Unitary circuits for strongly correlated fermions

TL;DR

This paper introduces a unitary circuit approach for efficiently simulating strongly correlated fermions in higher dimensions, avoiding nonlocal operators and enabling variational studies without a sign problem.

Contribution

It presents a novel fermionic unitary circuit scheme with a causal cone and a dynamical reordering method, improving computational efficiency and applicability to higher-dimensional models.

Findings

Efficient local expectation value computation for fermionic states.

Numerical validation on 9x9 and 6x6 fermionic lattice models.

Avoidance of the fermionic sign problem in variational simulations.

Abstract

We introduce a scheme for efficiently describing pure states of strongly correlated fermions in higher dimensions using unitary circuits featuring a causal cone. A local way of computing local expectation values is presented. We formulate a dynamical reordering scheme, corresponding to time-adaptive Jordan-Wigner transformation, that avoids nonlocal string operators. Primitives of such a reordering scheme are highlighted. Fermionic unitary circuits can be contracted with the same complexity as in the spin case. The scheme gives rise to a variational description of fermionic models not suffering from a sign problem. We present numerical examples on $9\times 9$ and $6\times 6$ fermionic lattice model to show the functioning of the approach.