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Tohru Koma

Publications and source records attributed to Tohru Koma.

At least 19 recordsLinked to original sources
arXiv2025

Superconductivity and Low Energy Excitations in an Attractive Hubbard Model

We study an attractive Hubbard model on bipartite lattices. In the grand canonical formalism,we prove the existence of superconducting long-range order in the ground state on Lieb lattices with the chemical potential corresponding to half filling. We also study the low-energy excitations above several ground states for the translationally invariant Hamiltonian. We prove the following: (i) The pairing excitations are gapless above the ground states when the number of fermions deviates from that of the half filling by the order of the volume. (ii) A certain class of single-fermion excitations shows a non-vanishing spectral gap above the ground state with an even number of fermions in a strong coupling and low-density regime.

math-ph↗
arXiv2025

Antiferromagnetic Long-Range Order in a Lattice Fermion Model

We study a lattice fermion model with antiferromagnetic interactions on the three-dimensional cubic lattice. The hopping term of the Hamiltonian has a Weyl-type dispersion. We prove that the model has reflection positivity. Moreover, by relying on the property, we prove the existence of the antiferromagnetic long-range order at low temperatures in a strong coupling regime.

math-ph↗
arXiv2025

Violation of Parity and Flavor Symmetries in a Nambu-Jona-Lasinio Model

We study a lattice Nambu-Jona-Lasinio model with certain continuous chiral and two-flavor symmetries. For the Hamiltonian of the model, we construct a ground state which breaks the parity and flavor symmetries. In our argument, the chiral symmetry plays a crucial role for proving the violation of the parity and flavor symmetries, although the model does not contain the so-called Wilson term.

hep-ph↗
arXiv2024

Nambu-Goldstone modes in a lattice Nambu-Jona-Lasinio model with multi flavor symmetries

We study a lattice Nambu-Jona-Lasinio model with SU(2) and SU(3) flavor symmetries of staggered fermions in the Kogut-Susskind Hamiltonian formalism. This type of four-fermion interactions has been widely used for describing low-energy behaviors of strongly interacting quarks as an effective model. In particular, we focus on the Nambu-Goldstone modes associated with the spontaneous breakdown of the flavor symmetries. In the strong coupling regime for the interactions, we prove the following: (i) For the spatial dimension $ν\ge 5$, the SU(3) model shows a long-range order at sufficiently low temperatures. (ii) In the case of the SU(2) symmetry, there appears a long-range order in the spatial dimension $ν\ge 3$ at sufficiently low temperatures. (iii) These results hold in the ground states as well. (iv) In general, if a long-range order emerges in this type of models, then there appear gapless excitations above the sector of the infinite-volume ground states. These are nothing but the Nambu-Goldstone modes associated with the spontaneous breakdown of the global rotational symmetry of flavors. (v) In particular, we establish that the number of the lineraly independent Nambu-Goldstone modes is equal to the number of the broken symmetry generators on the Hilbert space constructed from a certain symmetry-breaking infinite-volume ground state.

math-ph↗
arXiv2024

Spontaneous mass generation and chiral symmetry breaking in a lattice Nambu-Jona-Lasinio model

We study a lattice Nambu-Jona-Lasinio model with interacting staggered fermions in the Kogut-Susskind Hamiltonian formalism. The model has a discrete chiral symmetry but not the usual continuous chiral symmetry. In a strong coupling regime for the four-fermion interaction, we prove that the mass of the fermions is spontaneously generated at sufficiently low non-zero temperatures in the dimensions $ν\ge 3$ of the model and zero temperature in $ν\ge 2$. Due to the phase transition, the discrete chiral symmetry of the model is broken. Our analysis is based on the reflection positivity for fermions and the method of the infrared bound.

math-ph↗
arXiv2022

A Concrete Example of Fractional Chern Insulator

We present a concrete example of fractional Chern insulator whose fermion Hamiltonian consists of hopping and Coulomb repulsive interaction terms. Both of them are of finite range on the square lattice. In a strong coupling limit for the interaction Hamiltonian, we show that the Hall conductance is fractionally quantized to $1/2$ in the sense of the expectation value with respect to the four-fold degenerate ground state at the filling $3/8$. We also present a slightly different example in which there appears a long-range order of charge density wave with the Chern number $1$.

math-ph↗
arXiv2022

Stability of Majorana Edge Zero Modes against Interactions

We study an interacting Majorana chain with an open boundary condition. In the case without interactions, the system shows a prototypical Majorana edge zero mode in the sector of the ground state with a spectral gap above the sector. We prove that both of the Majorana edge zero mode and the non-vanishing spectral gap are stable against generic weak interactions whose fermion parity is even. We also deal with the corresponding ladder systems, and discuss the $\mathbb{Z}_2$ index for the Majorana edge zero modes.

math-ph↗
arXiv2022

$π$ Flux Phase and Superconductivity for Lattice Fermions Coupled to Classical Gauge Fields

We study superconducting lattice fermions coupled to classical gauge fields. Namely, without the gauge fields, the lattice fermions show superconducting long-range order. In the previous paper, the existence of the long-range order was proved by the present author. This paper is the continuing part of the previous one. More precisely, the interactions between fermions were assumed to be a Bardeen-Cooper-Schrieffer-type pairing which is a nearest-neighbour two-body interaction on the hypercubic lattice $\mathbb{Z}^d$ with the dimension $d\ge 3$. In the present paper, we deal with the corresponding gauged model by introducing classical U(1) gauge fields. We prove that a certain configuration of gauge fields which yields the $π$ flux for all the plaquettes in the lattice minimizes the ground-state energy of the fermion system. Since this configuration of the gauge fields exactly coincides with the hopping amplitudes of the Hamiltonian of the previous paper, the ground state of the whole system shows superconducting long-range order. Any configuration of gauge fields which is gauge-equivalent to this special configuration of the gauge fields also yields another ground state. However, if the Cooper pair correlations are averaged over the gauge-equivalent class, then they are vanishing except for the on-site correlation because the Cooper pair correlations are not necessarily gauge invariant. On the other hand, the string Cooper pair correlations which are gauge invariant always show the same long-range order for any configuration of gauge fields in the gauge-equivalent class.

math-ph↗
arXiv2022

Nambu-Goldstone Modes for Superconducting Lattice Fermions

We present a lattice model for superconducting fermions whose nearest-neighbour two-body interactions are a Bardeen-Cooper-Schrieffer-type pairing on the hypercubic lattice $\mathbb{Z}^d$ with the dimension $d\ge 3$. Although these effective interactions between two electrons are believed to be caused by electron-phonon interactions, we assume that the interactions between two electrons are of short range without phonons. For the model, we prove the existence of the long-range order of the superconductivity at low temperatures, and also prove the existence of a gapless excitation above the infinite-volume ground state. Namely, there appears a Nambu-Goldstone mode which is associated with the U(1) symmetry breaking. The corresponding Nambu-Goldstone boson is exactly a Cooper pair, which consists of spin up and down electrons.

math-ph↗
arXiv2021

Dispersion Relations of Nambu-Goldstone Modes

We study the energy-momentum relations of the Nambu-Goldstone modes in quantum antiferromagnetic Heisenberg models on a hypercubic lattice. This work is a sequel to the previous series about the models. We prove that the Nambu-Goldstone modes show a linear dispersion relation for the small momenta, i.e., the low energies of the Nambu-Goldstone excitations are proportional to the momentum of the spin wave above the infinite-volume ground states with symmetry breaking. Our method relies on the upper bounds for the susceptibilities which are derived from the reflection positivity of the quantum Heisenberg antiferromagnets. The method is also applicable to other systems when the corresponding upper bounds for the susceptibilities are justified.

math-ph↗
arXiv2021

Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes

We study edge modes in topological semimetals which have an energy band structure of ordinary semimetals but can be characterized by a Chern number. More specifically, we focus on a Qi-Wu-Zhang-type square-lattice model and a Haldane-type honeycomb model, both of which exhibit antichiral edge modes whose wave packets propagate in the same direction at both parallel edges of the strip. To obtain these analytical solutions of the edge modes, we apply the transfer matrix method which was developed in the previous work [Phys. Rev. B \textbf{101}, 014442 (2020)]. As a result, we show that the bulk-edge correspondence is broken down for a certain range of the model parameters. More precisely, when increasing the strength of a hopping amplitude of the Qi-Wu-Zhang-type model, the edge modes abruptly disappear, although the non-trivial Chern number does not change. In the Haldane-type model, for varying the model parameters, the edge modes do not necessarily disappear, and the non-trivial Chern number does not change. However, the energy spectral flows of the edge modes from the valence band to the conduction band are abruptly broken at a certain set of the model parameters.

cond-mat.mes-hall↗
arXiv2020

Stability of the Spectral Gap for Lattice Fermions

It is widely believed that the spectral gap above the Fermi sea ground state of lattice free fermions is stable against generic weak interactions. Quite recently, Hastings presented a new interesting idea to prove the stability for Majorana free fermions. He ingeniously used Majorana fermions so that the unperturbed Hamiltonian of the free fermion part is mapped into a frustration-free form. In this paper, we refine Hastings's argument, and give a complete proof of the stability of the spectral gap above the Fermi sea ground state against generic weak interactions for generic lattice free fermions.

math-ph↗
arXiv2020

Power-Law Decay Exponents of Nambu-Goldstone Transverse Correlations

We study a quantum antiferromagnetic Heisenberg model on a hypercubic lattice in three or higher dimensions $d\ge 3$. When a phase transition occurs with the continuous symmetry breaking, the nonvanishing spontaneous magnetization which is obtained by applying the infinitesimally weak symmetry breaking field is equal to the maximum spontaneous magnetization at zero or non-zero low temperatures. In addition, the transverse correlation in the infinite-volume limit exhibits a Nambu-Goldstone-type slow decay. In this paper, we assume that the transverse correlation decays by power law with distance. Under this assumption, we prove that the power is equal to $2-d$ at non-zero low temperatures, while it is equal to $1-d$ at zero temperature. The method is applied also to a quantum XY model and a classical Heisenberg model at non-zero low temperatures in three or higher dimensions. The resulting power is given by the same $2-d$ at non-zero low temperatures.

math-ph↗
arXiv2020

Maximum Spontaneous Magnetization and Nambu-Goldstone Mode

We study quantum antiferromagnetic Heisenberg models on a hypercubic lattice. We prove the following three theorems without any assumption: (i) The spontaneous magnetization which is obtained by applying the infinitesimally weak symmetry breaking field is equal to the maximum spontaneous magnetization at zero or non-zero low temperatures. (ii) When the spontaneous magnetization is non-vanishing at zero temperature, there appears a gapless excitation, Nambu-Goldstone mode, above an infinite-volume pure ground state. (iii) When the spontaneous magnetization is non-vanishing at zero or non-zero low temperatures, the transverse correlation in the infinite-volume limit exhibits a Nambu-Goldstone-type slow decay.

math-ph↗
arXiv2020

Oriented propagation of magnetization due to chiral edge modes in Kitaev-type models

Detecting chiral edge modes in topological materials has been intensively pursued in experiments. However, the phenomena caused by the modes are not yet elucidated theoretically. We study the dynamics of chiral spinon wave packets at the edge in Kitaev-type magnets. More precisely, by relying on the exact solvability of the models, we construct a spinon wave packet, localized edge magnetization, which shows oriented propagation along the edge, whose behavior is expected from the chiral character of the dispersion relation of the chiral edge modes. In general, this approach enables us to study not only spin transport in anisotropic magnets but also charge transport in Bogoliubov-de Gennes-type superconductors because it does not rely on a conserved quantity.

cond-mat.str-el↗
arXiv2020

Proof of the absence of long-range temporal orders in Gibbs states

We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system. One way of detecting such a symmetry breaking is to examine the time-dependence of a correlation function. If the large-distance behavior of the correlation function exhibits a nontrivial time-dependence in the thermodynamic limit, the system would develop a temporal long-range order, realizing a time crystal. In an earlier publication, we sketched a proof for the absence of such time dependence in the thermal equilibrium described by the Gibbs state [H. Watanabe and M. Oshikawa, Phys. Rev. Lett. 114, 251603 (2015)]. Here we present a complete proof and extend the argument to a more general class of stationary states than the Gibbs states.

cond-mat.stat-mech↗
arXiv2019

Majorana edge magnetization in the Kitaev honeycomb model

We propose an approach to detect the peculiarity of Majorana fermions at the edges of Kitaev magnets. As is well known, a pair of Majorana edge modes is realized when a single complex fermion splits into real and imaginary parts which are, respectively, localized at the left and right edges of a sample magnet. Reflecting both of this peculiarity of the Majorana fermions and the ground-state degeneracy caused by the existence of the Majorana edge zero modes, the spins at the edges of the sample magnet are expected to behave as a peculiar "free" spin which exhibits a unidirectional magnetization without any transverse magnetization when applied a sufficiently weak external magnetic field. For the Kitaev honeycomb model, we obtain the expression of the Majorana edge magnetization by relying on standard techniques to diagonalize a free fermion Hamiltonian. The magnetization profile thus obtained indeed shows the expected behavior. We also elucidate the relation between the Majorana edge flat band and the bulk winding number from a weak topological point of view.

cond-mat.str-el↗