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arXiv:2605.25231

Dynamical susceptibility and quantum Fisher information in the Su-Schrieffer-Heeger model with Hatsugai-Kohmoto interactions

Sepide Mohamadi, Jahanfar Abouie

Published May 24, 2026• 0 citations
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Abstract

We investigate the dynamical spin and charge susceptibilities and the associated quantum Fisher information in a class of interacting lattice models, with a primary focus on the Su-Schrieffer-Heeger model in the presence of Hatsugai-Kohmoto interactions. To provide a rigorous analytical benchmark, we contrast the response properties of the SSH-HK system with those of the single-band Hubbard and SSH-Hubbard models, treated within the random-phase approximation. While standard Hubbard-type interactions typically suppress excitation strength, we demonstrate that the SSH-HK model displays qualitatively distinct physical behavior arising from the interplay between SSH dimerization and the momentum-diagonal nature of the HK interaction. Leveraging the exact solvability of the HK term, we derive closed-form expressions for the dynamical susceptibility, revealing unique filling-controlled characteristics such as a finite response at zero wave vector and a pronounced restructuring of spectral weight across integer and fractional filling sectors. We show that the quantum Fisher information, defined as the frequency integral of the imaginary part of the susceptibility, serves as an efficient probe of these filling sectors, exhibiting distinct piecewise behavior that distinguishes integer from fractional fillings. Notably, our results indicate that the quantum Fisher information remains insensitive to topological transitions within uniform-density regimes, highlighting the limitations of standard dynamical response functions in characterizing band topology. These findings establish the SSH-HK model as a powerful analytical platform for exploring the competition between topology and strong correlations, demonstrating how dynamical susceptibilities and the quantum Fisher information provide complementary, experimentally accessible probes of many-body physics.

DOI
10.48550/arxiv.2605.25231

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We investigate the dynamical spin and charge susceptibilities and the associated quantum Fisher information in a class of interacting lattice models, with a primary focus on the Su-Schrieffer-Heeger model in the presence of Hatsugai-Kohmoto interactions. To provide a rigorous analytical benchmark, we contrast the response properties of the SSH-HK system with those of the single-band Hubbard and SSH-Hubbard models, treated within the random-phase approximation. While standard Hubbard-type interactions typically suppress excitation strength, we demonstrate that the SSH-HK model displays qualitatively distinct physical behavior arising from the interplay between SSH dimerization and the momentum-diagonal nature of the HK interaction. Leveraging the exact solvability of the HK term, we derive closed-form expressions for the dynamical susceptibility, revealing unique filling-controlled characteristics such as a finite response at zero wave vector and a pronounced restructuring of spectral weight across integer and fractional filling sectors. We show that the quantum Fisher information, defined as the frequency integral of the imaginary part of the susceptibility, serves as an efficient probe of these filling sectors, exhibiting distinct piecewise behavior that distinguishes integer from fractional fillings. Notably, our results indicate that the quantum Fisher information remains insensitive to topological transitions within uniform-density regimes, highlighting the limitations of standard dynamical response functions in characterizing band topology. These findings establish the SSH-HK model as a powerful analytical platform for exploring the competition between topology and strong correlations, demonstrating how dynamical susceptibilities and the quantum Fisher information provide complementary, experimentally accessible probes of many-body physics.
The interplay and competition of topology and electron--electron interactions have fascinated researchers since the discovery of topological insulators. The Su--Schrieffer--Heeger--Hubbard (SSH-Hubbard) model is a prototypical model which includes both nontrivial topology and interactions. Due to its simplicity, there are several artificial quantum systems which can realize such a model to a good approximation. Here we focus on the quarter-filled case, where interactions and dimerization open a charge gap. In particular, we study the single-particle spectral function for the extended SSH-Hubbard model with magnetic field and explore several parameter limits where effective model descriptions arise. In the strongly dimerized limit, we show that the low-energy excitations of the spectral function resemble a half-filled Hubbard model with effective dimer sites and renormalized couplings. For strong magnetic field and interactions, we find physics akin to the spinless Su--Schrieffer--Heeger model at half filling, featuring a noninteracting topological phase transition. Moreover, in light of the recent realization of this model in quantum dot simulation, we provide evidence for the stability of the topological phase towards moderate nonlocal interactions in the experimentally expected parameter range.
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.
We present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value gc{g}_{\mathrm{c}}gc​. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.
This study explores the ground-state phase diagram and topological properties of the spinless 1D Su-Schrieffer-Heeger (SSH) model with nearest-neighbor (NN) interactions at quarter filling. We analyze key physical quantities such as the local electron density distribution, correlation functions for bond-order-wave (BOW) and charge-density-wave (CDW) -- by integrating twisted boundary conditions with the Lanczos technique and employing high-precision numerical diagonalization methods, complemented by a mean-field approximation (MFA) based on bond-order and charge-density modulation analysis. This approach enables precise identification of phase transition critical points. Our results indicate that the system exhibits a topologically trivial band insulating (BI) phase for strong attractive interactions, with its upper boundary forming a downward-opening curve peaking at V/t≃−2.3V/t\simeq-2.3V/t≃−2.3 and extending to V/t≃−2.6V/t\simeq-2.6V/t≃−2.6. Within −2.6≤V/t≤−0.5-2.6 \leq V/t \leq -0.5−2.6≤V/t≤−0.5, a BOW phase emerges for ∣δt/t∣>0.45\left|δt/t\right| > 0.45∣δt/t∣>0.45, with its boundaries converging as ∣δt/t∣\left|δt/t\right|∣δt/t∣ decreases, terminating at a single point at ∣δt/t∣≃0.45\left|δt/t\right|\simeq0.45∣δt/t∣≃0.45. In other parameter regions, a CDW phase is realized. Through this analysis, we elucidate the topological properties of the interacting spinless SSH model at quarter filling, highlighting the competition among CDW, BOW, and BI phases. By tuning VVV and δtδtδt, the system exhibits diverse correlated phenomena, offering new insights into one-dimensional quantum phase transitions and the interplay between topology and order.
Understanding how topology survives in strongly correlated systems remains a central challenge, as most topological diagnostics rely on non-interacting band structures. Here we present a framework to characterize interacting topological phases within an effective single-particle description derived from the single-particle Green's function. Using the Su-Schrieffer-Heeger model with Hatsugai-Kohmoto interactions as an analytically tractable example, we construct the one-body reduced density matrix from the Green's function and use it to define an effective winding number together with quantum volume, a measurement of state geometry. These quantities allow us to distinguish three insulating phases including correlated Mott states directly from single-particle observables. Our results show that interacting topology can be interpreted in terms of the spectral weight distribution of single-particle excitations, providing an intuitive and computationally accessible route to diagnose topological phases in correlated systems. This approach is compatible with modern many-body simulation techniques and opens a pathway toward the identification of interacting topological materials.
The Hatsugai-Kohmoto (HK) model has recently been identified as a fixed-point description of Mottness that is stable against perturbing local interactions. This raises a natural question beyond the weak-perturbation regime: how does a finite local repulsion modify HK physics in real-space observables and local spectra? We address this question in a half-filled one-dimensional spinful fermion chain, where the HK interaction is supplemented by an onsite Hubbard repulsion. Using exact diagonalization in an open chain, we compute ground-state correlation functions and site-resolved local spectra. We find that the Hubbard term does not drive the system away from the HK-dominated regime. Instead, at moderate UHKU_{\rm HK}UHK​, a finite UHubU_{\rm Hub}UHub​ promotes the emergence of behavior characteristic of the pure HK chain at larger UHKU_{\rm HK}UHK​. This Hubbard-assisted strong-HK response is reflected consistently in the development of positive spin correlations, the suppression of single-particle coherence, the impurity-induced redistribution of local spectral weight, and the evolution of pairing correlations. As a control perturbation, we replace the onsite Hubbard interaction by a nearest-neighbor (NN) density interaction. In contrast to the Hubbard case, the HK and NN interactions display competing tendencies and do not reproduce the same strong-HK behavior. These results provide a nonperturbative real-space complement to the fixed-point stability of HK physics and show that the effect of an additional repulsive interaction depends sensitively on its spatial structure.