interacting regime of a periodic one-dimensional Bose gas. Our methods are exact diagonalization, finite-size Bethe ansatz, and the boson-fermion mapping in the Tonks-Girardeau limit.

• OSTI ID: 21408297
• Journal Information: Physical Review. A, Vol. 81, Issue 2; Other Information: DOI: 10.1103/PhysRevA.81.023625; (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
74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN GAS
EXCITATION
FERMIONS
HAMILTONIANS
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS
MEAN-FIELD THEORY
PERIODICITY
PHASE TRANSFORMATIONS
SOLITONS
STRONG INTERACTIONS
YRAST STATES
BASIC INTERACTIONS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
INTERACTIONS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
QUASI PARTICLES
VARIATIONS