Strong-coupling Expansions at Finite Temperatures: Application to Quantum Disordered and Quantum Critical Phases

TL;DR

This paper introduces a systematic high-order perturbative method combining finite-temperature many-body theory with cluster expansions, enabling accurate thermodynamic calculations of quantum disordered and critical phases across a broad temperature range.

Contribution

The authors develop a novel computational approach that extends perturbation theory with cluster expansions for high-order calculations at finite temperatures, applicable to complex quantum phases.

Findings

Method shows excellent convergence for thermodynamic properties across temperatures.

Almost perfect agreement with Quantum Monte Carlo at critical coupling.

Convergence issues only at very low temperatures.

Abstract

By combining conventional finite-temperature many-body perturbation theory with cluster expansions, we develop a systematic method to carry out high order arbitrary temperature perturbative calculations on the computer. The method is well suited to studying the thermodynamic properties of quantum disordered and quantum critical phases at finite temperatures. As an application, we calculate the magnetic susceptibility, internal energy and specific heat of the bilayer Heisenberg model. It is shown that for a wide range of coupling constants these expansions show excellent convergence at all temperatures. Comparing the direct series (without extrapolations) for the bulk susceptibility to Quantum Monte Carlo simulations we find an almost perfect agreement between the two methods even at the quantum critical coupling separating the dimerized and antiferromagnetic phases. The convergence fails only at very low temperatures, which are also difficult to reach by Quantum Monte Carlo simulations.