Casimir effect for lattice fermions

Abstract

We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Möbius) domain-wall fermion in $1+1$ dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of $N\ge 3$, the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Möbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.

8 pages, 5 figures; published version

References in corpus (64)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Exactly massless quarks on the lattice
• A Method for Simulating Chiral Fermions on the Lattice
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Chiral Fermions from Lattice Boundaries
• More about exactly massless quarks on the lattice
• Axial symmetries in lattice QCD with Kaplan fermions
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit
• An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
• Chiral transition in a finite system and possible use of finite size scaling in relativistic heavy ion collisions
• Quantum simulation of lattice gauge theories using Wilson fermions
• Domain wall fermions with improved gauge actions
• On the Phase Structure of QCD in a Finite Volume
• Mobius Fermions: Improved Domain Wall Chiral Fermions
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• Fermionic Casimir effect for parallel plates in the presence of compact dimensions with applications to nanotubes
• Volume and Quark Mass Dependence of the Chiral Phase Transition
• Fermionic Casimir densities in toroidally compactified spacetimes with applications to nanotubes
• The Effect of Fluctuations on the QCD Critical Point in a Finite Volume
• Finite-size effects on the phase structure of the Nambu-Jona-Lasinio model
• Casimir effect in Yang-Mills theory
• Volume Dependence of the Pion Mass in the Quark-Meson-Model
• Moebius Fermions
• Finite-size effects on the chiral phase diagram of four-fermion models in four dimensions
• Finite size effects in the Gross-Neveu model with isospin chemical potential
• Influence of quark boundary conditions on the pion mass in finite volume
• Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• The Casimir energy of a massive fermionic field confined in a d+1 dimensional slab-bag
• Strongly Interacting Fermions and Phases of the Casimir Effect
• Finite-size effects in pion condensation phenomena of dense baryonic matter in the NJL${}_2$ model
• Casimir Energy of Massless Fermions in the Slab-bag
• Interacting Fermions, Boundaries, and Finite Size Effects
• Functional approach to the fermionic Casimir effect
• Volume dependence of baryon number cumulants and their ratios
• Cooper pairing and finite-size effects in a NJL-type four-fermion model
• The Möbius Domain Wall Fermion Algorithm
• Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu--Jona-Lasinio model
• Nonperturbative Casimir effect and monopoles: compact Abelian gauge theory in two spatial dimensions
• The Casimir effect and deconfinement phase transition
• Casimir effect for nucleon parity doublets
• Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
• Thermodynamics of the ideal overlap quarks on the lattice
• Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD
• Finite-size effects on the Phase Structure of the Walecka Model
• Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model
• Generalized lattice Wilson-Dirac fermions in (1+1) dimensions for atomic quantum simulation and topological phases
• Chiral Symmetry Restoration from a Boundary
• Casimir energy calculations within the formalism of the noncompact lattice QED
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Boundary effects on constituent quark masses and on chiral susceptibility in a four-fermion interaction model
• Curvature and topological effects on dynamical symmetry breaking in a four- and eight-fermion interaction model
• Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory
• Casimir Effect on a Finite Lattice
• Zero-mode contribution and quantized first order phase transition in a droplet quark matter
• $D$ mesons as a probe of Casimir effect for chiral symmetry breaking
• Critical behaviour of an effective relativistic mean field model in the presence of magnetic background and boundaries
• Thermodynamics of free Domain Wall fermions
• Finite-sites corrections to the Casimir energy on a periodic lattice
• Four-Fermion Interaction Model on ${\mathcal{M}}^{D-1}\otimes S^1$
• Casimir energy in the compact QED on the lattice

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• Magnonic Casimir Effect in Ferrimagnets
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• Remnants of the nonrelativistic Casimir effect on the lattice
• Casimir effect in axion electrodynamics with lattice regularizations
• Non-Hermitian Casimir effect of magnons
• Precise Phase Structure in Four-fermion Interaction Model on Torus
• Dual chiral density wave induced oscillating Casimir effect
• The Casimir effect for nonlinear sigma models and the Mermin-Wagner-Hohenberg-Coleman theorem
• Effective model for pure Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ with Polyakov loops
• Lifshitz formulas for finite-density Casimir effect
• Casimir effect in magnetic dual chiral density waves
• Casimir effect for fermions on the lattice
• Lattice Fermionic Casimir effect in a Slab Bag and Universality