Study of high temperature QCD with chiral fermions Hidenori Fukaya (Osaka U.) for JLQCD collaboration S. Aoki, Y. Aoki, G. Cossu, HF, S. Hashimoto, T. Kaneko, C. Rohrhofer, K. Suzuki, in preparation.
JLQCD’s finite T project (2012~) 1. Nf=2 QCD with overlap fermions at fixed topology [ G. Cossu ] 2012-2013, on IBM BG/L, Hitachi SR11000 2. Nf=2 QCD with Mobius domain-wall fermions [G. Cossu, A.Tomiya ] 2013-2015, on IBM BG/Q. 3. Nf=2 QCD with MDW, finer and larger lattices [Y. Aoki, K. Suzuki, C. Rohrhofer] 2016-2020, on IBM BG/Q and Oakforest-PACS [today’s topic] 4. Nf=2+1 QCD with MDW started ! [I. Kanamori, Y. Nakamura joined.] 2020- Oakforest-PACS, Fugaku?
Results 2016-2019 (phase 3) Symanzik gauge action Nf=2 Mobius domain-wall fermion action m = [1-10] m phys 1/a = 0.075 fm (0.1fm in phase 2) Lt = 8,10,12,14 [T=190-330MeV] L=24,32,40,48 [1.8-3.6fm] 15000-30000trj. Checking overlap/domain-wall consistency with reweighting.
Results 2016-2019 (phase 3) Target observables are • Dirac spectrum • Topological charge, • axial U(1) susceptibility, • meson/baryon correlators, • chiral susceptibility.
Special focus = axial U(1) anomaly Anomalous WTI looks non-zero: but the real question is if to which only lattice QCD can answer.
Contents We study Nf=2 QCD with chiral fermions at ~m phys , focusing on U(1) anomaly. 2. Lattice setup 3. Numerical results • Dirac spectrum • Topology • U(1) susceptibility • Meson correlators • Chiral susceptibility 4. Summary ✔ 1. Introduction
Simulation setup Nf=2 flavor QCD 1/a = 2.6 GeV (0.075fm) Symanzik gauge action L=24,32,40,48 [1.8-3.6fm] Mobius domain-wall fermions with m res <1MeV Quark mass from 3MeV (< phys. pt. ~4MeV) to 30MeV. T=190, 220, 260, 330 MeV and higher. (Lt=8,10,12,14) Tc is estimated to be around 175MeV. z t
Overlap vs. Mobius domain-wall with L 5 =16. OV is obtained by exactly computing the sgn function for low-modes of H M . perfect chiral sym. good chiral sym. numerically m res ~ 1keV numerically m res ~ 1MeV
Violation of chiral symmetry enhanced at finite T Checking chiral sym. for EACH eigenmode Bad modes appear above Tc for a~0.1fm. [JLQCD (Cossu et al.) 2015, JLQCD(Tomiya et al.) 2016] Note: residual mass is (weighted) average of them. For T=0, gi are consistent with residual mass.
Overlap/domain-wall reweighting Essential for a > 0.1fm. [our previous work] DW and OV are consistent for a~0.08fm. (for Meson/Baryon study, we use DW) [this work].
Bonus = topology tunnelings For dynamical overlap fermion, Data at T=220MeV we needed to fix the topology. But DW + OV reweighting, we do not. Q (L=48) 3 m=0.001 m=0.0025 2 m=0.00375 m=0.005 1 0 -1 -2 -3 0 2000 4000 6000 8000 10000 12000 14000 trj
The use of overlap only in is NOT. Fake chiral zero modes appear. valence sector is dangerous ! density of zero modes consistent. But partially quenched OV In our work, reweighted OV and DW are 0.003 m=0.001 m=0.0025 0.0025 0.002 ρ ( λ =0) (GeV 3 ) 0.0015 0.001 0.0005 0 DW OV PQOV
Contents We study Nf=2 QCD with chiral fermions at ~m phys , focusing on U(1) anomaly. 2. Lattice setup Nf=2 QCD w/ MDWF and rewegihteg overlap. at T=190-330MeV near physical m~4MeV. 3. Numerical results • Dirac spectrum • Topology • U(1) susceptibility • Meson correlators • Chiral susceptibility 4. Summary ✔ 1. Introduction ✔
Dirac spectrum <latexit sha1_base64="4WGZkF1eYODlN+F0LVBhm/waU=">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</latexit> i-th eigenvalue of Dirac op. with gauge background A. <latexit sha1_base64="3BNFtR0K0OvroADqiGN7qsSxl+s=">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</latexit> <latexit sha1_base64="5zuiPyurghSOyYta5HyjSRM1LZg=">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</latexit> Zero eigenvalues are related to SU(2)xSU(2) <latexit sha1_base64="hvhUdwI5zDw54oy069BGj69qi0U=">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</latexit> theorem, breaking, through the Banks-Casher relation, and axial U(1) anomaly through the index ρ ( λ ) = 1 m → 0 lim lim V →∞ h ¯ qq i = πρ (0) X h δ ( λ � λ i ( A )) i V i λ i ( A ) : Z 1 d 4 x ✏ µ νρσ tr c F µ ν F ρσ n + − n − = 32 ⇡ 2
Dirac spectrum at T=220MeV * Strong supression of non-zero near zero modes. SU(2)? * DW and OV are consistent. * A remarkable peak at zero but disappears as m→0. U(1)A? β =4.30, T =220MeV, L =32(2.4fm) 0.06 overlap, m =0.01 overlap, m =0.005 0.05 overlap, m =0.00375 0.04 overlap, m =0.0025 ρ ( λ ) (GeV 3 ) overlap, m =0.001 0.03 domain-wall < - qq >/ π at T =0, m =0 0.02 0.01 0 0 50 100 150 200 λ (MeV)
Different volumes * except for L=24 m=0.01 (heaviest data, L/Lt=2) * 3 different volumes show consistent results β =4.30, T =220MeV 0.00018 L =24 (1.8fm), m =0.01 0.00016 L =32 (2.4fm), m =0.01 0.00014 L =40 (3.0fm), m =0.01 0.00012 m =0.005 A ( λ ) (GeV 4 ) m =0.00375 0.0001 m =0.0025 8x10 -5 6x10 -5 4x10 -5 2x10 -5 0 0 20 40 60 80 100 λ (MeV)
T=330MeV The larger T, the larger the pseudo-gap. T=260MeV T=220MeV T=195MeV β =4.24, T =195MeV, L =32(2.7fm) β =4.30, T =220MeV, L =32(2.4fm) 0.06 0.06 overlap, m =0.01 overlap, m =0.01 overlap, m =0.005 0.05 overlap, m =0.005 0.05 overlap, m =0.0025 overlap, m =0.00375 domain-wall 0.04 ρ ( λ ) (GeV 3 ) 0.04 overlap, m =0.0025 ρ ( λ ) (GeV 3 ) overlap, m =0.001 0.03 0.03 domain-wall < - qq >/ π at T =0, m =0 0.02 0.02 0.01 0.01 0 0 0 20 40 60 80 100 120 140 0 50 100 150 200 λ (MeV) λ (MeV) β =4.30, T =260MeV, L =32(2.4fm) β =4.30, T =330MeV, L =32(2.4fm) 0.06 0.06 overlap, m =0.015 overlap, m =0.04 overlap, m =0.01 overlap, m =0.02 0.05 0.05 overlap, m =0.008 overlap, m =0.015 0.04 overlap, m =0.005 0.04 overlap, m =0.01 ρ ( λ ) (GeV 3 ) ρ ( λ ) (GeV 3 ) overlap, m =0.003 (reweighted from 0.005) overlap, m =0.005 0.03 0.03 0.02 0.02 0.01 0.01 0 0 0 50 100 150 200 250 300 0 100 200 300 400 500 λ (MeV) λ (MeV)
(Near)zero mode peaks Consistent with zero BEFORE the chiral limit. 0.04 T =195 MeV ( β =4.24) 0.035 T =190 MeV ( β =4.30) T =220 MeV 0.03 T =260 MeV ρ ( λ =0) (GeV 3 ) T =330 MeV 0.025 0.02 0.015 0.01 0.005 0 0 20 40 60 80 100 120 m (MeV)
Contents We study Nf=2 QCD with chiral fermions at ~m phys , focusing on U(1) anomaly. 2. Lattice setup Nf=2 QCD w/ MDWF and rewegihteg overlap. at T=190-330MeV near physical m~4MeV. 3. Numerical results • Dirac spectrum has a peak but vanishes in the m→0 limit. • Topology • U(1) susceptibility • Meson correlators • Chiral susceptibility 4. Summary ✔ 1. Introduction ✔
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