Disentanglement approach to quantum spin ground states: field theory and stochastic simulation

Abstract

While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.