QCD on the Lattice

Wittig, Hartmut

doi:10.1007/978-3-030-38207-0_5

Cited by 3 publications

(5 citation statements)

References 410 publications

(402 reference statements)

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“…This reasoning is similar in spirit to the one discussed in [41][42][43]. Inserting ( 29) in ( 27) and using (8), we obtain for (24) the following:…”

Section: Intrinsic Quark Spin In the Nucleonmentioning

confidence: 57%

“…It is the delocalization of these zero modes and their interactions that is at the origin of the spontaneous breaking of chiral symmetry and the emergence of the light hadronic spectrum. Remarkably, this topological mechanism for mass generation leaves behind a distinct fingerprint: universal conductance-like fluctuations in the quark spectrum, predicted by the random matrix theory [23] and confirmed by lattice simulations [24].…”

Section: Zero Modesmentioning

confidence: 81%

“…In the QCD instanton vacuum, the U(1) axial charge fluctuates in the grand-canonical ensemble, with the fluctuations captured by the fluctuations of the topological charge Ñ = N + − N − . The gluon contribution in (24) follows from the normalized and connected three-point function asymptotically:…”

Section: Nucleon Topological Charge and Vacuum Topological Susceptibi...mentioning

confidence: 99%

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Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

Zahed

2022

Symmetry

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We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji′s invariant spin decomposition to discuss the spin budget of the nucleon as a quark–diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum.

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“…This reasoning is similar in spirit to the one discussed in [41][42][43]. Inserting ( 29) in ( 27) and using (8), we obtain for (24) the following:…”

Section: Intrinsic Quark Spin In the Nucleonmentioning

confidence: 57%

Section: Zero Modesmentioning

confidence: 81%

Section: Nucleon Topological Charge and Vacuum Topological Susceptibi...mentioning

confidence: 99%

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Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

Zahed

2022

Symmetry

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“…Detailed numerical simulations of light hadronic correlators in the QCD instanton vacuum [5] show remarkable agreement with direct lattice measurements [6], and a wealth of correlators extracted from data [5]. The universal conductance fluctuations in the zero mode region of the Dirac spectrum, predicted by random matrix theory [7] and confirmed by lattice simulations [8], show unequivocally the topological character of the origin of mass.…”

Section: Introductionmentioning

confidence: 62%

“…2. Sketch of the virtual Dirac spectrum for the disordered quark zero modes (left), and the universal spectral fluctuations measured in lattice generated gauge configurations (right) [8]. See text.…”

Section: B Spontaneous Breaking Of Chiral Symmetry and Conductance Fl...mentioning

confidence: 99%

Mass sum rule of hadrons in the QCD instanton vacuum

Zahed

2021

Preprint

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We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji s invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid.

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Spectroscopy with the tensor renormalization group method

Az-zahra,

Takeda,

Yamazaki

2024

Phys. Rev. D

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We present a spectroscopy scheme for the lattice field theory by using the tensor renormalization group method combining with the transfer matrix formalism. By using the scheme, we cannot only compute the energy spectrum for the lattice theory but also determine quantum numbers of the energy eigenstates. Furthermore, the 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. Second, 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 appropriate matrix elements represented by the tensor network. As a demonstration of the new scheme, we show the spectroscopy of the (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 Lüscher’s formula. Published by the American Physical Society 2024

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QCD on the Lattice

Cited by 3 publications

References 410 publications

Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

Mass sum rule of hadrons in the QCD instanton vacuum

Spectroscopy with the tensor renormalization group method

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