Quantum electronic circuits for multicritical Ising models

Abstract

Multicritical Ising models and their perturbations are paradigmatic models of statistical mechanics. In two space-time dimensions, these models provide a fertile testbed for investigation of numerous nonperturbative problems in strongly-interacting quantum field theories. In this work, analog superconducting quantum electronic circuit simulators are described for the realization of these multicritical Ising models. The latter arise as perturbations of the quantum sine-Gordon model with $p$-fold degenerate minima, $p=2,3,4,...$. The corresponding quantum circuits are constructed with Josephson junctions with $cos(n\ensuremath{\phi}+{\ensuremath{\delta}}_{n})$ potential with $1\ensuremath{\le}n\ensuremath{\le}p$ and ${\ensuremath{\delta}}_{n}\ensuremath{\in}[\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi}]$. The simplest case, $p=2$, corresponds to the quantum Ising model and can be realized using conventional Josephson junctions and the so-called $0\text{\ensuremath{-}}\ensuremath{\pi}$ qubits. The lattice models for the Ising and tricritical Ising models are analyzed numerically using the density matrix renormalization group technique. Evidence for the multicritical phenomena are obtained from computation of entanglement entropy of a subsystem and correlation functions of relevant lattice operators. The proposed quantum circuits provide a systematic approach for controlled numerical and experimental investigation of a wide range of nonperturbative phenomena occurring in low-dimensional quantum field theories.