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

Phonon spectral function of the one-dimensional Holstein-Hubbard model

We use the continuous-time interaction expansion (CT-INT) quantum Monte Carlo method to calculate the phonon spectral function of the one-dimensional Holstein-Hubbard model at half-filling. Our results are consistent with a soft-mode Peierls transition in the adiabatic regime, and the existence of a central peak related to long-range order in the Peierls phase. We explain a previously observed feature at small momenta in terms of a hybridization of charge and phonon excitations. Tuning the system from a Peierls to a metallic phase with a nonzero Hubbard interaction suppresses the central peak, but a significant renormalization of the phonon dispersion remains. In contrast, the dispersion is only weakly modified in the Mott phase. We discuss finite-size effects, the relation to the dynamic charge structure factor, as well as additional sum rules and their implications. Finally, we reveal the existence of a discrete symmetry in a continuum field theory of the Holstein model, which is spontaneously broken in the Peierls phase.Comment: 10 pages, 4 figure

Directed-Loop Quantum Monte Carlo Method for Retarded Interactions

The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out the bosons. This yields an exact algorithm that combines the highly-efficient loop updates available in the stochastic series expansion representation with the advantages of avoiding a direct sampling of the bosons. The application to electron-phonon models reveals that the method overcomes the previously detrimental issues of long autocorrelation times and exponentially decreasing acceptance rates. For example, the resulting dramatic speedup allows us to investigate the Peierls quantum phase transition on chains of up to $1282$ sites.Comment: 5 pages, 3 figures, supplemental material; final versio

Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model

We extend the continuous-time interaction-expansion quantum Monte Carlo method with respect to measuring observables for fermion-boson lattice models. Using generating functionals, we express expectation values involving boson operators, which are not directly accessible because simulations are done in terms of a purely fermionic action, as integrals over fermionic correlation functions. We also demonstrate that certain observables can be inferred directly from the vertex distribution, and present efficient estimators for the total energy and the phonon propagator of the Holstein model. Furthermore, we generalize the covariance estimator of the fidelity susceptibility, an unbiased diagnostic for phase transitions, to the case of retarded interactions. The new estimators are applied to half-filled spinless and spinful Holstein models in one dimension. The observed renormalization of the phonon mode across the Peierls transition in the spinless model suggests a soft-mode transition in the adiabatic regime. The critical point is associated with a minimum in the phonon kinetic energy and a maximum in the fidelity susceptibility.Comment: 12 pages, 4 figures, 1 table; final versio

Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models

We study one-dimensional Su-Schrieffer-Heeger (SSH) models with quantum phonons using a continuous-time quantum Monte Carlo method. Within statistical errors, we obtain identical results for the SSH model with acoustic phonons, and a related model with a coupling to an optical bond phonon mode. Based on this agreement, we first study the Peierls metal-insulator transition of the spinless SSH model, and relate it to the Kosterlitz-Thouless transition of a spinless Luttinger liquid. In the Peierls phase, the spectral functions reveal the single-particle and charge gap, and a central peak related to long-range order. For the spinful SSH model, which has a dimerized ground state for any nonzero coupling, we reveal a symmetry-related degeneracy of spin and charge excitations, and the expected spin and charge gaps as well as a central peak. Finally, we study the SSH-$UV$ model with electron-phonon and electron-electron interaction. We observe a Mott phase with critical spin and bond correlations at weak electron-phonon coupling, and a Peierls phase with gapped spin excitations at strong coupling. We relate our findings to the extended Hubbard model, and discuss the physical origin of the agreement between optical and acoustic phonons.Comment: 12 pages, 13 figure

Quantum spin chains with bond dissipation

We study the effect of bond dissipation on the one-dimensional antiferromagnetic spin-$1/2$ Heisenberg model. In analogy to the spin-Peierls problem, the dissipative bath is described by local harmonic oscillators that modulate the spin exchange coupling, but instead of a single boson frequency we consider a continuous bath spectrum $\propto \omega^s$. Using an exact quantum Monte Carlo method for retarded interactions, we show that for $s<1$ any finite coupling to the bath induces valence-bond-solid order, whereas for $s>1$ the critical phase of the isolated chain remains stable up to a finite critical coupling. We find that, even in the presence of the gapless bosonic spectrum, the spin-triplet gap remains well defined for any system size, from which we extract a dynamical critical exponent of $z=1$. We provide evidence for a Berezinskii-Kosterlitz-Thouless quantum phase transition that is governed by the SU(2)$_1$ Wess-Zumino-Witten model. Our results suggest that the critical properties of the dissipative system are the same as for the spin-Peierls model, irrespective of the different interaction range, i.e., power-law vs. exponential decay, of the retarded dimer-dimer interaction, indicating that the spin-Peierls criticality is robust with respect to the bosonic density of states.Comment: 18 pages, 12 figure

Ecology and conservation of sympatric tropical deer populations in the Greater Calakmul Region, south-eastern Mexico

The conservation and management of tropical deer populations need both knowledge of the ecology and natural history of deer and an understanding of the utilization of deer populations by humans. The south-eastern portion of the Yucatan Peninsula in Mexico is the region with the largest ungulate diversity in Mesoamerica, including three of the five species of deer found in Mexico. For centuries, human populations have been harvesting deer for subsistence in this region. Little is know on the ecology and conservation of ungulate populations undergoing subsistence harvesting in Mesamerica. This thesis is the result of a long-term study (1996-2001) on the population, community ecology and sustainable management of the Yucatan Peninsula brown brocket deer (Mazama pandora), red brocket deer (Mazama americana) and white-tailed deer (Odocoileus virginianus) in the Greater Calakmul Region՝ (GCR), south eastern Mexico. Chapter two addresses the estimation of deer abundance, densities, population structure and habitat use of sympatric populations of these three species of deer. Chapter three outlines the relationships of the deer diet with aspects of habitat ecology such as fruit phenology, availability and seasonality. Chapter four describes the spatial and temporal patterns of subsistence hunting of tropical deer populations with the use of a novel technique incorporating both GIS/GPS technologies and participatory research. The abundance of deer in the GCR remained stable during a continuous monitoring period of five years and no effects of hunting were detected in the populations of the two Mazama species. A steady decline was detected in the populations of white-tailed deer that might be attributed to over-harvesting by subsistence hunters. Densities of the three species of deer are similar or higher that those reported elsewhere in the Neotropics. Mazama americana presented strong preferences in habitat use for the Tall Perennial Forest, while M pandora and o. virginianus used habitats in relation with availability. The population structure of the three species of deer resembles a stable population with the majority of individuals found in younger age classes but older individuals still found in ages above 12 years old (the cementum annuli technique for age determination was used for the first time in a tropical deer population). Mazama americana is a frugivore deer with its diet composed of up to 80% fruits year-round, while M. pandora and o.virginianus are both frugivores and browsers. Fruit availability for deer was strongly linked with fruit phonological patterns of the major planit species composing the deer diet year-round. A critical period with low fruit availability and potential dietary stress for deer was found during the dry season (April-May). The Zapote tree {Manilkara zapota) might be a keystone plant resource in the region. Subsistence hunting of deer is widespread in the GCR region, but deer hunting seems to be sustainable in part due to the dynamic patterns in spatial and temporal location of hunters in the landscape. The spatial and temporal patterns of deer hunting might be responsible for the creation of natural refuges and source/sink areas for deer populations. The conservation and management of tropical deer populations in the GCR and Meso-America are discussed in the light of these findings