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arXiv:2406.10063 · Physical review. B./Physical review. B

Universal quasi-Fermi liquid physics of one-dimensional interacting fermions

Joshua D. Baktay, Adrian E. Feiguin, Julián Rincón

Published Sep 18, 2025• 1 citation
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Abstract

We present a class of one-dimensional, generic, spinless fermion lattice Hamiltonians that express quasi-Fermi liquid physics, manifesting both Luttinger and Fermi liquid features solely due to irrelevant interactions. Using infinite matrix product state techniques, we unveil its universal structure by calculating static and dynamic responses. Key features include a finite discontinuity in the momentum distribution at the Fermi level, despite power-law singularities in the spectral function protected by particle-hole symmetry. Away from half filling, Landau quasiparticles emerge. Charge dynamics show either high-energy bound states or a concentration of spectral weight within the continuum for attractive or repulsive interactions, respectively. These universal features are realized across multiple models and energy scales, thus reifying the quasi-Fermi liquid as a unique paradigm for one-dimensional fermions.

DOI
10.1103/ldl4-d4sw

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We present a class of one-dimensional, generic, spinless fermion lattice Hamiltonians that express quasi-Fermi liquid physics, manifesting both Luttinger and Fermi liquid features solely due to irrelevant interactions. Using infinite matrix product state techniques, we unveil its universal structure by calculating static and dynamic responses. Key features include a finite discontinuity in the momentum distribution at the Fermi level, despite power-law singularities in the spectral function protected by particle-hole symmetry. Away from half filling, Landau quasiparticles emerge. Charge dynamics show either high-energy bound states or a concentration of spectral weight within the continuum for attractive or repulsive interactions, respectively. These universal features are realized across multiple models and energy scales, thus reifying the quasi-Fermi liquid as a unique paradigm for one-dimensional fermions.
We present numerical evidence for a paradigm in one-dimensional interacting fermion systems, whose phenomenology has traits of both Luttinger liquids and Fermi liquids. This state, dubbed a quasi-Fermi liquid, possesses a discontinuity in its fermion occupation number at the Fermi momentum. The excitation spectrum presents particlelike quasiparticles and absence of holelike quasiparticles, giving rise instead to edge singularities. Such a state is realized in a one-dimensional spinless fermion lattice Hamiltonian by fine-tuning the interactions to a regime where they become irrelevant in the renormalization group sense. We show, using uniform infinite matrix products states and finite-entanglement scaling analysis, that the system ground state is characterized by a Luttinger parameter K=1K=1K=1 and a discontinuous jump in the fermion occupation number. We support the characterization with calculations of the spectral function that show a particle-hole asymmetry reflected in the existence of well-defined Landau quasiparticles above the Fermi level and edge singularities without the associated quasiparticles below. These results indicate that the quasi-Fermi liquid paradigm can be realized beyond the low-energy perturbative realm.
This thesis focuses on the development and application of tensor networks methods for simulating one-dimensional quantum many-body systems. The general aim is to unveil numerical evidence for a new universality class of 1D interacting fermion systems referred to as quasi-Fermi liquids (qFLs). Realizing such systems beyond a purely analytical context and elucidating their peculiar characteristics is the principle value of this thesis.Chapter 1 begins by introducing the essential physics of one-dimensional systems, known as Luttinger liquids relative to their higher dimensional counterparts. Then it introduces non-linear Luttinger liquids juxtaposed against the defining quasi-Fermi liquid (qFL) field theory that motivates the following lattice studies. Chapter 2 provides an in-depth review of matrix product states (MPS), the main methodology used to explore quasi-Fermi liquids. The chapter serves as a pedagogical introduction to the field and details those novel algorithmic developments necessary for the study of fermionic systems. The central result of this chapter is the section on finite entanglement scaling techniques applied to dynamic correlation functions. Chapter 3 begins the study of lattice models that exhibit quasi-Fermi liquid characteristics. Here we explore the ground states exclusively by computing their static correlation functions. The central results include Luttinger parameter phase space diagrams which demonstrate the existence of the quasi-Fermi liquid across multiple lattice models. Chapter 4 studies the excitations of the qFL lattice models. We begin with results from non-MPS based methods which were essential for benchmarking our novel application of MPS to fermionic spectral functions. The central results of the chapter are the power-law exponents that demonstrate the low-energy universality of the qFL and our analysis of the dynamic structure factor. Chapter 5 concludes with a recapitulation of the main results and an outlook on future work. The Appendix contains those tensor diagrams necessary for a numerical implementation of those algorithms introduced in Chapter 2.--Author's abstract
It is well known that, generically, one-dimensional interacting fermions cannot be described in terms of a Fermi liquid. Instead, they present a different phenomenology, that of a Tomonaga-Luttinger liquid: the Landau quasiparticles are ill defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such a liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both a Tomonaga-Luttinger liquid and a Fermi liquid. Similar to a Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates a finite discontinuity at the Fermi energy, which is a hallmark feature of a Fermi liquid. A possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.
We study one-dimensional spinless fermions at zero and finite temperature TTT using the density-matrix renormalization group. We consider nearest- as well as next-nearest-neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system algorithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power-law suppression of the momentum distribution n(k)n(k)n(k) function at T=0T=0T=0 can be directly observed over several orders of magnitude. At finite temperature, we show that n(k)n(k)n(k) obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.
We propose an interacting model that is exactly solvable in any spatial dimension and gives rise to a Fermi liquid (FL) featuring a pseudogapped (PG) single-particle spectral function and a vanishing quasiparticle (QP) weight at half-filling, without invoking Mott physics. The PG originates from a purely fermionic mechanism through emergent QPs arising from a correlated hopping interaction. By employing an appropriate coherent-state basis, we derive a Gaussian path-integral representation of the partition function, which enables systematic treatments of deviations from the Gaussian limit using standard many-body techniques, such as diagrammatic perturbation theory or mean-field theory. We explicitly demonstrate and discuss several properties of the exactly solvable limit on the square lattice, including the mechanism for temperature-dependent PG opening, the singular behavior of the self-energy, the violation of the Luttinger sum rule, and the role of Luttinger and Fermi surfaces. Finally, we explore quantum phase transitions between PG-FLs and Landau FLs.
We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass shell. At the same time, the spectral function displays a power-law singularity on the hole mass shell, similar to that in the Luttinger liquid.