In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free from the fermion sign problem, enabling efficient simulations of fermionic systems. We found that by shifting the pseudo-fermion energy based on the energy of a non-interacting fermion system, we can efficiently and reliably infer the energy of fermionic systems in various situations, from strong quantum degeneracy to weak quantum degeneracy. We have performed numerical simulations of quantum dots confined in a two-dimensional harmonic potential and found excellent agreement with benchmark results provided by other established methods. We believe that this pseudo-fermion propagator framework opens up new possibilities for numerical simulations of fermionic systems.In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free from the fermion sign problem, enabling efficient simulations of fermionic systems. We found that by shifting the pseudo-fermion energy based on the energy of a non-interacting fermion system, we can efficiently and reliably infer the energy of fermionic systems in various situations, from strong quantum degeneracy to weak quantum degeneracy. We have performed numerical simulations of quantum dots confined in a two-dimensional harmonic potential and found excellent agreement with benchmark results provided by other established methods. We believe that this pseudo-fermion propagator framework opens up new possibilities for numerical simulations of fermionic systems.

arXiv:2508.09557The Journal of Chemical PhysicsNov 3, 20253 citations

Informational features of Fermionic systems

Alessandro Tosini

The anticommutation of Fermionic fields raises the problem of simulating the evolution of Fermionic systems by means of commuting quantum systems, say qubits. We tackle [1,2] the issue of retaining locality of Fermionic operations considering local Fermionic modes as the elementary systems of an operational probabilistic theory. The locality of Fermionic operations, namely operations on systems that are not causally connected must commute, implies the parity superselection rule that inhibits the superposition of states with an even and an odd number of excitations. As a result the Fermionic theory lacks two distinctive traits of quantum theory, the local tomography and the monogamy of the entanglement.The anticommutation of Fermionic fields raises the problem of simulating the evolution of Fermionic systems by means of commuting quantum systems, say qubits. We tackle [1,2] the issue of retaining locality of Fermionic operations considering local Fermionic modes as the elementary systems of an operational probabilistic theory. The locality of Fermionic operations, namely operations on systems that are not causally connected must commute, implies the parity superselection rule that inhibits the superposition of states with an even and an odd number of excitations. As a result the Fermionic theory lacks two distinctive traits of quantum theory, the local tomography and the monogamy of the entanglement.

Proceedings of Frontiers of Fundamental Physics 14 — PoS(FFP14)Sep 15, 20160 citations

Many-Fermion Systems

WORLD SCIENTIFIC eBooksMar 1, 19980 citations

Many-Fermion Systems

WORLD SCIENTIFIC eBooksSep 8, 20140 citations

Open Quadratic Fermion Systems and Algebras of Affine Transformations

Tamura, Hiroshi

We study evolution of open quadratic fermion systems in the framework of the quantum Markovian semigroup approach. We show that the algebra concerning commutators of Liouvillians for systems of quadratic interacting fermions of finite number, say $\mathcal{N}$ , is isomorphic to that of certain affine transformations on the space of square matrices of size $\mathcal{N}$ . By the use of this algebraic structure, we present a perspective method for solving master equations of quadratic fermion systems. Here, we mainly deal with gauge invariant quadratic interacting fermion systems. We briefly mention similar algebraic structures for general quadratic fermion systems and quadratic boson systems. Keywords : open quantum system, Markovian quantum dynamical system, quadratic interacting Fermion, affine transformation, asymptotic behavior, skin effectWe study evolution of open quadratic fermion systems in the framework of the quantum Markovian semigroup approach. We show that the algebra concerning commutators of Liouvillians for systems of quadratic interacting fermions of finite number, say $\mathcal{N}$, is isomorphic to that of certain affine transformations on the space of square matrices of size $\mathcal{N}$. By the use of this algebraic structure, we present a perspective method for solving master equations of quadratic fermion systems. Here, we mainly deal with gauge invariant quadratic interacting fermion systems. We briefly mention similar algebraic structures for general quadratic fermion systems and quadratic boson systems. Keywords : open quantum system, Markovian quantum dynamical system, quadratic interacting Fermion, affine transformation, asymptotic behavior, skin effect

arXiv:2301.06069Jan 15, 20230 citations

\mathcal{N}

, is isomorphic to that of certain affine transformations on the space of square matrices of size

\mathcal{N}

. By the use of this algebraic structure, we present a perspective method for solving master equations of quadratic fermion systems. Here, we mainly deal with gauge invariant quadratic interacting fermion systems. We briefly mention similar algebraic structures for general quadratic fermion systems and quadratic boson systems. Keywords : open quantum system, Markovian quantum dynamical system, quadratic interacting Fermion, affine transformation, asymptotic behavior, skin effect