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arXiv:1306.0880 · Journal of Physics B Atomic Molecular and Optical Physics

Long-range order in one-dimensional spinless Fermi gas with attractive dipole–dipole interaction

Zhongbo Yan, Liang Chen, Shaolong Wan

Published Jun 26, 2014• 2 citations
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Abstract

One-dimensional spinless Fermi gas with attractive dipole-dipole interaction is investigated. Results obtained show when the interaction is weak, the excitation spectrum is linear and the superconducting correlation function decays as power law, indicating the validity of the Tomonaga-Luttinger (TL) liquid picture. However, when the interaction reaches a critical value, the excitation spectrum is nonlinear and the superconducting correlation function keeps finite for infinity separation, indicating real long-range order established and the breakdown of the TL liquid picture. We prove that the existence of long-range order is not in contradiction with the Hohenberg theorem and show that this system is related to the Kitaev toy model, therefore, it has potential applications for the future topological quantum computation.

DOI
10.1088/0953-4075/47/13/135302

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One-dimensional spinless Fermi gas with attractive dipole-dipole interaction is investigated. Results obtained show when the interaction is weak, the excitation spectrum is linear and the superconducting correlation function decays as power law, indicating the validity of the Tomonaga-Luttinger (TL) liquid picture. However, when the interaction reaches a critical value, the excitation spectrum is nonlinear and the superconducting correlation function keeps finite for infinity separation, indicating real long-range order established and the breakdown of the TL liquid picture. We prove that the existence of long-range order is not in contradiction with the Hohenberg theorem and show that this system is related to the Kitaev toy model, therefore, it has potential applications for the future topological quantum computation.
One-dimensional gas of spinless fermions with attractive dipole-dipole interaction is investigated. Results obtained show when the interaction is weak, the excitation spectrum is linear and the superconducting correlation function decays as power law, indicating the validity of the Tomonaga-Luttinger (TL) liquid picture. However, when the interaction reaches a critical value, the excitation spectrum is nonlinear and the superconducting correlation function keeps finite for infinity separation, indicating real long-range order established and the breakdown of the TL liquid picture. We prove that the existence of long-range order is not in contradiction with the Hohenberg theorem and show that this system is related to the Kitaev toy model, therefore, it has potential applications for the future topological quantum computation.
Interacting one-dimensional bosons with long range hopping decaying as a power law r−αr^{-α}r−α with distance rrr are considered with the renormalization group and the self-consistent harmonic approximation. For α≥3α\ge 3α≥3, the ground state is always a Tomonaga-Luttinger liquid, whereas for α<3α<3α<3, a ground state with long range order breaking the continuous global gauge symmetry becomes possible for sufficiently weak repulsion. At positive temperature, continuous symmetry breaking becomes restricted to α<2α<2α<2, and for 2<α<32<α<32<α<3, a Tomonaga-Luttinger liquid with the Tomonaga-Luttinger exponent diverging at low temperature is found.
We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines, we determine the phase boundary and the order parameter of the low-temperature (three-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1∝T(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1<K<2 range, which signifies attractive interaction between the spinless fermions in the Tomonaga-Luttinger liquid.
A translation invariant one-dimensional system of spinless fermions with a finite-range attraction experiences a quantum phase transition to a phase-separated state. While being a conventional Luttinger liquid for a small interaction strength, spinless fermions form a droplet with the size smaller than the available one-dimensional volume when the interaction strength exceeds some critical value. A particularly remarkable signature of the droplet formation is the change in the lower edge of the many-body excitation spectrum. In the homogeneous phase, it has a Luttinger-liquid shape of periodic arcs on top of the shallow parabolic dispersion of the center of mass. When the interaction strength is increased, the arcs disappear completely as soon as the droplet is formed. We perform an exact diagonalization study of this system with the focus on the signatures of the quantum phase transition and the droplet properties. The one-particle and density-density correlation functions, the pressure, the sound velocity, and the droplet density are examined. The value of the critical interaction strength obtained from numerical data reasonably agrees with a simple mean-field analytical estimate. Due to the boson-fermion correspondence valid in one dimension, our results also hold for hard-core bosons with a finite-range attraction.
The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.
The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.