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arXiv:2009.05586 · Physical Review Letters

Magnetism and Charge Order in the Honeycomb Lattice

Natanael C. Costa, Kazuhiro Seki, Sandro Sorella

Published Mar 12, 2021• 25 citations
arXivHTMLPDF

Abstract

Despite being relevant to better understand the properties of honeycomblike systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on interacting Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum Monte Carlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical points, and determine the behavior of the antiferromagnetic and charge-density wave phase transitions. We have, therefore, established the ground state phase diagram of the HHM for intermediate interaction strength, determining its behavior for different phonon frequencies. Our findings provide quantitative and qualitative descriptions of the model at intermediate coupling strengths, and may shed light on the emergence of many-body properties in honeycomblike systems.

DOI
10.1103/physrevlett.126.107205

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The effect of electron-phonon coupling on Dirac fermions was recently explored numerically on a honeycomb lattice, leading to precise quantitative values for the finite temperature and quantum critical points. In this paper, we use the unbiased determinant quantum Monte Carlo method to study the Holstein model on a half-filled staggered-flux square lattice and compare the results with the honeycomb lattice geometry, presenting results for a range of phonon frequencies $0.1\ensuremath{\leqslant}\ensuremath{\omega}\ensuremath{\leqslant}2.0$. We find that the interactions give rise to charge density wave order, but only above a finite coupling strength ${\ensuremath{\lambda}}_{\mathrm{crit}}$. The transition temperature is evaluated and presented in a ${T}_{c}\text{\ensuremath{-}}\ensuremath{\lambda}$ phase diagram. An accompanying mean-field theory calculation also predicts the existence of a quantum phase transition, but at a substantially smaller coupling strength.
The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin-liquid phase between the semimetal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo simulations to study the Holstein model on a honeycomb lattice and explore the role of electron- phonon interactions on Dirac fermions. We show that they give rise to charge-density-wave (CDW) order and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.
The spontaneous generation of charge-density-wave order in a Dirac fermion system via the natural mechanism of electron-phonon coupling is studied in the framework of the Holstein model on the honeycomb lattice. Using two independent and unbiased quantum Monte Carlo methods, the phase diagram as a function of temperature and coupling strength is determined. It features a quantum critical point as well as a line of thermal critical points. Finite-size scaling appears consistent with fermionic Gross-Neveu-Ising universality for the quantum phase transition and bosonic Ising universality for the thermal phase transition. The critical temperature has a maximum at intermediate couplings. Our findings motivate experimental efforts to identify or engineer Dirac systems with sufficiently strong and tunable electron-phonon coupling.
We study the ground state properties of the doped Hubbard model with strong interactions on the honeycomb lattice by the density matrix renormalization group (DMRG) method. At half-filling, due to the absence of minus sign problem, it is now well established by large-scale quantum Monte Carlo calculations that a Dirac semimetal to antiferromagnetic Mott insulator transition occurs with the increase of the interaction strength UUU for the Hubbard model on the honeycomb lattice. However, an understanding of the fate of the antiferromagnetic Mott insulator when holes are doped into the system is still lacking. In this work, by calculating the local spin and charge density for width-4 cylinders with DMRG, we discover a half-filled stripe order in the doped Hubbard model on the honeycomb lattice. We also perform complementary large-scale mean-field calculations with renormalized interaction strength. We observe half-filled stripe order and find stripe states with filling close to one half are nearly degenerate in energy.
The formation of charge-density-wave order in Dirac fermion systems via electron-phonon coupling represents a significant topic in condensed matter physics. In this work, we investigate this phenomenon within the Holstein model on the honeycomb lattice, with a specific focus on the effect of disorder. While the interplay between electron-electron interactions and disorder has long been a central theme in the field, recent attention has increasingly turned to the combined influence of disorder and electron-phonon coupling. Using determinant quantum Monte Carlo simulations, we concentrate on the phase transitions of charge-density-wave order on the honeycomb lattice. Disorder is introduced through the random hopping of electrons in the system, which can localize electrons via the Anderson effect. Our primary result is that disorder suppresses the charge-density-wave phase, and the interplay between disorder and electron-phonon interactions extends the phase area. We also determine the transition temperature βcβ_cβc​ to the ordered phase as a function of the electron-phonon coupling. Additionally, we observed a suppression of electron kinetic energy and dc conductivity under disorder, highlighting the role of Anderson localization in the degradation of electronic transport. These findings offer significant theoretical insight into the stability and critical phenomena of correlated phases in disordered two-dimensional systems.
Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of sss-wave pairing between charge and magnetic orders
We investigate the role of electron-electron and electron-phonon interactions in strongly correlated systems by performing unbiased quantum Monte Carlo simulations in the square lattice Hubbard-Holstein model at half-filling. We study the competition and interplay between antiferromagnetism (AFM) and charge-density wave (CDW), establishing its very rich phase diagram. In the region between AFM and CDW phases, we have found an enhancement of superconducting pairing correlations, favoring (nonlocal) sss-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case.