Strings, Projected Entangled Pair States, and variational Monte Carlo methods

TL;DR

This paper introduces string-bond states, a versatile class of quantum states that enable efficient Monte Carlo sampling for local observable expectation values, extending variational methods like DMRG to complex higher-dimensional systems.

Contribution

The paper proposes string-bond states and demonstrates their effectiveness for simulating many-body systems using a variational Monte Carlo approach.

Findings

Efficient computation of local observables using Monte Carlo sampling.

Applicability of string-bond states to higher-dimensional and irregular systems.

Numerical validation of the method on many-body systems.

Abstract

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in Quantum Information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational abgorithm which extends DMRG to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body sytems.