arXiv subjects

Tomislav Miškić

Publications and source records attributed to Tomislav Miškić.

2 recordsLinked to original sources

arXiv2026

Polaron formation as the vertex function problem: From Dyck's paths to self-energy Feynman diagrams

We present an iterative method for generating the complete set of self-energy Feynman diagrams at arbitrary order for the single-polaron problem with arbitrary linear coupling to the lattice. The approach combines a combinatorial representation of noncrossing diagrams, based on Dyck paths associated with Stieltjes-Rogers polynomials, with the constraints of the Ward-Takahashi identity to systematically incorporate vertex corrections. This construction yields a one-to-one correspondence between terms in the expansion based on Stieltjes-Rogers polynomials and diagrammatic contributions, and provides, through a sequence of simple steps, a closed, algorithmic framework for generating all diagrams of a given order, together with their relative weights. The method enables efficient, unbiased evaluation of diagrammatic series and improves the convergence of diagrammatic Monte Carlo by eliminating the need for stochastic weighting between different topologies. We further outline how the construction can be generalized to finite-density electron systems.

cond-mat.str-el↗

arXiv2025

Polarons with arbitrary nonlinear electron-phonon interaction

We develop an exact computational method based on numerical X-propagators for solving polaron models with arbitrary nonlinear couplings of local vibration modes to the electron density and magnitude of the hopping amplitude. Our approach covers various polaron models, some of which were impossible to treat by any existing approximation-free techniques. Moreover, it remains efficient in the most relevant but computationally challenging regime of phonon frequencies much smaller than the electron bandwidth. As a case study, we consider the double-well type nonlinear model with quadratic ($g_2<0$) and quartic ($g_4>0$) interactions describing a broad class of technologically important materials, such as quantum paraelectric compounds and halide perovskites. We observe, depending on the model parameters, three qualitatively different regimes: (i) quantum interplay of quartic and quadratic interactions which suppresses effects of the quadratic coupling, (ii) intermediate-coupling regime with exponential $\propto \exp(αg_2 Ω^{-1/4})$ scaling of the quasiparticle weight and mass renormalization, and (iii) strong-coupling asymptotic behavior.

cond-mat.str-el↗