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arXiv:2302.01964 · Physical review. B./Physical review. B

Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions

К. А. Матвеев

Published Feb 27, 2023• 0 citations
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Abstract

We study general features of the excitation spectrum of a system of one-dimensional chiral spinless fermions with short-range interactions. We show that the nature of the elementary excitations of such a system depends strongly on the nonlinearity of the underlying dispersion of the fermions. In the case of quadratic nonlinearity, the low-momentum excitations are essentially fermionic quasiparticles and quasiholes, whereas the high-momentum ones are classical harmonic waves and solitons. In the case of cubic nonlinearity, the nature of the elementary excitations does not depend on momentum and is determined by the strength of the interactions. At a certain critical value of the interaction strength, the excitation spectrum changes qualitatively, pointing to a dynamic phase transition in the system.

DOI
10.1103/physrevb.107.075438

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We study general features of the excitation spectrum of a system of one-dimensional chiral spinless fermions with short-range interactions. We show that the nature of the elementary excitations of such a system depends strongly on the nonlinearity of the underlying dispersion of the fermions. In the case of quadratic nonlinearity, the low-momentum excitations are essentially fermionic quasiparticles and quasiholes, whereas the high-momentum ones are classical harmonic waves and solitons. In the case of cubic nonlinearity, the nature of the elementary excitations does not depend on momentum and is determined by the strength of the interactions. At a certain critical value of the interaction strength, the excitation spectrum changes qualitatively, pointing to a dynamic phase transition in the system.
We report an evidence for a phase separation in a one-dimensional continuous system of spinless fermions with a short-range attractive interaction. It is based on the numerical study of the momentum-dependent ground state energy. While at small interaction strengths it has a conventional Luttinger-liquid shape of periodic arcs on top of the shallow finite-size-induced parabola, the arcs fade away and finally vanish at some finite critical interaction strength. We interpret this result as a condensation of fermions into a liquid one-dimensional droplet and support this conclusion by further arguments.
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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.
We study the real-space pairing instability of spinless fermions on a two-dimensional square lattice with short-range attractive interactions. Various symmetries of the pairing order parameter are considered. It is found that in both nonflux and flux phases the most stable pairing state is chiral and anisotropic. It breaks both the parity and the time-reversal symmetries. The quasiparticle excitation has a minimum gap which could be much smaller than its average over the Fermi surface. The temperature dependence of the order parameter and the critical magnetic field are found to be similar to those of the classical BCS solutions. A possible connection with the high-temperature superconductivity is discussed.
We study the real-space pairing instability of spinless fermions on a two-dimensional square lattice with short-range attractive interactions. Various symmetries of the pairing order parameter are considered. It is found that in both nonflux and flux phases the most stable pairing state is chiral and anisotropic. It breaks both the parity and the time-reversal symmetries. The quasiparticle excitation has a minimum gap which could be much smaller than its average over the Fermi surface. The temperature dependence of the order parameter and the critical magnetic field are found to be similar to those of the classical BCS solutions. A possible connection with the high-temperature superconductivity is discussed.