Critical Behavior of the Schwinger Model via Gauge-Invariant VUMPS†
Date: 2/13, 15:00~16:00
Room: D413 at Institutes of Natural Sciences
Speaker: Kohei Fujikura (The University of Tokyo)
Abstract: In this talk, I discuss the Hamiltonian formulation of lattice gauge theory using the uniform matrix product state and its application to the single flavor Schwinger model. We perform simulations based on the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with θ = π are known to exhibit first-order phase transitions for fermion masses above a critical value, at which a second-order phase transition occurs. Our algorithm enables a precise determination of the critical point in the continuum theory.
Entanglement area law in interacting bosons: from Bose-Hubbard, $\phi$4, and beyond†
Date: 1/24, 14:00~15:00
Room: D413 at Institutes of Natural Sciences
Speaker: Donghoon Kim (RIKEN)
Abstract: The entanglement area law is a foundational principle that characterizes the informational structure in quantum many-body systems, essential for algorithms based on tensor network representations. Historically, this principle has been well understood under two critical assumptions: systems should possess bounded local energy and involve short-range interactions. However, extending the area law to include unbounded local energy and long-range interactions remains a crucial challenge, particularly in boson systems where traditional assumptions do not hold. In this study, we prove the area law across a broad range of interacting boson systems, incorporating cases from the Bose-Hubbard and $\phi^4$ models and those involving long-range interactions. We also introduce an efficient Matrix Product States (MPS) method for approximating quantum ground states. These advancements provide practical insights for simulating boson systems, including those with long-range interactions, and developing effective quantum simulation techniques.
Computational lattice foundation of generalized symmetry and its applications†
Date: 11/22, 14:00~15:00
Room: D413 at Institutes of Natural Sciences
Speaker: Okuto Morikawa (RIKEN)
Abstract: Topology and symmetry in non-Abelian gauge theories are considered with lattice regularization. Recently, the concept of symmetry has been generalized; the important ingredients are given by higher-form, higher-group, and non-invertible symmetries. First, we start by extending Luescher’s construction of topology on the lattice. Thus, we recover the SU(N)/Z_N principal bundle structure from lattice SU(N) gauge fields coupling to Z_N 2-form gauge fields. We then explicitly demonstrate the fractional topological charge. Our construction is applied to analyzing the higher-group and non-invertible symmetries in the SU(N) gauge theory. Also, the theoretical understanding provides a computational foundation for those in lattice simulations. We carry out numerical simulations by using the open code on GitHub <https://github.com/o-morikawa/Gaugefields.jl>, which gives an available implementation of higher-form gauge fields.
Spectroscopy of chimera baryons: Top partners of a composite Higgs model with Sp(4) gauge group†
Date: 11/1, 14:00~15:00
Room: D413 at Institutes of Natural Sciences
Speaker: Ho Hsiao (CCS)
Abstract: In the context of Composite Higgs Models, where the standard model Higgs is interpreted as a pseudo Nambu-Goldstone Boson emerging from a new strong sector, baryons formed by matters in different representations, known as chimera baryons, could serve as top partners. The chimera baryon sharing the same quantum number as the top quark can mix with it, effectively lifting the mass of the top quark. We report our lattice results of the spectrum of low-lying chimera baryons in the quenched approximation on an Sp(4) gauge theory. We perform the spin and parity projections to separate the states and study their mass hierarchy. Particularly, we investigate the chiral extrapolation of chimera baryon masses. To accomplish this, we use a fitting function inspired by QCD chiral Effective Field Theory. We employ Akaike Information Criterion to determine the best fit among different data sets. Additionally, we conduct a sense check on the fitting procedure, confirming its validity and reliability. Last, we present the continuum and massless limit of chimera baryon masses.
The index of lattice Dirac operators and K-theory†
Date: 10/4, 14:00~15:00
Room: D413 at Institutes of Natural Sciences
Speaker: Hidenori Fukaya (Osaka University)
Abstract: We mathematically show an equality between the index of the Dirac
operator on a flat continuum torus and the $\eta$ invariant of the
Wilson Dirac operator with a negative mass when the lattice spacing is
sufficiently small. Unlike the standard approach, our formulation
using $K$-theory does not require the Ginsparg-Wilson relation or the
modified chiral symmetry on the lattice. We prove that a one-parameter
family of continuum massive Dirac operators and the corresponding
Wilson Dirac operators belong to the same equivalence class of the
$K^1$ group at a finite lattice spacing. Their indices, which are
evaluated by the spectral flow or equivalently by the $\eta$ invariant
at finite masses, are proved to be equal.
Abstract: We present a spectroscopy scheme for the lattice field theory by using tensor
renormalization group method combining with the transfer matrix formalism. By
using the scheme, we can not only compute the energy spectrum for the lattice
theory but also determine quantum numbers of the energy eigenstates.
Furthermore, wave function of the corresponding eigenstate can also be
computed. The first step of the scheme is to coarse-grain the tensor network of
a given lattice model by using the higher order tensor renormalization group,
and then after making a matrix corresponding to a transfer matrix from the
coarse-grained tensors, its eigenvalues are evaluated to extract the energy
spectrum. Secondly, the quantum number of the eigenstates can be identified by
a selection rule that requires to compute matrix elements of an associated
insertion operator. The matrix elements can be represented by an impurity
tensor network and computed by the coarse-graining scheme. Moreover, we can
compute the wave function of the energy eigenstate by putting the impurity
tensor at each point in space direction of the network. Additionally, the
momentum of the eigenstate can also be identified by computing an appropriate
matrix elements represented by tensor network. As a demonstration of the new
scheme, we show the spectroscopy of (1+1)d Ising model and compare it with
exact results. We also present a scattering phase shift obtained from
two-particle state energy using Luscher's formula.
Determination of Semileptonic Form Factors for $\bar{B} \to D^{\ast} \ell \bar{\nu}$ Decays†
日時: 6/21, 14:00~15:00
場所: 自然D413
講演者: 崔在敦 (CCS)
概要: Preliminary results on the semileptonic form factors $h_{A_1}(w)$ for the $\bar{B} \to D^{\ast} \ell \bar{\nu}$ decays are presented. Here, the Oktay-Kronfeld (OK) action is used for the charm and bottom valence quarks and the HISQ action is done for light quarks. The Newton method combined with the scanning method is used to find a good initial guess for the $\chi^2$ minimizer in the fitting of the 2pt correlation functions. Some preliminary results for $h_{A_1}(w)/\rho_{A_1}$ at zero recoil ($w=1$) is presented. A MILC HISQ ensemble ($a = 0.12$ fm, $M_{\pi}$ = 220 MeV, and $N_f = 2 + 1 + 1$ flavors) is used here.
概要: シータ項とはゲージ理論に許される冗長な項であり、系に純粋に量子的な効果を与える。さらに、$\theta = \pi$の特殊な場合を除いて、CP対称性を明示的に破る。理論的な興味にもかかわらず、シータ項の効果をモンテカルロ法によって解析することは符号問題のため困難であり、これまで主にテンソルネットワーク法や量子アルゴリズムがその解析に用いられてきた。本発表では、シータ項つきのシュウィンガー模型（1＋1次元時空の量子電気力学）が、ボソン化法と呼ばれるフェルミオン系を等価なボソン系に変換する手法を用いることで、極めて単純なモンテカルロ計算によって第一原理計算可能であることを指摘する[1]。この手法の正当性と有効性を、他の手法から得られた計算結果との比較より実証した後、有限温度・有限シータ領域における閉じ込め力の精密計算を行い、この領域における閉じ込めの様相を定量的に明らかにする[1]。さらに、作用レベルではCP不変な$\theta = \pi$でのシュウィンガー模型の、有限温度・有限フェルミオン質量領域での相構造を、量子イジング鎖とのユニバーサリティという観点と本手法を組み合わせることで決定する[2]。
References
[1] H. Ohata, “Monte Carlo study of Schwinger model without the sign problem”, JHEP 12, 007 (2023), arXiv:2303.05481 [hep-lat].
[2] H. Ohata, “Phase diagram near the quantum critical point in Schwinger model at θ = π: analogy with quantum Ising chain”, PTEP 2024, 013B02 (2024), arXiv:2311.04738 [hep-lat].
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