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Physical review. B./Physical review. B

Transport phenomena and correlation dynamics of a one-dimensional effective Hamiltonian equivalent to the hexagonal Harper model

Santanu Dhara, Dibyajyoti Sahu, Manvendra Singh, Suhas Gangadharaiah

Published Apr 19, 2024• 0 citations

Abstract

The phase diagram of the one-dimensional hexagonal Harper (HH) model reveals the presence of two metallic phases and one insulating phase, separated by critical lines and a bicritical point. In our work, we investigate transport in the different phases by considering both the isolated and open system scenario. For the case of the isolated system, we study the single-particle dynamics at the bicritical point and along the critical lines. We find that the single-particle wave packet dynamics is superdiffusive in the critical regions with the transport at the bicritical point faster than that along the critical lines. In addition, we study domain wall (DW) dynamics via unconventional multiparticle states in the two metallic phases. The DW state is constructed by partially filling half of the chain while the other half is kept empty; the dynamics of this state reveals distinct behavior in the deep metallic regime of the two metallic phases. Interestingly, the distinct behavior is absent if one instead considers a fully filled half chain. For the open system scenario, we study transport in the nonequilibrium steady state (NESS). We observe that in the critical regions, transport is subdiffusive in nature. Moreover, we find that the transport scaling exponents for the open system scenario are the same at the bicritical point and along the critical lines, unlike the closed system case. In addition, we observe an even-odd size effect on the NESS density and current and on the optimal system-bath coupling parameter (corresponding to the maximum current) in the deep metallic regime of the HH model.

DOI: 10.1103/physrevb.109.134204

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Recent studies of quantum many-body dynamics uncover many intriguing phenomena of thermalization and localization in the presence of a quasiperiodic potential. In this paper, the authors study nonequilibrium steady states of the one-dimensional interacting Aubry-Andre-Harper model by taking advantage of tensor network-based algorithms. In a weak potential regime, they find a superdiffusive to subdiffusive transition in spin transport within the thermal phase. The correlation structure of the steady states derived from the quantum mutual information shows an unusual oscillation pattern before reaching the localization transition. Our results suggest a rich phase diagram for the model.

We consider charge and spin transport in the one-dimensional Hubbard model at infinite temperature, half-filling, and zero magnetization. Implementing matrix-product-operator simulations of the nonequilibrium steady states of boundary-driven open Hubbard chains for up to 100 sites we find clear numerical evidence of diffusive transport for weak driving and any (nonzero and finite) value of the interaction

U

. In addition, nonequilibrium steady states are characterized by nonzero spin-up spin-down density-density correlations. For maximal driving, on the other hand, we find an insulating behavior and cosine-shaped density profiles.

Employing the projective formalism of determinant quantum Monte Carlo (DQMC) simulations, we meticulously explore the ground-state phase diagram and critical behavior of the half-filled Hubbard model on a square-hexagon-octagon (SHO) lattice. This lattice, a two-dimensional (2D) structure comprising squares, hexagons, and octagons, is representative of the biphenylene network (BPN). Our findings reveal an intriguing ground-state phase diagram, featuring an antiferromagnetic (AFM) Mott insulating phase enveloped by three valence-bond-solid-like (VBS-like) insulating phases. Analyzing the single-particle gap, spin gap, and single-particle spectral function, we observe that the metallic state in the noninteracting case becomes unstable under the influence of Hubbard

U

. This interaction drives the system into a hexagon insulating phase before transitioning into an AFM Mott insulating phase. To quantify the critical exponents, we use finite-size scaling techniques. The critical exponents of quantum critical points between the AFM Mott insulating phase and two insulating phases, plaquette insulator, and ethylene insulator, closely align with the 3D O(3) universality class. However, the critical exponents of quantum critical points between the hexagon insulating phase and the AFM Mott insulating phase deviate from the 3D O(3) universality class. This deviation can be attributed to the coupling effect between the fluctuations of magnetic order parameters and very low-energy fermionic excitations. Our comprehensive study not only advances the understanding of correlation effects on the SHO lattice but also sheds light on the less-explored critical exponents in a weakly insulating quantum critical point.

We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\ensuremath{\alpha}$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a nonequilibrium steady-state charge transport, and (ii) time dynamics of an initially localized single-particle excitation in the absence of boundary reservoirs. In both variants, anomalous superdiffusive behavior is observed for $1<\ensuremath{\alpha}<1.5$, and for $\ensuremath{\alpha}>1.5$ the setup is effectively short ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behavior in open quantum systems.