Monte Carlo simulations of two-dimensional fermion systems with string-bond states

Abstract

We describe an application of variational Monte Carlo to two-dimensional fermionic systems within the recently developed tensor-network string-bond state (SBS) ansatz. We use a combination of variational Monte Carlo and stochastic optimization to optimize the matrix-product state matrices representing the ground state. We present results for a two-dimensional spinless fermion model including nearest-neighbor Coulomb interactions and determine using finite-size scaling the phase boundary between charge-ordered insulating and metallic phases. This approach can treat frustrated systems and be easily extended to for fermions with spin.

Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states

“…Despite its apparent simplicity, however, the phase diagram cannot be determined with high precision using existing numerical approaches and several questions remain open. These include the nature of the charge ordered phase 25,26 and the precise position of the phase boundary 20,21,[25][26][27][28] . Several state of the art variational wavefunctions have been applied to solve this model including the so called stringbond states 27 and tensor-product projected states 28 (at half filling), as well as fermionic projected entangledpair states (IPEPS) 29 at arbitrary filling in the grand canonical ensemble.…”

“…These include the nature of the charge ordered phase 25,26 and the precise position of the phase boundary 20,21,[25][26][27][28] . Several state of the art variational wavefunctions have been applied to solve this model including the so called stringbond states 27 and tensor-product projected states 28 (at half filling), as well as fermionic projected entangledpair states (IPEPS) 29 at arbitrary filling in the grand canonical ensemble. In this work we use neural network states to systematically investigate the phase diagram in the fixed particle subspace by considering a large collection of model parameters.…”

“…Although the phase diagram has been investigated using a variety of techniques 20,21,[25][26][27][28][29]31 , there still exist open questions concerning the precise location of the phase boundary, (particularly at half occupation 20,21,27,28 ) as well as the nature of the chargeordered phase in the vicinity of the critical point 26 .…”

“…In particular, at half-occupation (n = 0.5), the phase transition from a metallic phase to a checkerboard charge-ordered insulating phase is detected by the socalled charge structure factor S(π, π), defined as the k = (π, π) component of the Fourier transform of the two-point correlation function averaged over lattice locations 20,21,27,28 .…”

Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity

“…For other spatial dimensions, this model has been studied using the analytical methods such as perturbation theory, 32 perturbative-variational approach, 33 Hartree-Fock approximation, 34,35 as well as numerical techniques including cluster approximation, 36,37 quantum Monte Carlo, 38,39 exact diagonalization, 10 fermionic projected entangled-pair states, 40 and variational Monte Carlo. [41][42][43] . One of the basic issues is the phases and their stability.…”