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Springer eBooks

Role of symmetry in the study of quasi one-dimensional systems

I. Božović, Milan Vujičić, Fedor Herbut, Milan Damnjanović

Published Apr 6, 2008• 2 citations
Publisher
DOI
10.1007/3-540-09241-2_76

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We show that a generalized charge SU (2) symmetry of the one-dimensional (1D) Hubbard model in an infinitesimal flux ϕ generates half-filling states from metallic states which lead to a finite charge stiffness D ( T ) at finite temperature T , whose T -dependence we study. Our results are of general nature for many integrable quantum lattice systems, reveal the microscopic mechanisms behind their exotic T > 0 transport properties and the interplay with T = 0 quantum-phase transitions, and contribute to the further understanding of the transport of charge in systems of interacting ultracold fermionic atoms in 1D optical lattices, quasi-1D compounds, and 1D nanostructures.

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This paper gives a systematic review on studies of dimensional effects in pure- and quasi-two-dimensional (2D) Bose gases, focusing on the role of dimensionality in the fundamental relation among the universal behavior of breathing mode, scale invariance and dynamic symmetry. First, we illustrate the emergence of universal breathing mode in the case of pure 2D Bose gases, and elaborate on its connection with the scale invariance of the Hamiltonian and the hidden SO(2, 1) symmetry. Next, we proceed to quasi-2D Bose gases, where excitations are frozen in one direction and the scattering behavior exhibits a 3D to 2D crossover. We show that the original SO(2, 1) symmetry is broken by arbitrarily small 2D effects in scattering, which consequently shifts the breathing mode from the universal frequency. The predicted shift rises significantly from the order of 0.5% to more than 5% in transiting from the 3D-scattering to the 2D-scattering regime. Observing this dimensional effect directly would present an important step in revealing the interplay between dimensionality and quantum fluctuations in quasi-2D.
One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit cell, which forms a periodic ladder-shaped system. Using tight-binding models, group-theoretical considerations, and standard band topology, we uncover the influence of bound states in the continuum (BICs) and quasi-BICs formed in the original finite geometry on the creation of nontrivial band states. By designing various textures for the onsite energies, we discovered a topological band inversion between quasi-BIC-induced bands, leading to the emergence of topologically protected edge states that are characterized by a quantized Zak phase. Additionally, we found an on-site configuration that exhibits robust flat bands, induced by a symmetry-protected BIC and linked to special one-sided localized edge states. We present a detailed analysis of the mechanisms driving both effects and discuss the crucial role of symmetry in characterizing the topological phases of these systems.
We show that a generalized charge SU (2) symmetry of the one-dimensional (1D) Hubbard model in an infinitesimal flux ϕ generates half-filling states from metallic states which lead to a finite charge stiffness D ( T ) at finite temperature T , whose T -dependence we study. Our results are of general nature for many integrable quantum lattice systems, reveal the microscopic mechanisms behind their exotic T > 0 transport properties and the interplay with T = 0 quantum-phase transitions, and contribute to the further understanding of the transport of charge in systems of interacting ultracold fermionic atoms in 1D optical lattices, quasi-1D compounds, and 1D nanostructures.