Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant

Abstract

Ab-initio Monte Carlo simulations of strongly-interacting fermionic systems are plagued by the fermion sign problem, making the non-perturbative study of many interesting regimes of dense quantum matter, or of theories of odd numbers of fermion flavors, challenging. Moreover, typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on the meron cluster algorithm, which can solve the fermion sign problem in a class of models without involving the determinant. We develop and benchmark new meron algorithms to simulate fermions coupled to ${\mathbb{Z}}_2$ and $U(1)$ gauge fields in the presence of appropriate four-fermi interactions. Such algorithms can be used to uncover potential exotic properties of matter, particularly relevant for quantum simulator experiments. We demonstrate the emergence of the Gauss' Law at low temperatures for a $U(1)$ model in $(1+1)-$d.

5 pages, 4 figures, 1 table

References in corpus (10)

• Probing many-body dynamics on a 51-atom quantum simulator
• Continuous-time Monte Carlo methods for quantum impurity models
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Competing density-wave orders in a one-dimensional hard-boson model
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Diagrammatic Determinantal methods: projective schemes and applications to the Hubbard-Holstein model
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• A simple fermionic model of deconfined phases and phase transitions
• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Robust Fermi liquid instabilities in sign problem-free models

Cited by in corpus (1)

• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model