Finite-Size Effects of a Many-Fermion System

In this note, we discuss the effective mass of quasiparticles in finite sized $ν= 1/2$ systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for $ν= 1/2$ systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.In this note, we discuss the effective mass of quasiparticles in finite sized $ν= 1/2$ systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for $ν= 1/2$ systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.

arXiv:cond-mat/9709081Sep 5, 19970 citations

Simple Models of Many-Fermion Systems

Joachim Alexander Maruhn, P.‐G. Reinhard, E. Suraud

Springer eBooksJan 1, 201044 citations

Jordan-Wigner mapping between quantum-spin and fermionic Casimir effects

Katsumasa Nakayama, Kei Suzuki

The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.

cond-mat.stat-mechCross-listedarXiv:2601.18867Jan 28, 20260 citations

``Bare'' Effective Mass in Finite Sized

ν= 1/2

Systems

In this note, we discuss the effective mass of quasiparticles in finite sized

ν= 1/2

systems in the lowest Landau level, given a natural notion we have of the Fermi surface in these finite sized systems. The effective mass is related to the difference between instantaneous density-density response functions of the ground state and excited states of the system; we do a finite size calculation for this difference for

ν= 1/2

systems with 7, 8 and 9 fermions, and conjecture how the difference must look in the thermodynamic limit.