Current-driven Tricritical Point in Large-Nc Gauge Theory Shin - PowerPoint PPT Presentation

Strings and Fields 2020, YITP Nov. 16th, 2020 Poster #10 Current-driven Tricritical Point in Large-Nc Gauge Theory Shin Nakamura (Chuo U.) Ref. [T. Imaizumi, M. Matsumoto and S.N., PRL124 (2020) 19, 191603]

Motivation Phase diagram: summary of macroscopic states of systems 𝑈 One direction to explore new physics: introduction of new parameters into the phase diagram. 𝜈 𝐾 : electric current as a new parameter 𝐾 of the phase diagram. My question: Any new phenomena in the presence of current?

Why current? 𝐾 is rather new: Nature of materials in the presence of 𝐾 is not yet understood well. Because, 𝐾 ∙ 𝐹 produces heat and entropy. out of equilibrium When 𝐾 and 𝐹 are constant, the system is in a Non-equilibrium Steady State (NESS). 𝑈 Extension of phase diagram into NESS. 𝜈 • Any new phase structure in NESS? 𝐾 • Any new phenomena in NESS? Nonequilibrium

Any new phenomena in the presence of current? This question is shared with researchers including experimental physicists. http://www.ss.scphys.kyoto-u.ac.jp/kibanS_h29-33/en/event.html

In this talk, We find a novel TCP (tricritical point) that is realized only in the presence of 𝐾 . [T. Imaizumi, M. Matsumoto and S.N., PRL124 (2020) 19, 191603] Broken phase TCP Symmetric phase 𝐶 gap (I will explain the details of this figure later.)

What is TCP? A point at which three-phase coexistence terminates. 𝑆 1st-order line 𝑆 triple line: 3-phase coexistence 1st-order 2nd-order line surface 2nd-order line TCP 𝑅 𝑄 TCP When 𝑅 = 0 𝑄 1st-order line 𝑆 3d phase diagram with 2nd-order point parameters 𝑄, 𝑅 and 𝑆. CP Our case: 𝑄 → 𝐾 𝑄

We employ holography Because we can attack non-equilibrium physics. Microscopic theory Macroscopic quantity Coarse graining Expectation value of physical quantity Connection between UV and IR. An advantage of holography It has already been “encoded” in the geometry. In holography, the expectation values are obtained (by GKP-W) once we have the dual geometry.

Our system The D3-D7 system [Karch and Katz, 2002] 𝑇𝑉(𝑂 𝑑 ) 𝒪 = 4 SYM + 𝒪 = 2 hypermultiplet of mass 𝑛 2 𝑂 𝑑 ≫ 1 at finite temperature 𝑈. at 𝑂 𝑑 ≫ 1 with 𝜇 = 𝑕 YM Our system: 𝑛 ≠ 0 with 𝐹 𝑦 𝐾 𝑦 , 𝐶 𝑨 at 𝑈 . Our parameters 𝑛 𝐾 𝐶 Because of the 𝑈 , 𝑈 3 , 𝑈 2 . conformal symmetry 𝑟 𝜒 1 𝜒 2 “Chiral symmetry” at 𝑛 = 0 : 𝑟 If 𝑛 =0, we have a global U(1) symmetry under 𝑟 → 𝑟𝑓 𝑗𝛽 , when ത 𝑟𝑟 = 0 . [Babington, Erdmenger, Evans, Guralnik and Kirsch, 2008]

D-brane configurations AdS 5 (AdS-BH at 𝑈 > 0 ) S 5 0 1 2 3 4 5 6 7 8 9 ○ ○ ○ ○ D3 ○ ○ ○ ○ ○ ○ ○ ○ D7 𝑠 S 2 : radius sin 𝜄 𝑠 sin 𝜄 𝑛 ≠ 0 D7 𝑛 𝑛 = 0 𝑠 cos 𝜄 BH symmetric under a U(1) chiral symmetry.

U(1) symmetry breaking by magnetic field 𝐶 The U(1) symmetry can be broken 𝑠 sin 𝜄 when we introduce (a strong enough) magnetic field 𝐶 . [Filev et. al. 2007] 𝑠 cos 𝜄 symmetric configuration BH If we apply the electric field 𝐹 , this “ symmetry-broken conductor phase ” can also be possible.

The order parameter The global U(1) symmetry under 𝑟 → 𝑟𝑓 𝑗𝛽 , when ത 𝑟𝑟 = 0 . 𝑠 sin 𝜄 𝑠 cos 𝜄 BH Chiral condensate ത 𝑟𝑟 is the order parameter. The shape of the D7 is described by the function θ (r). When 𝑛 = 0 , the − −  = + + 1 3 ( ) const. ...... r mr r chiral condensate ത 𝑟𝑟 is  = sin ( ) r r r m → given by this coefficient.

Conductivity [Karch and O’Bannon, 2007] The nonlinear conductivity of the D3-D7 system can be computed by using the GKP-W prescription. 𝐾 = 𝜏 𝐹 𝐹 The conductivity is computed even in the presence of external magnetic field 𝐶 . [Ammon, Ngo and O’Bannon, 2009]

What we have observed for 𝑛 = 0 1/𝐶 𝐶 1st TCP Broken phase 2nd 2nd 𝐾 1st TCP 𝐶 gap Broken phase Symmetric phase 𝐾 TCP 𝑈 : fixed Symmetric phase 𝐶 gap

What is TCP? A point at which three-phase coexistence terminates. 𝑆 1st-order line 𝑆 triple line: 3-phase coexistence 1st-order 2nd-order line surface 2nd-order line TCP 𝑅 𝑄 TCP When 𝑅 = 0 𝑄 1st-order line 𝑆 3d phase diagram with 2nd-order point parameters 𝑄, 𝑅 and 𝑆. CP We choose 𝑄 → 𝐾 𝑄

The 3rd parameter: 𝑛 If 𝑛 corresponds to the 3rd parameter, crossover should be observed at 𝑛 ≠ 0. 𝐶 crossover CP 𝐾 Crossover 𝑛 = 0.01 We observed crossover.

Our phase diagram 𝑈 2 /𝐶 triple line: 3-phase coexistence 1st-order 𝑈 2 /𝐶 surface 1st-order line 2nd-order line 2nd-order line 𝑛/𝑈 TCP TCP 𝐾/𝑈 3 When 𝑛 = 0 𝐾/𝑈 3 𝑈 2 /𝐶 1st-order line This TCP is observed only at 2nd-order point 𝐾 ≠ 0 CP where the system is a NESS. Current-driven 𝐾/𝑈 3 nonequilibrium TCP When 𝑛 ≠ 0

Critical exponents: equilibrium case 𝑑 − 𝑈) 𝛾 Order parameter ∝ (𝑈 𝜈 triple line: 3-phase coexistence 1st-order surface 2nd-order line 𝑛 Landau theory TCP for equilibrium systems 𝛾 = 1/2 at CP 𝑈 Example of equilibrium 𝛾 = 1/4 at TCP phase diagram of 2-flavor QCD. [Halaz, Jackson, Shrock, Stephanov and Verbaarschot, 1998]

Our case 𝑟𝑟 ∝ 𝐾 𝑑 − 𝐾 𝛾 Let us use 𝐾 : ത 1/𝐶 triple line: 3-phase coexistence 1st-order surface 2nd-order line 𝑛 TCP 𝐾 Landau theory for equilibrium systems 𝛾 = 0.4993 ≈ 1/2 at CP 𝛾 = 1/2 at CP 𝛾 = 0.2503 ≈ 1/4 at TCP 𝛾 = 1/4 at TCP

Summary • We discovered a novel tricritical point (TCP) and associated phase transitions that appear only in NESS at 𝐾 ≠ 0 . • The obtained critical exponent 𝛾 agreed with that of the Landau theory if we replace 𝑈 of the Landau theory with 𝐾 . Further directions • Other critical exponents? (work in progress) • Possible observation in experiments?