Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid

The two-dimensional Holstein-Hubbard model is studied by means of continuous-time quantum Monte Carlo simulations. Using renormalization-group-invariant correlation ratios and finite-size extrapolation, the critical temperature of the charge-density-wave transition is determined as a function of coupling strength, phonon frequency, and Hubbard repulsion. The phase transition is demonstrated to be in the universality class of the two-dimensional Ising model and detectable via the fidelity susceptibility. The structure of the ground-state phase diagram and the possibility of a bipolaronic metal with a single-particle gap above $T_c$ are explored.Comment: 8 pages, 9 figures; expanded version including Holstein-Hubbard result

Density waves in strongly correlated quantum chains

We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fr\"ohlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons, competing fermion-boson and fermion-fermion interactions, as well as symmetry-protected topological states in fermion and anyon models.Comment: 15 pages, 17 figures; focused review article for an EPJ B topical issue on "Coexistence of long-range orders in low-dimensional systems". Comments welcome

Correlated atomic wires on substrates. II. Application to Hubbard wires

In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely paramagnetic Mott insulators, Luttinger liquids, and spin-$1/2$ Heisenberg chains. The validity of the effective ladder models is assessed by studying the convergence with the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate

Lang-Firsov approaches to polaron physics: From variational methods to unbiased quantum Monte Carlo simulations

We review variational and quantum Monte Carlo approaches based on (extended) Lang-Firsov transformations of the Hamiltonian. Derivations for one, two and many electrons are given, and results for the Holstein polaron, the Holstein-Hubbard bipolaron, and the spinless Holstein model at finite carrier densities are presented.Comment: 40 pages, 15 figures, to be published in Polarons in Advanced Materials, Ed. A. S. Alexandrov (Canopus/Springer Publishing, Bristol) (2007); V2: typo in authors list correcte

Ground-state and spectral properties of an asymmetric Hubbard ladder

We investigate a ladder system with two inequivalent legs, namely a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wavenumbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.Comment: published versio

Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry

We consider a model of Dirac fermions in $2+1$ dimensions with dynamically generated, anticommuting SO(3) N\'eel and Z$_2$ Kekul\'e mass terms that permits sign-free quantum Monte Carlo simulations. The phase diagram is obtained from finite-size scaling and includes a direct and continuous transition between the N\'eel and Kekul\'e phases. The fermions remain gapped across the transition, and our data support an emergent SO(4) symmetry unifying the two order parameters. While the bare symmetries of our model do not allow for spinon-carrying Z$_3$ vortices in the Kekul\'e mass, the emergent SO(4) invariance permits an interpretation of the transition in terms of deconfined quantum criticality. The phase diagram also features a tricritical point at which N\'eel, Kekul\'e, and semimetallic phases meet. The present, sign-free approach can be generalized to a variety of other mass terms and thereby provides a new framework to study exotic critical phenomena.Comment: 5 pages, 5 figures, to appear in Phys. Rev. Let

Correlated atomic wires on substrates. I. Mapping to quasi-one-dimensional models

We present a theoretical study of correlated atomic wires deposited on substrates in two parts. In this first part, we propose lattice models for a one-dimensional quantum wire on a three-dimensional substrate and map them onto effective two-dimensional lattices using the Lanczos algorithm. We then discuss the approximation of these two-dimensional lattices by narrow ladder models that can be investigated with well-established methods for one-dimensional correlated quantum systems, such as the density-matrix renormalization group or bosonization. The validity of this approach is studied first for noninteracting electrons and then for a correlated wire with a Hubbard electron-electron repulsion using quantum Monte Carlo simulations. While narrow ladders cannot be used to represent wires on metallic substrates, they capture the physics of wires on insulating substrates if at least three legs are used. In the second part [arXiv:1704.07359], we use this approach for a detailed numerical investigation of a wire with a Hubbard-type interaction on an insulating substrate