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

Holstein polaron in two and three dimensions by quantum Monte Carlo

A recently developed quantum Monte Carlo approach to the Holstein model with one electron [PRB 69, 024301 (2004)] is extended to two and three dimensional lattices. A moderate sign problem occurs, which is found to diminish with increasing system size in all dimensions, and not to affect simulations significantly. We present an extensive study of the influence of temperature, system size, dimensionality and model parameters on the small-polaron cross over. Results are extrapolated to remove the error due to the Trotter discretization, which significantly improves the accuracy. Comparison with existing work and other quantum Monte Carlo methods is made. The method can be extended to the many-electron case.Comment: 14 pages, 11 figure

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

Carrier-density effects in many-polaron systems

Many-polaron systems with finite charge-carrier density are often encountered experimentally. However, until recently, no satisfactory theoretical description of these systems was available even in the framework of simple models such as the one-dimensional spinless Holstein model considered here. In this work, previous results obtained using numerical as well as analytical approaches are reviewed from a unified perspective, focussing on spectral properties which reveal the nature of the quasiparticles in the system. In the adiabatic regime and for intermediate electron-phonon coupling, a carrier-density driven crossover from a polaronic to a rather metallic system takes place. Further insight into the effects due to changes in density is gained by calculating the phonon spectral function, and the fermion-fermion and fermion-lattice correlation functions. Finally, we provide strong evidence against the possibility of phase separation.Comment: 13 pages, 6 figures, accepted for publication in J. Phys.: Condens. Matter; final versio