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arXiv:2501.19023 · Physical review. B./Physical review. B

Emergence of topological non-Fermi liquid phases in a modified Su-Schrieffer-Heeger chain with long-range interactions

Sepide Mohamadi, Jahanfar Abouie

Published Apr 16, 2025• 6 citations
arXivHTMLPDF

Abstract

In this study, we investigate the emergence of a topological non-Fermi liquid (NFL) phase in a modified Su-Schrieffer-Heeger (SSH) chain model subjected to long-range interactions characterized by the Hatsugai-Kohmoto (HK) model. While Fermi liquid theory has been instrumental in understanding low-temperature properties of metals, it fails to account for the complex behaviors exhibited by strongly correlated systems, where interactions lead to emergent phenomena such as non-Fermi liquid behavior. Our analysis reveals that the SSH-HK model supports a rich ground state phase diagram, exhibiting distinct NFL phases marked by many-body Zak phases of $2\ensuremath{\pi}$ and 0, corresponding to topological and trivial NFL states, respectively. We demonstrate that the topological NFL state manifests unique electronic polarization characteristics akin to those in the noninteracting SSH model. Through exact diagonalization of the interacting SSH-HK Hamiltonian, we explore the spectral functions and density of states, revealing significant departures from traditional quasiparticle behavior in various particle number sectors. Our findings extend the understanding of topological non-Fermi liquids and their potential implications for high-temperature superconductivity and other correlated electron systems, highlighting the intricate interplay between topology and strong electron correlations.

DOI
10.1103/physrevb.111.165129

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In this study, we investigate the emergence of a topological non-Fermi liquid (NFL) phase in a modified Su-Schrieffer-Heeger (SSH) chain model subjected to long-range interactions characterized by the Hatsugai-Kohmoto (HK) model. While Fermi liquid theory has been instrumental in understanding low-temperature properties of metals, it fails to account for the complex behaviors exhibited by strongly correlated systems, where interactions lead to emergent phenomena such as non-Fermi liquid behavior. Our analysis reveals that the SSH-HK model supports a rich ground state phase diagram, exhibiting distinct NFL phases marked by many-body Zak phases of 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ and 0, corresponding to topological and trivial NFL states, respectively. We demonstrate that the topological NFL state manifests unique electronic polarization characteristics akin to those in the noninteracting SSH model. Through exact diagonalization of the interacting SSH-HK Hamiltonian, we explore the spectral functions and density of states, revealing significant departures from traditional quasiparticle behavior in various particle number sectors. Our findings extend the understanding of topological non-Fermi liquids and their potential implications for high-temperature superconductivity and other correlated electron systems, highlighting the intricate interplay between topology and strong electron correlations.
Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.
The interacting SSH model provides an ideal ground to study the interplay between topologically insulating phases and electron-electron interactions. We study the polarization density as a topological invariant and provide an analytic treatment of its behavior in the low-energy sector of the one-dimensional interacting SSH model. By formulating the topological invariant in terms of Green's functions, we use the low-energy field theory of the Thirring model to derive the behavior of the polarization density. We show that polarization density in the continuum theory describes the usual topological insulating phases. Still, it contains an extra factor from the fields' scaling dimensions in the low-energy quantum field theory. We interpret this as a measure of the modified charge of the new excitations in the system. We find two distinct contributions: a renormalization of the electronic charge eee of a Fermi liquid because of quasiparticle smearing and an additional contribution coming from the topological charge of the soliton arising in the bosonized version of the Thirring model, the sine-Gordon model.
Topological insulators have attracted numerous attentions recent years, where the Su-Schrieffer-Heeger (SSH) model is one of the most studied models. While the interacting version of it has been explored recently, the interplay between interactions and long-range hoppings merit further investigations. In this work, we uncover a rich phase diagram of the interacting SSH model with extended-range hoppings, in which it consists of several topological phases, two novel superconducting-like (SC-like) phases and five distinct charge-density-wave (CDW) phases. We substantiate that the SC-like and two CDW phases are direct consequences of imbalanced interactions and extended-range hoppings. We derive the order parameters (OPs) for each of the phases and verify them in large-system simulations, finding consistency with the entanglement entropy and the fidelity in capturing the phase transitions. In contrast to the non-interacting case where the favored hoppings are unidirectional in the topological phases, the derived OPs suggest non-unidirectional hoppings are possible under the influence of interactions.
The paradigm of Landau Fermi liquid theory has successfully described the low-energy behavior of numerous metallic systems. However, a growing number of experimental observations in strongly correlated electron materials, such as high-temperature superconductors and heavy fermion compounds, defy this conventional description, exhibiting what is known as non-Fermi liquid (NFL) behavior. These exotic states lack well-defined quasiparticle excitations, displaying anomalous scaling laws and transport properties. Ultracold atomic gases have emerged as highly controllable quantum simulators for strongly correlated matter, offering unprecedented access to tunable interaction strengths, dimensionality, and lattice geometries. This paper explores the potential of ultracold fermionic gases to unveil and characterize NFL behavior. We review the theoretical underpinnings of Landau Fermi liquid theory and its breakdown, survey prominent theoretical models for NFL states, and highlight experimental techniques in ultracold atomic systems pertinent to their detection. Specific attention is given to phenomena such as the BCS-BEC crossover, quantum criticality, and pseudogap phases in ultracold fermions, where strong interactions are expected to lead to deviations from quasiparticle descriptions. We discuss experimental signatures like anomalous spectral functions, linear-in-temperature resistivity analogs, and deviations in thermodynamic properties, proposing how these could be observed and analyzed in current and future ultracold atom platforms. This research aims to leverage the purity and tunability of atomic gases to gain fundamental insights into the nature of NFL states, contributing to a broader understanding of quantum many-body physics beyond the conventional quasiparticle picture.
A strange metal state appears in many strongly correlated materials from the cuprates, pnictides, and twisted bilayer graphenes to even bosonic systems. Enormous efforts are being made to unravel the nature of the non-Fermi liquid (NFL) which underlies the strange metallicity, yet progress is rather slow. Understanding the NFL behavior is crucial, in addition to its importance in replacing the Fermi liquid paradigm, in that NFL is the normal state from which new states of matter emerge like high temperature superconductivity. Here, we report the appearance of an NFL phase in a discontinuous metal-NFL-insulator transition in a ``non-engineered'' Hamiltonian of the Holstein model away from half-filling. The discontinuity of the phase transition between NFL and Fermi liquid metal renders the ground state at the phase boundary a mixture between them over an extended range like the extended criticality observed in cuprates and other quantum materials. The dynamical mean-field theory was employed in combination with Wilson's numerical renormalization group technique. We identify the origin of the NFL metal phase as the opening of a spin gap in the absence of a charge gap. Also, strong lattice fluctuations emerge at the boundary which should enhance superconductivity.
This pedagogic review aims to give a gentle introduction to an exactly solvable model, the Hatsugai-Kohmoto (HK) model, which has infinite-ranged interaction but conserves the center of mass. Although this model is invented in 1992, intensive studies on its properties ranging from unconventional superconductivity, topological ordered states to non-Fermi liquid behaviors are made since 2020. We focus on its emergent non-Fermi liquid behavior and provide discussion on its thermodynamics, single-particle and two-particle correlation functions. Perturbation around solvable limit has also been explored with the help of perturbation theory, renormalization group and exact diagonalization calculation. We hope the present review will be helpful for graduate students or researchers interested in HK-like models or more generic strongly correlated electron systems.