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Register a new userLattice exciton-polaron problem by quantum Monte Carlo simulations
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Exciton-polaron formation in one-dimensional lattice models with short or long-range carrier-phonon interaction is studied by quantum Monte Carlo simulations. Depending on the relative sign of electron and hole-phonon coupling, the exciton-polaron size increases or decreases with increasing interaction strength. Quantum phonon fluctuations determine the (exciton-)polaron size and yield translation-invariant states at all finite couplings.
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We present the first approximation free diagrammatic Monte Carlo study of a lattice polaron interacting with an acoustic phonon branch through the deformation potential. Weak and strong coupling regimes are separated by a self-trapping region where quantum resonance between various possible lattice deformations is seen in the ground state properties, spectral function, and optical conductivity. The unique feature of such polaron is the interplay between long- and short wavelength acoustic vibrations creating a composite phonon cloud and leading to persistent self-trapping due to the existence of multiple quasi-stable states. This results in a spectral response whose structure is much more complex than in any of the previously considered polaron models.
Building on a recent investigation of the Shastry-Sutherland model [S. Wessel et al., Phys. Rev. B 98, 174432 (2018)], we develop a general strategy to eliminate the Monte Carlo sign problem near the zero temperature limit in frustrated quantum spin models. If the Hamiltonian of interest and the sign-problem-free Hamiltonian---obtained by making all off-diagonal elements negative in a given basis---have the same ground state and this state is a member of the computational basis, then the average sign returns to one as the temperature goes to zero. We illustrate this technique by studying the triangular and kagome lattice Heisenberg antiferrromagnet in a magnetic field above saturation, as well as the Heisenberg antiferromagnet on a modified Husimi cactus in the dimer basis. We also provide detailed appendices on using linear programming techniques to automatically generate efficient directed loop updates in quantum Monte Carlo simulations.
A path-integral representation is constructed for the Jahn-Teller polaron (JTP). It leads to a perturbation series that can be summed exactly by the diagrammatic Quantum Monte Carlo technique. The ground-state energy, effective mass, spectrum and density of states of the three-dimensional JTP are calculated with no systematic errors. The band structure of JTP interacting with dispersionless phonons, is found to be similar to that of the Holstein polaron. The mass of JTP increases exponentially with the coupling constant. At small phonon frequencies, the spectrum of JTP is flat at large momenta, which leads to a strongly distorted density of states with a massive peak at the top of the band.
We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D*D matrices with D up to 48. The computational cost of our scheme formally scales as ND^3, whereas standard MPS approaches and the related density matrix renromalization group method scale as ND^5 and ND^6, respectively, for periodic systems.
We tutorially review the determinantal Quantum Monte Carlo method for fermionic systems, using the Hubbard model as a case study. Starting with the basic ingredients of Monte Carlo simulations for classical systems, we introduce aspects such as importance sampling, sources of errors, and finite-size scaling analyses. We then set up the preliminary steps to prepare for the simulations, showing that they are actually carried out by sampling discrete Hubbard-Stratonovich auxiliary fields. In this process the Greens function emerges as a fundamental tool, since it is used in the updating process, and, at the same time, it is directly related to the quantities probing magnetic, charge, metallic, and superconducting behaviours. We also discuss the as yet unresolved minus-sign problem, and two ways to stabilize the algorithm at low temperatures.
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