Path integral Monte Carlo study of the interacting quantum double-well model: Quantum phase transition and phase diagram

TL;DR

This study uses path integral Monte Carlo methods with an exact single-particle action to analyze the quantum phase transition and phase diagram of an interacting quantum double-well chain, revealing universality with the 2D Ising model.

Contribution

It introduces an improved PIMC approach using the exact single-particle action to accurately determine the phase diagram and critical behavior of the quantum double-well chain.

Findings

Quantum phase transition studied via finite-size scaling.

Critical exponents match 2D Ising universality class.

Phase diagram mapped for different potential depths.

Abstract

The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling and the critical exponents are shown to be compatible with the classical two-dimensional (2D) Ising universality class -- not only in the order-disorder limit (deep potential wells) but also in the displacive regime (shallow potential wells).