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Kazue Matsuyama

Publications and source records attributed to Kazue Matsuyama.

At least 19 recordsLinked to original sources
arXiv2026

BCS states and D-wave condensates in the 2D Hubbard model

We consider states of BCS form in the 2D Hubbard model which, starting from some arbitrary point in state space in the neighborhood of a Hartree-Fock ground state, are relaxed within that BCS ansatz to local minima of the energy. As in the Hartree-Fock approximation there are a vast number of local minima, nearly degenerate in energy. What is new, and unlike the conventional Hartree-Fock states, is that there is a region in parameter space where these local minima are clearly associated with d-wave condensates of the form $d_{x^2-y^2}$ in the underdoped region. There are also indications of $d_{xy}$ condensation in the overdoped region, at least in this approximation to the 2D Hubbard model, as well as condensates over a range of parameters on triangular lattices.

cond-mat.supr-con↗
arXiv2024

A Variational Improvement of the Hartree-Fock Approach to the 2D Hubbard Model

We consider a refinement of the usual Hartree-Fock method applied to the 2D Hubbard model, in Nambu spinor formulation. The new element is the addition of a "condensate inducing" term proportional to a variational parameter h to the Hartree-Fock Hamiltonian, which generates an s- or d-wave condensate at zero temperature. This modified Hartree-Fock Hamiltonian is used only to generate variational trial states; energy expectation values are computed in the full two-dimensional Hubbard Hamiltonian with no modification. It is found that there exist trial states with non-vanishing condensates which are lower in energy than the standard Hartree-Fock ground states. However, these lower energy condensate states exist only in a spatially inhomogeneous (stripe) phase. No lowering of energy, relative to the Hartree-Fock ground state, is found in the spatially homogenous region of the U-density phase plane.

cond-mat.str-el↗
arXiv2023

Hartree-Fock with Nambu spinors, and d-wave condensation in the 2D Hubbard model

The usual Hartree-Fock approximation to the Hubbard model is based on eigenstates of the electron number operator. But this formulation is not unique. A different (and inequivalent) version, formulated in terms of Nambu two-component spinors, is based on eigenstates of the difference between the numbers of spin up and spin down electrons, with electron density dependent on parameters $U,t,t'$ and chemical potential $μ$. The advantage of this formulation is that electron pairing condensates can be directly computed. We show that in the ground states away from half-filling, obtained in this "Nambu" Hartree-Fock approximation, a discrete rotation symmetry is spontaneously broken, and the condensates exhibit the expected d-wave form in momentum space. We also show that the Mott insulator electron configuration is obtained in this formulation at large $U/t$ and half-filling, and roughly locate the boundary, in the hole doping$-$$U/t$ plane, between a region of local antiferromagnetism and stripe/domain formation, and the region of d-wave condensation.

cond-mat.str-el↗
arXiv2022

Quantum excitations of static charges in the Ginzburg-Landau model of superconductivity

We point out that in superconductors there may exist localized quantum excitations of the electric and condensate fields surrounding a static charge, which cannot be interpreted as simply the ground state of the screened charge plus some number of massive photons. This is illustrated via a lattice Monte Carlo calculation of the energy spectrum of a pair of separated static charges in an effective Ginzburg-Landau model of superconductivity.

cond-mat.supr-con↗
arXiv2022

Multiplicity, localization, and domains in the Hartree-Fock ground state of the two-dimensional Hubbard model

We explore certain properties of the Hartree-Fock approximation to the ground state of the two-dimensional Hubbard model, emphasizing the fact that in the Hartree approach there is an enormous multiplicity of self-consistent solutions which are nearly degenerate in energy, reminiscent of a spin glass, but which may differ substantially in other bulk properties. It is argued that this multiplicity is physically relevant at low temperatures. We study the localization properties of the one-particle wavefunctions comprising the Hartree-Fock states, and find that these are unlocalized at small and moderate values of U/t, in particular in the stripe region, but become highly localized at values corresponding to strong repulsion. We also find rectangular domains as well as stripes in the stripe region of the phase diagram, and study pair correlations in the neighborhood of half-filling.

cond-mat.str-el↗
arXiv2021

Symmetry, Confinement, and the Higgs Phase

We show that the Higgs and confinement phases of a gauge Higgs theory, with the Higgs field in the fundamental representation of the gauge group, are distinguished both by a broken or unbroken realization of the global center subgroup of the gauge group, and by the type of confinement in each phase. This is color confinement in the Higgs phase, and a stronger property, which we call "separation-of-charge" confinement, in the confining phase.

hep-lat↗
arXiv2021

Excitations of static isolated fermions in the Higgs phase of gauge Higgs theory

A spectrum of localized excitations of isolated static fermions has been discovered in several different gauge Higgs theories. In lattice numerical simulations, we show that the charged elementary particles can have the spectrum of excitations in the Higgs phase of SU(3) gauge Higgs theory, $q=2$ Abelian Higgs theory, Landau-Ginzburg theory, and in chiral U(1) gauge Higgs theory. Possibly these excited states of the isolated fermions can be observed in ARPES studies of conventional superconductors. Also, we consider that similar kinds of excitations could exist in other gauge Higgs theories, such as the electroweak sector of the Standard Model.

hep-lat↗
arXiv2021

Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions

In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose ergodicity at high densities on a large lattice, as a result of both Pauli exclusion and strong Coulomb repulsion. In particular we study particle hopping susceptibilities and the tendency towards particle localization. It is found that the appearance and existence of quantum phase transitions in this model, in the case of high density and strong Coulomb repulsion, depends on the starting configuration of particle trajectories in the numerical simulation. We argue that this breakdown may be the Euclidean time version of a breakdown of the eigenstate thermalization hypothesis in real time quantization.

cond-mat.dis-nn↗
arXiv2021

Excitations of isolated static charges in the charge $q=2$ abelian Higgs model

We present lattice Monte Carlo evidence of stable excitations of isolated static charges in the Higgs phase of the charge $q=2$ abelian Higgs model. These localized excitations are excited states of the interacting fields surrounding the static charges. Since the $q=2$ abelian Higgs model is a relativistic version of the Landau-Ginzburg effective action of a superconductor, we conjecture that excited states of this kind might be relevant in a condensed matter context. Taken together with recent related work in SU(3) gauge Higgs theory, our result suggests that a massive fermion excitation spectrum may be a general feature of gauge Higgs theories.

hep-lat↗
arXiv2020

The Higgs phase as a spin glass, and the transition between varieties of confinement

We propose that the Higgs phase of a gauge Higgs theory is the phase of spontaneously broken custodial symmetry, and present a new gauge invariant order parameter for custodial symmetry breaking which is very closely analogous to the Edwards-Anderson order parameter for spin glasses. Custodial symmetry is a global symmetry acting on the Higgs field alone, and we show here that the spin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgs phase of broken custodial symmetry, coincides with the transition between two distinct types of confinement. These are color confinement in the Higgs phase, and a stronger version of confinement, which we have termed "separation-of-charge" confinement, in the QCD-like phase.

hep-th↗
arXiv2019

Cuprates and center vortices: A QCD confinement mechanism in a high-Tc context

It is suggested that the center vortex confinement mechanism, familiar in hadronic physics, may have some relevance to high-T$_\text{c}$ phenomena. We focus specifically on the transition from the superconducting phase to the pseudogap phase. There is evidence of a vortex liquid in the latter phase, in which the pairing responsible for superconductivity still exists, but superconductivity itself does not. An analogy, drawn from particle physics, may be the Higgs to confinement phase transition in an SU(N) gauge theory, where the confined phase is a vortex liquid, and the Higgs phase is a phase of a broken global $Z_N$ symmetry. We illustrate this idea with numerical simulations of a spatially asymmetric U(1) gauge-Higgs model, with lattice artifact monopoles suppressed. We show the existence of a Higgs (superconductor) to confinement (vortex liquid) phase, explicitly identifying vortices in lattice configurations generated in the confined phase, and showing that they produce an area-law falloff in planar Wilson loops, which may be measurable experimentally. The superconducting phase is a phase of broken global Z$_\text{2}$ symmetry.

cond-mat.str-el↗
arXiv2019

The nature of symmetry breaking in the superconducting ground state

The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local and gauge dependent. For that reason they are also ambiguous as a guide to phase structure. We point out that a global subgroup of the local U(1) gauge symmetry may be regarded, in analogy to non-abelian theories, as a "custodial" symmetry affecting the matter field alone, and construct, along the lines of our previous work, a new gauge-invariant criterion for breaking symmetries of this kind. It is shown that spontaneous breaking of custodial symmetry is a necessary condition for the existence of spontaneous symmetry breaking of a global subgroup of the (abelian or non-abelian) gauge group in any given gauge, and a sufficient condition for the existence of spontaneous breaking of a global subgroup of the gauge group in some gauge. As an illustration we compute numerically, in the lattice version of the Ginzburg-Landau model, the phase boundaries of the theory and the order parameters associated with various symmetries in each phase.

cond-mat.supr-con↗
arXiv2018

On the distinction between color confinement, and confinement

The property of color confinement ("C confinement"), meaning that all asymptotic particle states are color neutral, holds not only in QCD, but also in gauge-Higgs theories deep in the Higgs regime. In this talk we describe a new and stronger confinement criterion, separation-of-charge confinement or "S$_c$ confinement," which is an extension of the Wilson area-law criterion to gauge + matter theories. We will show that there is a transition between S$_c$ and C confinement in the phase plane of gauge-Higgs theories, and we will also explain what symmetry is actually broken in the Higgs phase of a gauge-Higgs theory.

hep-lat↗
arXiv2018

What symmetry is actually broken in the Higgs phase of a gauge-Higgs theory?

In SU($N$) gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N \ne 2$. We construct a gauge-invariant order parameter for the breaking of these global symmetries in the Higgs sector, and calculate numerically the transition lines, in coupling-constant space, for SU(2) and SU(3) gauge theories with unimodular Higgs fields. The order parameter is non-local, and therefore its non-analyticity does not violate the theorem proved by Osterwalder and Seiler. We then show that there exists a transition, in gauge-Higgs theories, between two types of confinement: ordinary color neutrality in the Higgs region, and a stronger condition, which we have called "separation-of-charge confinement," in the confinement region. We conjecture that the symmetry-breaking transition coincides with the transition between these two physically different types of confinement.

hep-th↗
arXiv2017

A confinement criterion for gauge theories with matter fields

A generalization of the Wilson loop area-law criterion is proposed, which is applicable to gauge theories with matter in the fundamental representation of the gauge group. This new criterion, like the area law, is stronger than the statement that asymptotic particle states are massive color singlets, which holds even for theories described by the Brout-Englert-Higgs mechanism.

hep-lat↗
arXiv2016

Origin of Kinks in Energy Dispersion of Strongly Correlated Matter

We investigate the origin of ubiquitous low energy kinks found in Angle Resolved Photoemission (ARPES) experiments in a variety of correlated matter. Such kinks are unexpected from weakly interacting electrons and hence identifying their origin should lead to fundamental insights in strongly correlated matter. We devise a protocol for extracting the kink momentum and energy from the experimental data which relies solely on the two asymptotic tangents of each dispersion curve, away from the feature itself. It is thereby insensitive to the different shapes of the kinks as seen in experiments. The body of available data is then analyzed using this method. We proceed to discuss two alternate theoretical explanations of the origin of the kinks. Some theoretical proposals invoke local Bosonic excitations (Einstein phonons or other modes with spin or charge character), located exactly at the energy of observed kinks, leading to a momentum independent self energy of the electrons. A recent alternate is the theory of extremely correlated Fermi liquids (ECFL). This theory predicts kinks in the dispersion arising from a momentum dependent self energy of correlated electrons. We present the essential results from both classes of theories, and identify experimental features that can help distinguish between the two mechanisms. The ECFL theory is found to be consistent with currently available data on kinks in the nodal direction of cuprate superconductors, but conclusive tests require higher resolution energy distribution curve data.

cond-mat.str-el↗
arXiv2015

A simple phenomenological model for describing the normal state single particle spectral function of high temperature superconductors

Describing the normal state single particle spectral function line shapes of high temperature superconductors remains an important goal in condensed matter physics. Recently, we have proposed a phenomenological extremely correlated Fermi liquid (pECFL) model that promises to accomplish this goal and that is uniquely distinguished from other models. Here, we present an even more simplified phenomenological model, which we refer to as the aECFL model, that performs practically at the same level as the pECFL model. Noting the similarities of the aECFL model and the pECFL model, as well as the differences between the two models, we emphasize the universal significance of the $ω$-dependence of the so-called caparison factor in the ECFL model.

cond-mat.supr-con↗