Localized magnetic states in metals

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Physica c-superconductivity and its applications

The self-learning Monte Carlo method (SLMC), using a trained effective model to guide Monte Carlo sampling processes, is a powerful general-purpose numerical method recently introduced to speed up simulations in (quantum) many-body systems. In this Rapid Communication, we further improve the efficiency of SLMC by enforcing physical symmetries on the effective model. We demonstrate its effectiveness in the Holstein Hamiltonian, one of the most fundamental many-body descriptions of electron-phonon coupling. Simulations of the Holstein model are notoriously difficult due to a combination of the typical cubic scaling of fermionic Monte Carlo and the presence of extremely long autocorrelation times. Our method addresses both bottlenecks. This enables simulations on large lattices in the most difficult parameter regions, and an evaluation of the critical point for the charge density wave transition at half filling with high precision. We argue that our work opens a research area of quantum Monte Carlo, providing a general procedure to deal with ergodicity in situations involving Hamiltonians with multiple, distinct low-energy states.

Symmetry-enforced self-learning Monte Carlo method applied to the Holstein model

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

Charge-Density-Wave Transitions of Dirac Fermions Coupled to Phonons.

The electron–electron and electron–phonon interactions play an important role in correlated materials, being key features for spin, charge and pair correlations. Thus, here we investigate their effects 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, favouring (nonlocal) s-wave pairs. Our study sheds light over past inconsistencies in the literature, in particular the emergence of CDW in the pure Holstein model case. Electron-phonon correlations are integral to understand the properties of conventional superconductors but it is also thought they may be important for unconventional high-Tc superconductivity. Here, the authors investigate the interplay between antiferromagnetic ordering and charge density wave formation in 2D square lattice Hubbard-Holstein model at half-filling using unbiased quantum Monte Carlo simulations, and demonstrate an intermediate phase with enhancement of s-wave pairing correlations.

Phase diagram of the two-dimensional Hubbard-Holstein model

The Holstein model describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge-density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature T_{cdw} for CDW order and also uncover several novel features of diagonal long-range order in the phase diagram, including a competition between charge patterns at momenta q=(π,π) and q=(0,π) which lends insight into the relationship between Fermi surface nesting and the wave vector at which charge order occurs. We also demonstrate SC order at half filling in situations where a nonzero bandwidth sufficiently suppresses T_{cdw}.

Phonon Dispersion and the Competition between Pairing and Charge Order.

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.

https://link.aps.org/accepted/10.1103/PhysRevLett.122.077602

Charge Order in the Holstein Model on a Honeycomb Lattice.

Over the past several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon modes and the on-site charge density. A quite different, and interesting, case is one in which the phonons live on the bonds, and hence modulate the electron hopping. This situation, described by the Su-Schrieffer-Heeger (SSH) Hamiltonian, has so far only been studied with quantum Monte Carlo in one dimension. Here we present results for the 2D SSH model, show that a bond ordered wave (BOW) insulator is present in the ground state at half filling, and argue that a critical value of the electron-phonon coupling is required for its onset, in contradistinction with the 1D case where BOW exists for any nonzero coupling. We determine the precise nature of the bond ordering pattern, which has hitherto been controversial, and the critical transition temperature, which is associated with a spontaneous breaking of ${\mathcal{Z}}_{4}$ symmetry.

Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model.

The periodic Anderson model is widely studied to understand strong correlation physics and especially the competition of antiferromagnetism and singlet formation. In this paper we extend quantum Monte Carlo work on lattices with uniform numbers of neighbors to geometries in which the conduction electron sites can have variable coordination $z$. This situation is relevant both to recently discovered magnetic quasicrystals and also to magnetism in doped heavy fermion systems. Our key results are the presence of antiferromagnetic order at weak interorbital hybridization ${V}_{fd}$, and a delay in singlet formation to larger values of ${V}_{fd}$ on sites with larger $z$. The staggered magnetization tends to be larger on sites with higher $z$, providing insight into the behavior to be expected in crown, dice, and CaVO lattices.

Magnetic correlations in a periodic Anderson model with nonuniform conduction electron coordination

We theoretically study how reflection asymmetry affects the neutral exciton diamagnetic coefficient in self-assembled InGaAs/GaAs semiconductor wobbled quantum rings. The previously proposed mapping method is used to simulate the exciton wave function and energy in the rings. The description is suited to clarify the important question of the exciton diamagnetic coefficient stability in the rings with broken reflection symmetry. Our simulation results confirm that the exciton wave function of the reflection symmetrical (balanced) wobbled ring is distributed equally over two potential valleys corresponding to the hills in the ring's shape. At the same time, even a very small reflectional imbalance in the geometry and (or) material content of the wobbled rings destroys the ringlike shape of the exciton wave function and causes the localization of the function in one of the potential valleys of the ring (dotlike shape of the exciton wave function). This leads to a rapid decrease of the exciton diamagnetic coefficient. Our calculation results are in good agreement with recent experimental observations.

https://ir.nctu.edu.tw:443/bitstream/11536/22560/1/f075e49eea8f661b090f63fbe338933a.pdf

W.-T. Chiu

Papers

Phonon Dispersion and the Competition between Pairing and Charge Order.

Charge Order in the Holstein Model on a Honeycomb Lattice.

Quantum Monte Carlo Simulations of the 2D Su-Schrieffer-Heeger Model.

Magnetic correlations in a periodic Anderson model with nonuniform conduction electron coordination

Exciton wave function localization and exciton diamagnetic coefficient in semiconductor quantum rings without reflection symmetry