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Journal Articles

Kondo effect with Wilson fermions

Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei

Physical Review D, 104(9), p.094515_1 - 094515_11, 2021/11

We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter region realizing the Aoki phase. Our findings will be useful for understanding the roles of heavy impurities in Dirac semimetals, topological insulators, and lattice simulations.

Journal Articles

Lattice-fermionic Casimir effect and topological insulators

Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei

Physical Review Research (Internet), 3(2), p.023201_1 - 023201_23, 2021/06

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the M$"o$bius domain-wall fermion formulation, in the $$1+1$$, $$2+1$$, and $$3+1$$ dimensional spacetime with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

Journal Articles

Casimir effect for lattice fermions

Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei

Physics Letters B, 809, p.135713_1 - 135713_7, 2020/10

 Times Cited Count:2 Percentile:57.67(Astronomy & Astrophysics)

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 (M$"o$bius) 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 $$N geq 3$$, 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 M$"o$bius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.

Oral presentation

Casimir effect for lattice fermions; Naive, Wilson, and domain-wall

Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei

no journal, , 

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 (M$"o$bius) 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 $$N geq 3$$, 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 M$"o$bius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.

Oral presentation

Kondo effect for Wilson fermion

Ishikawa, Tsutomu*; Nakayama, Katsumasa*; Suzuki, Kei

no journal, , 

no abstracts in English

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