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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

 Times Cited Count:1 Percentile:0.01(Astronomy & Astrophysics)

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:3 Percentile:56.93(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.

Journal Articles

$$D$$ mesons as a probe of Casimir effect for chiral symmetry breaking

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

Physical Review D, 100(3), p.034016_1 - 034016_14, 2019/08

 Times Cited Count:4 Percentile:35.9(Astronomy & Astrophysics)

We propose $$D$$ mesons as probes to investigate finite-volume effects for chiral symmetry breaking at zero and finite temperatures. By using the 2+1-flavor linear sigma model with constituent light quarks, we analyze the Casimir effects for the $$sigma$$ mean fields; the chiral symmetry is rapidly restored by the antiperiodic boundary for light quarks, and the chiral symmetry breaking is catalyzed by the periodic boundary. We also show the phase diagram of the $$sigma$$ mean fields on the volume and temperature plane. For $$D$$ mesons, we employ an effective model based on the chiral-partner structure, in which the volume dependence of $$D$$ mesons is induced by the $$sigma$$ mean fields. We find that $$D_s$$ mesons are less sensitive to finite volume than $$D$$ mesons, which is caused by the insensitivity of $$sigma_s$$ mean fields. An anomalous mass shift of $$D$$ mesons at high temperature with the periodic boundary will be useful in examinations with lattice QCD simulations. The dependence on the number of compactified spatial dimensions is also studied.

Oral presentation

Casimir effect and spontaneous chiral symmetry braking in D mesons

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

no journal, , 

D mesons are expected to be clear probes of the chiral condensate. For the Casimir effect in the QCD vacuum, non-perturbative properties of the QCD vacuum are modified by the volume size and boundary conditions. In this talk, we focus on the modification of the chiral symmetry breaking by the Casimir effect and the response of D mesons. By using an effective Lagrangian based on chiral partner structures for D mesons, we discuss the dependences on volume, boundary, and temperature, and the applications to lattice QCD simulations.

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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